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js8call/JS8.cpp
Allan Bazinet a51bc2be25 Break out common JS8 encode function
2025-01-22 20:22:29 -08:00

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/**
* (C) 2025 Allan Bazinet <w6baz@arrl.net> - All Rights Reserved
**/
#include "JS8.hpp"
#include <algorithm>
#include <array>
#include <cmath>
#include <complex>
#include <cstdint>
#include <functional>
#include <initializer_list>
#include <limits>
#include <mutex>
#include <numeric>
#include <stdexcept>
#include <string>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <vector>
#include <boost/crc.hpp>
#include <boost/multi_index_container.hpp>
#include <boost/multi_index/key.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/ranked_index.hpp>
#include <fftw3.h>
#include <vendor/Eigen/Dense>
#include <QDebug>
#include <QObject>
#include <QThread>
/******************************************************************************/
// Here be Dragons
/******************************************************************************/
// Avoiding namespace pollution issues due to things like #define NSPS
// in the mainline for the moment, while testing this in parallel.
extern std::mutex fftw_mutex;
extern struct dec_data {
short int d2[720000]; // sample frame buffer for sample collection
struct
{
int nutc; // UTC as integer, HHMM
bool ndiskdat; // true ==> data read from *.wav file
int nfqso; // User-selected QSO freq (kHz)
bool newdat; // true ==> new data, must do long FFT
int npts8; // npts for c0() array
int nfa; // Low decode limit (Hz) (filter min)
int nfb; // High decode limit (Hz) (filter max)
bool syncStats; // only compute sync candidates
int kin; // number of frames written to d2
int kposA; // starting position of decode for submode A
int kposB; // starting position of decode for submode B
int kposC; // starting position of decode for submode C
int kposE; // starting position of decode for submode E
int kposI; // starting position of decode for submode I
int kszA; // number of frames for decode for submode A
int kszB; // number of frames for decode for submode B
int kszC; // number of frames for decode for submode C
int kszE; // number of frames for decode for submode E
int kszI; // number of frames for decode for submode I
int nsubmode; // which submode to decode (-1 if using nsubmodes)
int nsubmodes; // which submodes to decode
bool nagain;
int ndepth;
int napwid;
int nmode;
int nranera;
char datetime[20];
char mycall[12];
} params;
} dec_data;
/******************************************************************************/
// Compilation Utilities
/******************************************************************************/
namespace
{
// Full-range cosine function using symmetries of cos(x). std::cos
// isn't constexpr until C++20, and we're targeting C++17 at the
// moment. We only use this function during compilation; std::cos
// is the better choice at runtime. Once we move to requiring a
// C++20 compiler, we can just use std::cos.
constexpr auto
cos(double x)
{
constexpr auto RAD_360 = M_PI * 2;
constexpr auto RAD_180 = M_PI;
constexpr auto RAD_90 = M_PI_2;
// Polynomial approximation of cos(x) for x in [0, RAD_90],
// Accuracy here in theory is 1e-18, but double precision
// itself is only 1-e16, so within the domain of doubles,
// this should be extremely accurate.
constexpr auto cos = [](double const x)
{
constexpr std::array coefficients =
{
1.0, // Coefficient for x^0
-0.49999999999999994, // Coefficient for x^2
0.041666666666666664, // Coefficient for x^4
-0.001388888888888889, // Coefficient for x^6
0.000024801587301587, // Coefficient for x^8
-0.00000027557319223986, // Coefficient for x^10
0.00000000208767569878681, // Coefficient for x^12
-0.00000000001147074513875176, // Coefficient for x^14
0.0000000000000477947733238733 // Coefficient for x^16
};
auto const x2 = x * x;
auto const x4 = x2 * x2;
auto const x6 = x4 * x2;
auto const x8 = x4 * x4;
auto const x10 = x8 * x2;
auto const x12 = x8 * x4;
auto const x14 = x12 * x2;
auto const x16 = x8 * x8;
return coefficients[0]
+ coefficients[1] * x2
+ coefficients[2] * x4
+ coefficients[3] * x6
+ coefficients[4] * x8
+ coefficients[5] * x10
+ coefficients[6] * x12
+ coefficients[7] * x14
+ coefficients[8] * x16;
};
// Reduce x to [0, RAD_360)
x -= static_cast<long long>(x / RAD_360) * RAD_360;
// Map x to [0, RAD_180]
if (x > RAD_180) x = RAD_360 - x;
// Map x to [0, RAD_90] and evaluate the polynomial;
// flip the sign for angles in the second quadrant.
return x > RAD_90 ? -cos(RAD_180 - x) : cos(x);
};
}
/******************************************************************************/
// Constants
/******************************************************************************/
namespace
{
/* COMMON PARAMETERS */
// !Common
//
// parameter (KK=87) !Information bits (75 + CRC12)
// parameter (ND=58) !Data symbols
// parameter (NS=21) !Sync symbols (3 @ Costas 7x7)
// parameter (NN=NS+ND) !Total channel symbols (79)
// parameter (ASYNCMIN=1.5) !Minimum Sync
// parameter (NFSRCH=5) !Search frequency range in Hz (i.e., +/- 2.5 Hz)
// parameter (NMAXCAND=300) !Maxiumum number of candidate signals
// Parameter Value Description
// KK 87 Number of information bits (75 message bits + 12 CRC bits).
// ND 58 Number of data symbols in the JS8 transmission.
// NS 21 Number of synchronization symbols (3 Costas arrays of size 7).
// NN 79 Total number of channel symbols (NN = NS + ND).
// ASYNCMIN 1.5 Minimum sync value for successful decoding.
// NFSRCH 5 Search frequency range in Hz (±2.5 Hz).
// NMAXCAND 300 Maximum number of candidate signals.
constexpr int N = 174; // Total bits
constexpr int K = 87; // Message bits
constexpr int M = N - K; // Check bits
constexpr int KK = 87; // Information bits (75 + CRC12)
constexpr int ND = 58; // Data symbols
constexpr int NS = 21; // Sync symbols (3 @ Costas 7x7)
constexpr int NN = NS + ND; // Total channel symbols (79)
constexpr float ASYNCMIN = 1.5f; // Minimum sync
constexpr int NFSRCH = 5; // Search frequency range in Hz (i.e., +/- 2.5 Hz)
constexpr std::size_t NMAXCAND = 300; // Maxiumum number of candidate signals
constexpr int NFILT = 1400; // Filter length
constexpr int NTMAX = 60;
constexpr int NROWS = 8;
constexpr int NFOS = 2;
constexpr int NSSY = 4;
constexpr int NP = 3200;
constexpr int NP2 = 2812;
constexpr float TAU = 2.0f * M_PI;
constexpr auto ZERO = std::complex<float>{0.0f, 0.0f};
constexpr int MAX_BUFFER_SIZE = NTMAX * 12000;
// Key for the constants that follow:
//
// NSUBMODE - ID of the submode
// NCOSTAS - Which JS8 Costas Arrays to use
// NSPS - Number of samples per second
// NTXDUR - Duration of the transmission in seconds.
// NDOWNSPS - Number of samples per symbol after downsampling.
// NDD - Parameter used in waveform tapering and related calculations. XXX
// JZ - Range of symbol offsets considered during decoding.
// ASTART - Start delay in seconds for decoding.
// BASESUB - XXX
// NMAX - Samples in input wave
// NSTEP - Rough time-sync step size
// NHSYM - Number of symbol spectra (1/4-sym steps)
// NDOW - Downsample factor to 32 samples per symbol
// NQSYMBOL - Downsample factor of a quarter symbol
/* A MODE DECODER */
struct ModeA
{
// Static constants
inline static constexpr int NSUBMODE = 0;
inline static constexpr auto NCOSTAS = JS8::Costas::Type::ORIGINAL;
inline static constexpr int NSPS = 1920;
inline static constexpr int NTXDUR = 15;
inline static constexpr int NDOWNSPS = 32;
inline static constexpr int NDD = 100;
inline static constexpr int JZ = 62;
inline static constexpr float ASTART = 0.5f;
inline static constexpr float BASESUB = 40.0f;
// Derived parameters
inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
inline static constexpr int NMAX = NTXDUR * 12000;
inline static constexpr int NFFT1 = NSPS * NFOS;
inline static constexpr int NSTEP = NSPS / NSSY;
inline static constexpr int NHSYM = NMAX / NSTEP - 3;
inline static constexpr int NDOWN = NSPS / NDOWNSPS;
inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
inline static constexpr int NDFFT1 = NSPS * NDD;
inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
inline static constexpr int NP2 = NN * NDOWNSPS;
inline static constexpr float TSTEP = NSTEP / 12000.0f;
inline static constexpr int JSTRT = ASTART / TSTEP;
inline static constexpr float DF = 12000.0f / NFFT1;
};
/* B MODE DECODER */
struct ModeB
{
// Static constants
inline static constexpr int NSUBMODE = 1;
inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
inline static constexpr int NSPS = 1200;
inline static constexpr int NTXDUR = 10;
inline static constexpr int NDOWNSPS = 20;
inline static constexpr int NDD = 100;
inline static constexpr int JZ = 144;
inline static constexpr float ASTART = 0.2f;
inline static constexpr float BASESUB = 39.0f;
// Derived parameters
inline static constexpr float AZ = (12000.0f / NSPS) * 0.8f;
inline static constexpr int NMAX = NTXDUR * 12000;
inline static constexpr int NFFT1 = NSPS * NFOS;
inline static constexpr int NSTEP = NSPS / NSSY;
inline static constexpr int NHSYM = NMAX / NSTEP - 3;
inline static constexpr int NDOWN = NSPS / NDOWNSPS;
inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
inline static constexpr int NDFFT1 = NSPS * NDD;
inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
inline static constexpr int NP2 = NN * NDOWNSPS;
inline static constexpr float TSTEP = NSTEP / 12000.0f;
inline static constexpr int JSTRT = ASTART / TSTEP;
inline static constexpr float DF = 12000.0f / NFFT1;
};
/* C MODE DECODER */
struct ModeC
{
// Static constants
inline static constexpr int NSUBMODE = 2;
inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
inline static constexpr int NSPS = 600;
inline static constexpr int NTXDUR = 6;
inline static constexpr int NDOWNSPS = 12;
inline static constexpr int NDD = 120;
inline static constexpr int JZ = 172;
inline static constexpr float ASTART = 0.1f;
inline static constexpr float BASESUB = 38.0f;
// Derived parameters
inline static constexpr float AZ = (12000.0f / NSPS) * 0.6f;
inline static constexpr int NMAX = NTXDUR * 12000;
inline static constexpr int NFFT1 = NSPS * NFOS;
inline static constexpr int NSTEP = NSPS / NSSY;
inline static constexpr int NHSYM = NMAX / NSTEP - 3;
inline static constexpr int NDOWN = NSPS / NDOWNSPS;
inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
inline static constexpr int NDFFT1 = NSPS * NDD;
inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
inline static constexpr int NP2 = NN * NDOWNSPS;
inline static constexpr float TSTEP = NSTEP / 12000.0f;
inline static constexpr int JSTRT = ASTART / TSTEP;
inline static constexpr float DF = 12000.0f / NFFT1;
};
/* E MODE DECODER */
struct ModeE
{
// Static constants
inline static constexpr int NSUBMODE = 4;
inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
inline static constexpr int NSPS = 3840;
inline static constexpr int NTXDUR = 30; // XXX 28
inline static constexpr int NDOWNSPS = 32;
inline static constexpr int NDD = 94; // XXX 90
inline static constexpr int JZ = 32;
inline static constexpr float ASTART = 0.5f;
inline static constexpr float BASESUB = 42.0f;
// Derived parameters
inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
inline static constexpr int NMAX = NTXDUR * 12000;
inline static constexpr int NFFT1 = NSPS * NFOS;
inline static constexpr int NSTEP = NSPS / NSSY;
inline static constexpr int NHSYM = NMAX / NSTEP - 3;
inline static constexpr int NDOWN = NSPS / NDOWNSPS;
inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
inline static constexpr int NDFFT1 = NSPS * NDD;
inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
inline static constexpr int NP2 = NN * NDOWNSPS;
inline static constexpr float TSTEP = NSTEP / 12000.0f;
inline static constexpr int JSTRT = ASTART / TSTEP;
inline static constexpr float DF = 12000.0f / NFFT1;
};
/* I MODE DECODER */
struct ModeI
{
// Static constants
inline static constexpr int NSUBMODE = 8;
inline static constexpr auto NCOSTAS = JS8::Costas::Type::MODIFIED;
inline static constexpr int NSPS = 384;
inline static constexpr int NTXDUR = 4;
inline static constexpr int NDOWNSPS = 12;
inline static constexpr int NDD = 125;
inline static constexpr int JZ = 250;
inline static constexpr float ASTART = 0.1f;
inline static constexpr float BASESUB = 36.0f;
// Derived parameters
inline static constexpr float AZ = (12000.0f / NSPS) * 0.64f;
inline static constexpr int NMAX = NTXDUR * 12000;
inline static constexpr int NFFT1 = NSPS * NFOS;
inline static constexpr int NSTEP = NSPS / NSSY;
inline static constexpr int NHSYM = NMAX / NSTEP - 3;
inline static constexpr int NDOWN = NSPS / NDOWNSPS;
inline static constexpr int NQSYMBOL = NDOWNSPS / 4;
inline static constexpr int NDFFT1 = NSPS * NDD;
inline static constexpr int NDFFT2 = NDFFT1 / NDOWN;
inline static constexpr int NP2 = NN * NDOWNSPS;
inline static constexpr float TSTEP = NSTEP / 12000.0f;
inline static constexpr int JSTRT = ASTART / TSTEP;
inline static constexpr float DF = 12000.0f / NFFT1;
};
// Tunable settings; degree of the polynomial used for the baseline
// curve fit, and the percentile of the span at which to sample. In
// general, a 5th degree polynomial and the 10th percentile should
// be optimal.
constexpr auto BASELINE_DEGREE = 5;
constexpr auto BASELINE_SAMPLE = 10;
// We're going to do a pairwise Estrin's evaluation of the polynomial
// coefficients, so it's critical that the degree of the polynomial is
// odd, resulting in an even number of coefficients.
static_assert(BASELINE_DEGREE & 1, "Degree must be odd");
static_assert(BASELINE_SAMPLE >= 0 &&
BASELINE_SAMPLE <= 100, "Sample must be a percentage");
// Since we know the degree of the polynomial, and thus the number of
// nodes that we're going to use, we can do all the trigonometry work
// required to calculate the Chebyshev nodes in advance, by computing
// them over the range [0, 1]; we can then scale these at runtime to
// a span of any size by simple multiplication.
//
// Downside to this with C++17 is that std::cos() is not yet constexpr,
// as it is in C++20, so we must provide our own implementation until
// then.
constexpr auto BASELINE_NODES = []()
{
// Down to the actual business of generating Chebyshev nodes
// suitable for scaling; once we move to C++20 as the minimum
// compiler, we can remove the cos() function above and instead
// call std::cos() here, as it's required to be constexpr in
// C++20 and above, and presumably it'll be of high quality.
auto nodes = std::array<double, BASELINE_DEGREE + 1>{};
constexpr auto slice = M_PI / (2.0 * nodes.size());
for (std::size_t i = 0; i < nodes.size(); ++i)
{
nodes[i] = 0.5 * (1.0 - cos(slice * (2.0 * i + 1)));
}
return nodes;
}();
}
/******************************************************************************/
// Local Types
/******************************************************************************/
namespace
{
// Support storage of arbitrary types, index by an enum class.
template<typename T,
typename E>
class EnumArray
{
static_assert(std::is_enum_v<E>, "E must be an enum type");
std::array<T, static_cast<std::size_t>(E::count)> array;
public:
// Constructors
constexpr EnumArray() = default;
constexpr EnumArray(std::initializer_list<T> init)
{
if (init.size() > array.size())
throw std::out_of_range("Too many elements in initializer_list");
std::size_t i = 0;
for (const auto& value : init)
{
array[i++] = value;
}
// Zero-fill remaining elements if initializer list is smaller than the array
for (; i < array.size(); ++i)
{
array[i] = T{};
}
}
// Subscript operators
constexpr T& operator[](E e)
{
return array[static_cast<std::underlying_type_t<E>>(e)];
}
constexpr const T& operator[](E e) const
{
return array[static_cast<std::underlying_type_t<E>>(e)];
}
// Iteration support
constexpr auto begin() noexcept { return array.begin(); }
constexpr auto end() noexcept { return array.end(); }
constexpr auto begin() const noexcept { return array.begin(); }
constexpr auto end() const noexcept { return array.end(); }
};
// Encapsulates the first-order search results provided by syncjs8().
struct Sync
{
float freq;
float step;
float sync;
// Constructor for convenience.
Sync(float const freq,
float const step,
float const sync)
: freq(freq)
, step(step)
, sync(sync)
{}
};
// Tag structs so that we can refer to multi index container indices
// by a descriptive tag instead of by the index of the index. These
// don't need to be anything but a name.
namespace Tag
{
struct Freq {};
struct Rank {};
struct Sync {};
}
// Container indexing Sync objects in useful ways, used by syncjs8().
namespace MI = boost::multi_index;
using SyncIndex = MI::multi_index_container
<
Sync,
MI::indexed_by
<
MI::ordered_non_unique<
MI::tag<Tag::Freq>,
MI::key<&Sync::freq>
>,
MI::ranked_non_unique<
MI::tag<Tag::Rank>,
MI::key<&Sync::sync>
>,
MI::ordered_non_unique<
MI::tag<Tag::Sync>,
MI::key<&Sync::sync>,
std::greater<>
>
>
>;
// Represents a decoded message, i.e., the 3-bit message type
// and the 12 bytes that result in decoding a message.
class Decode
{
public:
int type;
std::string data;
Decode(int type,
std::string data)
: type(type)
, data(std::move(data))
{}
bool
operator == (Decode const & other) const noexcept
{
return type == other.type &&
data == other.data;
}
struct Hash
{
std::size_t
operator()(Decode const & decode) const noexcept
{
std::size_t const h1 = std::hash<int>{}(decode.type);
std::size_t const h2 = std::hash<std::string>{}(decode.data);
return h1 ^ (h2 << 1);
}
};
using Map = std::unordered_map<Decode, int, Hash>;
};
}
/******************************************************************************/
// Belief Propagation Decoder
/******************************************************************************/
namespace
{
constexpr int BP_MAX_ROWS = 7; // Max rows per column in Nm
constexpr int BP_MAX_CHECKS = 3; // Max checks per bit in Mn
constexpr int BP_MAX_ITERATIONS = 30; // Max iterations in BP decoder
constexpr std::array<std::array<int, BP_MAX_CHECKS>, N> Mn =
{{
{0, 24, 68},
{1, 4, 72},
{2, 31, 67},
{3, 50, 60},
{5, 62, 69},
{6, 32, 78},
{7, 49, 85},
{8, 36, 42},
{9, 40, 64},
{10, 13, 63},
{11, 74, 76},
{12, 22, 80},
{14, 15, 81},
{16, 55, 65},
{17, 52, 59},
{18, 30, 51},
{19, 66, 83},
{20, 28, 71},
{21, 23, 43},
{25, 34, 75},
{26, 35, 37},
{27, 39, 41},
{29, 53, 54},
{33, 48, 86},
{38, 56, 57},
{44, 73, 82},
{45, 61, 79},
{46, 47, 84},
{58, 70, 77},
{0, 49, 52},
{1, 46, 83},
{2, 24, 78},
{3, 5, 13},
{4, 6, 79},
{7, 33, 54},
{8, 35, 68},
{9, 42, 82},
{10, 22, 73},
{11, 16, 43},
{12, 56, 75},
{14, 26, 55},
{15, 27, 28},
{17, 18, 58},
{19, 39, 62},
{20, 34, 51},
{21, 53, 63},
{23, 61, 77},
{25, 31, 76},
{29, 71, 84},
{30, 64, 86},
{32, 38, 50},
{36, 47, 74},
{37, 69, 70},
{40, 41, 67},
{44, 66, 85},
{45, 80, 81},
{48, 65, 72},
{57, 59, 65},
{60, 64, 84},
{0, 13, 20},
{1, 12, 58},
{2, 66, 81},
{3, 31, 72},
{4, 35, 53},
{5, 42, 45},
{6, 27, 74},
{7, 32, 70},
{8, 48, 75},
{9, 57, 63},
{10, 47, 67},
{11, 18, 44},
{14, 49, 60},
{15, 21, 25},
{16, 71, 79},
{17, 39, 54},
{19, 34, 50},
{22, 24, 33},
{23, 62, 86},
{26, 38, 73},
{28, 77, 82},
{29, 69, 76},
{30, 68, 83},
{21, 36, 85},
{37, 40, 80},
{41, 43, 56},
{46, 52, 61},
{51, 55, 78},
{59, 74, 80},
{0, 38, 76},
{1, 15, 40},
{2, 30, 53},
{3, 35, 77},
{4, 44, 64},
{5, 56, 84},
{6, 13, 48},
{7, 20, 45},
{8, 14, 71},
{9, 19, 61},
{10, 16, 70},
{11, 33, 46},
{12, 67, 85},
{17, 22, 42},
{18, 63, 72},
{23, 47, 78},
{24, 69, 82},
{25, 79, 86},
{26, 31, 39},
{27, 55, 68},
{28, 62, 65},
{29, 41, 49},
{32, 36, 81},
{34, 59, 73},
{37, 54, 83},
{43, 51, 60},
{50, 52, 71},
{57, 58, 66},
{46, 55, 75},
{0, 18, 36},
{1, 60, 74},
{2, 7, 65},
{3, 59, 83},
{4, 33, 38},
{5, 25, 52},
{6, 31, 56},
{8, 51, 66},
{9, 11, 14},
{10, 50, 68},
{12, 13, 64},
{15, 30, 42},
{16, 19, 35},
{17, 79, 85},
{20, 47, 58},
{21, 39, 45},
{22, 32, 61},
{23, 29, 73},
{24, 41, 63},
{26, 48, 84},
{27, 37, 72},
{28, 43, 80},
{34, 67, 69},
{40, 62, 75},
{44, 48, 70},
{49, 57, 86},
{47, 53, 82},
{12, 54, 78},
{76, 77, 81},
{0, 1, 23},
{2, 5, 74},
{3, 55, 86},
{4, 43, 52},
{6, 49, 82},
{7, 9, 27},
{8, 54, 61},
{10, 28, 66},
{11, 32, 39},
{13, 15, 19},
{14, 34, 72},
{16, 30, 38},
{17, 35, 56},
{18, 45, 75},
{20, 41, 83},
{21, 33, 58},
{22, 25, 60},
{24, 59, 64},
{26, 63, 79},
{29, 36, 65},
{31, 44, 71},
{37, 50, 85},
{40, 76, 78},
{42, 55, 67},
{46, 73, 81},
{39, 51, 77},
{53, 60, 70},
{45, 57, 68},
}};
struct CheckNode
{
int valid_neighbors;
std::array<int, BP_MAX_ROWS> neighbors;
};
constexpr std::array<CheckNode, M> Nm =
{{
{6, {0, 29, 59, 88, 117, 146, 0}},
{6, {1, 30, 60, 89, 118, 146, 0}},
{6, {2, 31, 61, 90, 119, 147, 0}},
{6, {3, 32, 62, 91, 120, 148, 0}},
{6, {1, 33, 63, 92, 121, 149, 0}},
{6, {4, 32, 64, 93, 122, 147, 0}},
{6, {5, 33, 65, 94, 123, 150, 0}},
{6, {6, 34, 66, 95, 119, 151, 0}},
{6, {7, 35, 67, 96, 124, 152, 0}},
{6, {8, 36, 68, 97, 125, 151, 0}},
{6, {9, 37, 69, 98, 126, 153, 0}},
{6, {10, 38, 70, 99, 125, 154, 0}},
{6, {11, 39, 60, 100, 127, 144, 0}},
{6, {9, 32, 59, 94, 127, 155, 0}},
{6, {12, 40, 71, 96, 125, 156, 0}},
{6, {12, 41, 72, 89, 128, 155, 0}},
{6, {13, 38, 73, 98, 129, 157, 0}},
{6, {14, 42, 74, 101, 130, 158, 0}},
{6, {15, 42, 70, 102, 117, 159, 0}},
{6, {16, 43, 75, 97, 129, 155, 0}},
{6, {17, 44, 59, 95, 131, 160, 0}},
{6, {18, 45, 72, 82, 132, 161, 0}},
{6, {11, 37, 76, 101, 133, 162, 0}},
{6, {18, 46, 77, 103, 134, 146, 0}},
{6, {0, 31, 76, 104, 135, 163, 0}},
{6, {19, 47, 72, 105, 122, 162, 0}},
{6, {20, 40, 78, 106, 136, 164, 0}},
{6, {21, 41, 65, 107, 137, 151, 0}},
{6, {17, 41, 79, 108, 138, 153, 0}},
{6, {22, 48, 80, 109, 134, 165, 0}},
{6, {15, 49, 81, 90, 128, 157, 0}},
{6, {2, 47, 62, 106, 123, 166, 0}},
{6, {5, 50, 66, 110, 133, 154, 0}},
{6, {23, 34, 76, 99, 121, 161, 0}},
{6, {19, 44, 75, 111, 139, 156, 0}},
{6, {20, 35, 63, 91, 129, 158, 0}},
{6, {7, 51, 82, 110, 117, 165, 0}},
{6, {20, 52, 83, 112, 137, 167, 0}},
{6, {24, 50, 78, 88, 121, 157, 0}},
{7, {21, 43, 74, 106, 132, 154, 171}},
{6, {8, 53, 83, 89, 140, 168, 0}},
{6, {21, 53, 84, 109, 135, 160, 0}},
{6, {7, 36, 64, 101, 128, 169, 0}},
{6, {18, 38, 84, 113, 138, 149, 0}},
{6, {25, 54, 70, 92, 141, 166, 0}},
{7, {26, 55, 64, 95, 132, 159, 173}},
{6, {27, 30, 85, 99, 116, 170, 0}},
{6, {27, 51, 69, 103, 131, 143, 0}},
{6, {23, 56, 67, 94, 136, 141, 0}},
{6, {6, 29, 71, 109, 142, 150, 0}},
{6, {3, 50, 75, 114, 126, 167, 0}},
{6, {15, 44, 86, 113, 124, 171, 0}},
{6, {14, 29, 85, 114, 122, 149, 0}},
{6, {22, 45, 63, 90, 143, 172, 0}},
{6, {22, 34, 74, 112, 144, 152, 0}},
{7, {13, 40, 86, 107, 116, 148, 169}},
{6, {24, 39, 84, 93, 123, 158, 0}},
{6, {24, 57, 68, 115, 142, 173, 0}},
{6, {28, 42, 60, 115, 131, 161, 0}},
{6, {14, 57, 87, 111, 120, 163, 0}},
{7, {3, 58, 71, 113, 118, 162, 172}},
{6, {26, 46, 85, 97, 133, 152, 0}},
{5, {4, 43, 77, 108, 140, 0, 0}},
{6, {9, 45, 68, 102, 135, 164, 0}},
{6, {8, 49, 58, 92, 127, 163, 0}},
{6, {13, 56, 57, 108, 119, 165, 0}},
{6, {16, 54, 61, 115, 124, 153, 0}},
{6, {2, 53, 69, 100, 139, 169, 0}},
{6, {0, 35, 81, 107, 126, 173, 0}},
{5, {4, 52, 80, 104, 139, 0, 0}},
{6, {28, 52, 66, 98, 141, 172, 0}},
{6, {17, 48, 73, 96, 114, 166, 0}},
{6, {1, 56, 62, 102, 137, 156, 0}},
{6, {25, 37, 78, 111, 134, 170, 0}},
{6, {10, 51, 65, 87, 118, 147, 0}},
{6, {19, 39, 67, 116, 140, 159, 0}},
{6, {10, 47, 80, 88, 145, 168, 0}},
{6, {28, 46, 79, 91, 145, 171, 0}},
{6, {5, 31, 86, 103, 144, 168, 0}},
{6, {26, 33, 73, 105, 130, 164, 0}},
{5, {11, 55, 83, 87, 138, 0, 0}},
{6, {12, 55, 61, 110, 145, 170, 0}},
{6, {25, 36, 79, 104, 143, 150, 0}},
{6, {16, 30, 81, 112, 120, 160, 0}},
{5, {27, 48, 58, 93, 136, 0, 0}},
{6, {6, 54, 82, 100, 130, 167, 0}},
{6, {23, 49, 77, 105, 142, 148, 0}},
}};
// Belief Propagation Decoder
int
bpdecode174(std::array<float, N> const & llr,
std::array<int8_t, K> & decoded,
std::array<int8_t, N> & cw)
{
// Initialize messages and variables
std::array<std::array<float, BP_MAX_CHECKS>, N> tov = {}; // Messages to variable nodes
std::array<std::array<float, BP_MAX_ROWS>, M> toc = {}; // Messages to check nodes
std::array<std::array<float, BP_MAX_ROWS> , M> tanhtoc = {}; // Tanh of messages
std::array<float, N> zn = {}; // Bit log likelihood ratios
std::array<int, M> synd = {}; // Syndrome for checks
int ncnt = 0;
int nclast = 0;
// Initialize toc (messages from bits to checks)
for (int i = 0; i < M; ++i) {
for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
toc[i][j] = llr[Nm[i].neighbors[j]];
}
}
// Iterative decoding
for (int iter = 0; iter <= BP_MAX_ITERATIONS; ++iter) {
// Update bit log likelihood ratios
for (int i = 0; i < N; ++i) {
zn[i] = llr[i] + std::accumulate(tov[i].begin(), tov[i].begin() + BP_MAX_CHECKS, 0.0f);
}
// Check if we have a valid codeword
for (int i = 0; i < N; ++i) cw[i] = zn[i] > 0 ? 1 : 0;
int ncheck = 0;
for (int i = 0; i < M; ++i) {
synd[i] = 0;
for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
synd[i] += cw[Nm[i].neighbors[j]];
}
if (synd[i] % 2 != 0) ++ncheck;
}
if (ncheck == 0)
{
// Extract decoded bits (last N-M bits of codeword)
std::copy(cw.begin() + M, cw.end(), decoded.begin());
// Count errors
int nerr = 0;
for (int i = 0; i < N; ++i) {
if ((2 * cw[i] - 1) * llr[i] < 0.0f) {
++nerr;
}
}
return nerr;
}
// Early stopping criterion
if (iter > 0) {
int nd = ncheck - nclast;
ncnt = (nd < 0) ? 0 : ncnt + 1;
if (ncnt >= 5 && iter >= 10 && ncheck > 15) {
return -1;
}
}
nclast = ncheck;
// Send messages from bits to check nodes
for (int i = 0; i < M; ++i) {
for (int j = 0; j < Nm[i].valid_neighbors; ++j) {
int ibj = Nm[i].neighbors[j];
toc[i][j] = zn[ibj];
for (int k = 0; k < BP_MAX_CHECKS; ++k) {
if (Mn[ibj][k] == i) {
toc[i][j] -= tov[ibj][k];
}
}
}
}
// Send messages from check nodes to variable nodes
for (int i = 0; i < M; ++i) {
for (int j = 0; j < 7; ++j) { // Fixed range [0, 7) to match Fortran's 1:7, could be nrw[j], or 7 logically
tanhtoc[i][j] = std::tanh(-toc[i][j] / 2.0f);
}
}
for (int i = 0; i < N; ++i) {
for (int j = 0; j < BP_MAX_CHECKS; ++j) {
int ichk = Mn[i][j];
if (ichk >= 0) {
float Tmn = 1.0f;
for (int k = 0; k < Nm[ichk].valid_neighbors; ++k) {
if (Nm[ichk].neighbors[k] != i) {
Tmn *= tanhtoc[ichk][k];
}
}
tov[i][j] = 2.0f * std::atanh(-Tmn);
}
}
}
}
return -1; // Decoding failed
}
}
/******************************************************************************/
// Local Routines
/******************************************************************************/
namespace
{
constexpr std::string_view alphabet = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-+";
static_assert(alphabet.size() == 64);
// Function that either translates valid JS8 message characters to their
// corresponding 6-bit word value, or throws. This will end up doing a
// direct index operation into a 256-byte table, the creation of which
// must be constexpr under C++17.
constexpr auto alphabetWord = []()
{
constexpr std::uint8_t invalid = 0xff;
constexpr auto words = []()
{
std::array<std::uint8_t, 256> words{};
for (auto & word : words) word = invalid;
for (std::size_t i = 0; i < alphabet.size(); ++i)
{
words[static_cast<std::uint8_t>(alphabet[i])] = static_cast<std::uint8_t>(i);
}
return words;
}();
return [words](char const value)
{
if (auto const word = words[value];
word != invalid)
{
return word;
}
throw std::runtime_error("Invalid character in message");
};
}();
// Sanity check key bounds of the 6-bit encoding table.
static_assert(alphabetWord('0') == 0);
static_assert(alphabetWord('A') == 10);
static_assert(alphabetWord('a') == 36);
static_assert(alphabetWord('-') == 62);
static_assert(alphabetWord('+') == 63);
template <typename T>
std::uint16_t
CRC12(T const & range)
{
return boost::augmented_crc<12, 0xc06>(range.data(),
range.size()) ^ 42;
}
bool
checkCRC12(std::array<std::int8_t, KK> const & decoded)
{
std::array<uint8_t, 11> bits = {};
for (std::size_t i = 0; i < decoded.size(); ++i)
{
if (decoded[i]) bits[i / 8] |= (1 << (7 - (i % 8)));
}
// Extract the received CRC-12.
uint16_t crc = (static_cast<uint16_t>(bits[9] & 0x1F) << 7) |
(static_cast<uint16_t>(bits[10]) >> 1);
// Clear bits that correspond to the CRC in the last bytes.
bits[9] &= 0xE0;
bits[10] = 0x00;
// Compute CRC and indicate if we have a match.
return crc == CRC12(bits);
}
int
calculateNPass(int const ndepth)
{
switch (ndepth)
{
case 1: return 1; // No subtraction, 1 pass, belief propagation only
case 2: return 3; // Subtraction, 3 passes, belief propagation only
default: return 4; // Subtraction, 4 passes, belief propagation + OSD for ndepth >= 3
}
}
std::string
extractmessage174(std::array<int8_t, KK> const & decoded)
{
std::string message;
// Ensure received CRC matches computed CRC.
if (checkCRC12(decoded))
{
message.reserve(12);
// Decode the message from the 72 data bits
std::array<uint8_t, 12> words;
for (std::size_t i = 0; i < 12; ++i)
{
words[i] = (decoded[i * 6 + 0] << 5) |
(decoded[i * 6 + 1] << 4) |
(decoded[i * 6 + 2] << 3) |
(decoded[i * 6 + 3] << 2) |
(decoded[i * 6 + 4] << 1) |
(decoded[i * 6 + 5] << 0);
}
// Map 6-bit words to the alphabet
for (auto const word : words) message += alphabet[word];
}
return message;
}
// Parity matrix for JS8 message generation.
//
// This should be 952 bytes in size; to store an 87x87 matrix of bits,
// you need 7569 bits, which requires 119 64-bit values, or 952 bytes.
//
// Background here is that this is a low-density parity check code (LDPC),
// generated using the PEG algorithm. In short, true values in a row i of
// the matrix define which of the 87 message bits must be summed, modulo
// 2, to produce the ith parity check bit. Decent references on this are:
//
// 1. https://wsjt.sourceforge.io/FT4_FT8_QEX.pdf
// 2. https://inference.org.uk/mackay/PEG_ECC.html
// 3. https://github.com/Lcrypto/classic-PEG-
//
// The data used was harvested from the original 'ldpc_174_87_params.f90',
// but you'll note that the rows have been reordered here, because this
// isn't Fortran; C++ is row-major, not column-major.
constexpr auto parity = []()
{
constexpr std::size_t Rows = 87;
constexpr std::size_t Cols = 87;
using ElementType = std::uint64_t;
constexpr std::size_t ElementSize = std::numeric_limits<ElementType>::digits;
constexpr auto matrix = []()
{
constexpr std::array<std::string_view, Rows> Data =
{
"23bba830e23b6b6f50982e", "1f8e55da218c5df3309052", "ca7b3217cd92bd59a5ae20",
"56f78313537d0f4382964e", "6be396b5e2e819e373340c", "293548a138858328af4210",
"cb6c6afcdc28bb3f7c6e86", "3f2a86f5c5bd225c961150", "849dd2d63673481860f62c",
"56cdaec6e7ae14b43feeee", "04ef5cfa3766ba778f45a4", "c525ae4bd4f627320a3974",
"41fd9520b2e4abeb2f989c", "7fb36c24085a34d8c1dbc4", "40fc3e44bb7d2bb2756e44",
"d38ab0a1d2e52a8ec3bc76", "3d0f929ef3949bd84d4734", "45d3814f504064f80549ae",
"f14dbf263825d0bd04b05e", "db714f8f64e8ac7af1a76e", "8d0274de71e7c1a8055eb0",
"51f81573dd4049b082de14", "d8f937f31822e57c562370", "b6537f417e61d1a7085336",
"ecbd7c73b9cd34c3720c8a", "3d188ea477f6fa41317a4e", "1ac4672b549cd6dba79bcc",
"a377253773ea678367c3f6", "0dbd816fba1543f721dc72", "ca4186dd44c3121565cf5c",
"29c29dba9c545e267762fe", "1616d78018d0b4745ca0f2", "fe37802941d66dde02b99c",
"a9fa8e50bcb032c85e3304", "83f640f1a48a8ebc0443ea", "3776af54ccfbae916afde6",
"a8fc906976c35669e79ce0", "f08a91fb2e1f78290619a8", "cc9da55fe046d0cb3a770c",
"d36d662a69ae24b74dcbd8", "40907b01280f03c0323946", "d037db825175d851f3af00",
"1bf1490607c54032660ede", "0af7723161ec223080be86", "eca9afa0f6b01d92305edc",
"7a8dec79a51e8ac5388022", "9059dfa2bb20ef7ef73ad4", "6abb212d9739dfc02580f2",
"f6ad4824b87c80ebfce466", "d747bfc5fd65ef70fbd9bc", "612f63acc025b6ab476f7c",
"05209a0abb530b9e7e34b0", "45b7ab6242b77474d9f11a", "6c280d2a0523d9c4bc5946",
"f1627701a2d692fd9449e6", "8d9071b7e7a6a2eed6965e", "bf4f56e073271f6ab4bf80",
"c0fc3ec4fb7d2bb2756644", "57da6d13cb96a7689b2790", "a9fa2eefa6f8796a355772",
"164cc861bdd803c547f2ac", "cc6de59755420925f90ed2", "a0c0033a52ab6299802fd2",
"b274db8abd3c6f396ea356", "97d4169cb33e7435718d90", "81cfc6f18c35b1e1f17114",
"481a2a0df8a23583f82d6c", "081c29a10d468ccdbcecb6", "2c4142bf42b01e71076acc",
"a6573f3dc8b16c9d19f746", "c87af9a5d5206abca532a8", "012dee2198eba82b19a1da",
"b1ca4ea2e3d173bad4379c", "b33ec97be83ce413f9acc8", "5b0f7742bca86b8012609a",
"37d8e0af9258b9e8c5f9b2", "35ad3fb0faeb5f1b0c30dc", "6114e08483043fd3f38a8a",
"cd921fdf59e882683763f6", "95e45ecd0135aca9d6e6ae", "2e547dd7a05f6597aac516",
"14cd0f642fc0c5fe3a65ca", "3a0a1dfd7eee29c2e827e0", "c8b5dffc335095dcdcaf2a",
"3dd01a59d86310743ec752", "8abdb889efbe39a510a118", "3f231f212055371cf3e2a2"
};
constexpr std::size_t Total = (Rows * Cols + ElementSize - 1);
constexpr std::size_t Count = Total / ElementSize;
constexpr std::array<std::uint8_t, 4> Masks = {0x8, 0x4, 0x2, 0x1};
std::array<ElementType, Count> data{};
for (std::size_t row = 0; row < Rows; ++row)
{
std::size_t col = 0;
for (auto const c : Data[row])
{
std::uint8_t const value = (c >= '0' && c <= '9') ? c - '0' :
(c >= 'a' && c <= 'f') ? c - 'a' + 10 :
(c >= 'A' && c <= 'F') ? c - 'A' + 10 : throw "Invalid hex";
for (auto const mask : Masks)
{
if (col >= Cols) break;
if (value & mask)
{
auto const index = row * Cols + col;
data[index / ElementSize] |= (ElementType(1) << (index % ElementSize));
}
++col;
}
}
}
return data;
}();
return [matrix](std::size_t const row,
std::size_t const col)
{
auto const index = row * Cols + col;
return (matrix[index / ElementSize] >>
(index % ElementSize)) & 1;
};
}();
constexpr auto gen = []()
{
using GeneratorMatrix = std::array<std::array<int8_t, N>, K>;
using HexStringArray = std::array<std::string_view, M>;
// Example parity bit definitions in hexadecimal format
constexpr HexStringArray g = {
"23bba830e23b6b6f50982e", "1f8e55da218c5df3309052", "ca7b3217cd92bd59a5ae20",
"56f78313537d0f4382964e", "29c29dba9c545e267762fe", "6be396b5e2e819e373340c",
"293548a138858328af4210", "cb6c6afcdc28bb3f7c6e86", "3f2a86f5c5bd225c961150",
"849dd2d63673481860f62c", "56cdaec6e7ae14b43feeee", "04ef5cfa3766ba778f45a4",
"c525ae4bd4f627320a3974", "fe37802941d66dde02b99c", "41fd9520b2e4abeb2f989c",
"40907b01280f03c0323946", "7fb36c24085a34d8c1dbc4", "40fc3e44bb7d2bb2756e44",
"d38ab0a1d2e52a8ec3bc76", "3d0f929ef3949bd84d4734", "45d3814f504064f80549ae",
"f14dbf263825d0bd04b05e", "f08a91fb2e1f78290619a8", "7a8dec79a51e8ac5388022",
"ca4186dd44c3121565cf5c", "db714f8f64e8ac7af1a76e", "8d0274de71e7c1a8055eb0",
"51f81573dd4049b082de14", "d037db825175d851f3af00", "d8f937f31822e57c562370",
"1bf1490607c54032660ede", "1616d78018d0b4745ca0f2", "a9fa8e50bcb032c85e3304",
"83f640f1a48a8ebc0443ea", "eca9afa0f6b01d92305edc", "3776af54ccfbae916afde6",
"6abb212d9739dfc02580f2", "05209a0abb530b9e7e34b0", "612f63acc025b6ab476f7c",
"0af7723161ec223080be86", "a8fc906976c35669e79ce0", "45b7ab6242b77474d9f11a",
"b274db8abd3c6f396ea356", "9059dfa2bb20ef7ef73ad4", "3d188ea477f6fa41317a4e",
"8d9071b7e7a6a2eed6965e", "a377253773ea678367c3f6", "ecbd7c73b9cd34c3720c8a",
"b6537f417e61d1a7085336", "6c280d2a0523d9c4bc5946", "d36d662a69ae24b74dcbd8",
"d747bfc5fd65ef70fbd9bc", "a9fa2eefa6f8796a355772", "cc9da55fe046d0cb3a770c",
"f6ad4824b87c80ebfce466", "cc6de59755420925f90ed2", "164cc861bdd803c547f2ac",
"c0fc3ec4fb7d2bb2756644", "0dbd816fba1543f721dc72", "a0c0033a52ab6299802fd2",
"bf4f56e073271f6ab4bf80", "57da6d13cb96a7689b2790", "81cfc6f18c35b1e1f17114",
"481a2a0df8a23583f82d6c", "1ac4672b549cd6dba79bcc", "c87af9a5d5206abca532a8",
"97d4169cb33e7435718d90", "a6573f3dc8b16c9d19f746", "2c4142bf42b01e71076acc",
"081c29a10d468ccdbcecb6", "5b0f7742bca86b8012609a", "012dee2198eba82b19a1da",
"f1627701a2d692fd9449e6", "35ad3fb0faeb5f1b0c30dc", "b1ca4ea2e3d173bad4379c",
"37d8e0af9258b9e8c5f9b2", "cd921fdf59e882683763f6", "6114e08483043fd3f38a8a",
"2e547dd7a05f6597aac516", "95e45ecd0135aca9d6e6ae", "b33ec97be83ce413f9acc8",
"c8b5dffc335095dcdcaf2a", "3dd01a59d86310743ec752", "14cd0f642fc0c5fe3a65ca",
"3a0a1dfd7eee29c2e827e0", "8abdb889efbe39a510a118", "3f231f212055371cf3e2a2"
};
// Convert a hex string to a generator matrix row
constexpr auto parse_hex_row = [](std::string_view hex, std::array<int8_t, N>& row) {
for (size_t j = 0; j < hex.size(); ++j) {
uint8_t const c = hex[j];
std::uint8_t const value = (c >= '0' && c <= '9') ? c - '0' :
(c >= 'a' && c <= 'f') ? c - 'a' + 10 :
(c >= 'A' && c <= 'F') ? c - 'A' + 10 : throw "Invalid hex";
for (int bit = 0; bit < 4; ++bit) {
size_t col = j * 4 + bit;
if (col < N && (value & (1 << (3 - bit)))) {
row[col] = 1;
}
}
}
};
GeneratorMatrix gen = {}; // Initialize to zero
for (int i = 0; i < M; ++i) {
parse_hex_row(g[i], gen[i]);
}
// Add identity matrix for the systematic bits
for (int i = 0; i < K; ++i) {
gen[i][M + i] = 1;
}
return gen;
}();
using GeneratorMatrix = std::array<std::array<int8_t, N>, K>;
void
mrbencode(std::array<int8_t, K> const & message,
std::array<int8_t, N> & codeword,
GeneratorMatrix const & g2)
{
codeword.fill(0);
for (int i = 0; i < K; ++i) {
if (message[i] == 1) {
for (int j = 0; j < N; ++j) {
codeword[j] ^= g2[i][j];
}
}
}
}
// XXX this is a Q&D interpretation of the intent of the
// original Fortran, rather than a direct translation.
int
osd174(std::array<float, N> const & rx,
int const ndeep,
std::array<int8_t, K> & decoded,
std::array<int8_t, N> & cw,
float & dmin)
{
// Hard decisions
std::array<int8_t, N> hdec = {};
for (int i = 0; i < N; ++i) {
hdec[i] = (rx[i] >= 0) ? 1 : 0;
}
// Compute absolute values for reliability
std::array<float, N> absrx = {};
std::transform(rx.begin(), rx.end(), absrx.begin(), [](float x) { return std::abs(x); });
// Indices sorted by reliability
std::array<int, N> indices = {};
std::iota(indices.begin(), indices.end(), 0);
std::sort(indices.begin(), indices.end(), [&absrx](int a, int b) {
return absrx[a] > absrx[b];
});
// Reorder generator matrix
GeneratorMatrix genmrb = {};
for (int i = 0; i < K; ++i) {
for (int j = 0; j < N; ++j) {
genmrb[i][j] = gen[i][indices[j]];
}
}
std::array<int8_t, N> hdec_reordered = {};
for (int i = 0; i < N; ++i) {
hdec_reordered[i] = hdec[indices[i]];
}
// Gaussian elimination
for (int id = 0; id < K; ++id) {
int pivot_col = -1;
for (int col = id; col < N; ++col) {
if (genmrb[id][col] == 1) {
pivot_col = col;
break;
}
}
if (pivot_col == -1) {
continue; // No pivot found
}
if (pivot_col != id) {
for (int row = 0; row < K; ++row) {
std::swap(genmrb[row][id], genmrb[row][pivot_col]);
}
std::swap(indices[id], indices[pivot_col]);
}
for (int row = 0; row < K; ++row) {
if (row != id && genmrb[row][id] == 1) {
for (int col = 0; col < N; ++col) {
genmrb[row][col] ^= genmrb[id][col];
}
}
}
}
// Initialize m0 and compute c0
std::array<int8_t, K> m0 = {};
for (int i = 0; i < K; ++i) {
m0[i] = hdec_reordered[i];
}
std::array<int8_t, N> c0 = {};
mrbencode(m0, c0, genmrb);
// Compute initial Euclidean distance
int nhardmin = std::inner_product(hdec_reordered.begin(), hdec_reordered.end(), c0.begin(), 0,
std::plus<>(), [](int a, int b) { return a ^ b; });
dmin = std::inner_product(hdec_reordered.begin(), hdec_reordered.end(), c0.begin(), 0.0f,
std::plus<>(), [&absrx](int a, int b) { return (a ^ b) * absrx[b]; });
cw = c0;
// If no deeper decoding needed
if (ndeep == 0) {
std::copy(cw.begin() + M, cw.end(), decoded.begin());
return nhardmin;
}
// Perform deeper decoding
for (int iorder = 1; iorder <= ndeep; ++iorder) {
std::vector<int8_t> mi(K, 0);
std::fill(mi.end() - iorder, mi.end(), 1);
do {
std::array<int8_t, K> me = {};
for (int i = 0; i < K; ++i) {
me[i] = m0[i] ^ mi[i];
}
std::array<int8_t, N> ce = {};
mrbencode(me, ce, genmrb);
int nxor = std::inner_product(ce.begin(), ce.end(), hdec_reordered.begin(), 0,
std::plus<>(), [](int a, int b) { return a ^ b; });
float dd = std::inner_product(ce.begin(), ce.end(), hdec_reordered.begin(), 0.0f,
std::plus<>(), [&absrx](int a, int b) { return (a ^ b) * absrx[b]; });
if (dd < dmin) {
dmin = dd;
cw = ce;
nhardmin = nxor;
}
} while (std::prev_permutation(mi.begin(), mi.end()));
}
// Reorder the codeword to original order
std::array<int8_t, N> cw_reordered = {};
for (int i = 0; i < N; ++i) {
cw_reordered[indices[i]] = cw[i];
}
cw = cw_reordered;
// Extract the decoded message
std::copy(cw.begin() + M, cw.end(), decoded.begin());
return nhardmin; // Return the number of hard errors
}
}
/******************************************************************************/
// Decoder Template Class
/******************************************************************************/
// Mode-parameterized decoder class; presently a work in progress.
namespace
{
template <typename Mode>
class Decoder
{
// Plan types
enum class Plan
{
DS,
BB,
CF,
CB,
SD,
CS,
count
};
// Data members
std::array<float, Mode::NFFT1> nuttal;
std::array<std::array<std::array<std::complex<float>, Mode::NDOWNSPS>, 7>, 3> csyncs;
std::array<std::complex<float>, Mode::NMAX> filter;
std::array<std::complex<float>, Mode::NMAX> cfilt;
std::array<std::complex<float>, Mode::NDFFT1 / 2 + 1> ds_cx;
std::array<std::complex<float>, Mode::NFFT1 / 2 + 1> sd;
std::array<float, Mode::NMAX> dd;
std::array<std::complex<float>, Mode::NDOWNSPS> csymb;
std::array<std::array<float, Mode::NHSYM>, Mode::NSPS> s;
std::array<float, Mode::NSPS> savg;
std::array<float, Mode::NSPS> sbase;
std::array<std::complex<float>, NP> cd0;
SyncIndex sync;
EnumArray<fftwf_plan, Plan> plans = {};
JS8::Event::Emitter emitEvent;
static constexpr auto Costas = JS8::Costas::array(Mode::NCOSTAS);
// Fore and aft tapers to reduce spectral leakage during the
// downsampling process. We can compute these at compile time.
static constexpr auto Taper = []
{
std::array<std::array<float, Mode::NDD + 1>, 2> taper{};
for (size_t i = 0; i <= Mode::NDD; ++i)
{
float const value = 0.5f * (1.0f + cos(i * M_PI / Mode::NDD));
taper[1][ i] = value; // TailTaper (original taper)
taper[0][Mode::NDD - i] = value; // HeadTaper (reversed taper)
}
return taper;
}();
// Baseline computation support.
using Points = Eigen::Matrix<double, BASELINE_NODES.size(), 2>;
using Vandermonde = Eigen::Matrix<double, BASELINE_NODES.size(),
BASELINE_NODES.size()>;
using Coefficients = Eigen::Vector<double, BASELINE_NODES.size()>;
Points p;
Vandermonde V;
Coefficients c;
// Polynomial evaluation using Estrin's method, loop is unrolled at
// compile time. A compiler should emit SIMD instructions from what
// it sees here when the optimizer is involved, but even without it,
// we'll likely see fused multiply-add instructions.
template <Eigen::Index... I>
inline auto
evaluate(std::size_t const i,
std::integer_sequence<Eigen::Index, I...>) const
{
auto baseline = 0.0;
auto exponent = 1.0;
((baseline += (c[I * 2] + c[I * 2 + 1] * i) * exponent, exponent *= i * i), ...);
return static_cast<float>(baseline);
}
// Driver for the loop unrolling above, since at present we're limited
// to targeting C++17; when we can target C++20 or later, these can be
// combined into one function.
inline auto
evaluate(std::size_t const i) const
{
return evaluate(i, std::make_integer_sequence<Eigen::Index,
Coefficients::SizeAtCompileTime / 2>{});
}
// XXX still working on this one.
std::optional<Decode>
js8dec(bool const syncStats,
float const nfqso,
int const ndepth,
int const napwid,
bool const lsubtract,
bool const nagain,
float & f1,
float & xdt,
int & nharderrors,
float & dmin,
float & xsnr)
{
constexpr float FR = 12000.0f / Mode::NFFT1; // Frequency resolution
constexpr float FS2 = 12000.0f / Mode::NDOWN;
constexpr float DT2 = 1.0f / FS2;
auto const index = static_cast<int>(std::round(f1 / FR)); // Closest index
float const scaled_value = 0.1f * (sbase[index] - Mode::BASESUB); // Adjust and scale
float const xbase = std::pow(10.0f, scaled_value); // Convert to linear scale
float delfbest = 0.0f;
int ibest = 0;
// Downsample the signal and prepare for processing.
js8_downsample(f1);
// Initial guess for the start of the signal.
int i0 = static_cast<int>(std::round((xdt + Mode::ASTART) * FS2));
float smax = 0.0f;
// Search for the best synchronization offset.
for (int idt = i0 - Mode::NQSYMBOL;
idt <= i0 + Mode::NQSYMBOL;
++idt)
{
float const sync = syncjs8d(idt, 0.0f);
if (sync > smax) {
smax = sync;
ibest = idt;
}
}
// Improved estimate for DT.
float const xdt2 = ibest * DT2;
// Fine frequency synchronization
i0 = static_cast<int>(std::round(xdt2 * FS2));
smax = 0.0f;
for (int ifr = -NFSRCH;
ifr <= NFSRCH;
++ifr)
{
float const delf = ifr * 0.5f;
float const sync = syncjs8d(i0, delf);
if (sync > smax) {
smax = sync;
delfbest = delf;
}
}
// Frequency tweaking.
float const dphi = -delfbest * ((2.0f * M_PI) / FS2); // Phase increment
std::complex<float> const wstep = std::polar(1.0f, dphi); // Step for phase rotation
std::complex<float> w = {1.0f, 0.0f}; // Cumlative phase
for (int i = 0; i < NP2; ++i)
{
w *= wstep; // Update cumulative phase
cd0[i] *= w; // Apply phase shift
}
// Adjust the frequency and time offset.
xdt = xdt2;
f1 += delfbest;
float const sync = syncjs8d(i0, 0.0f);
std::array<std::array<float, NN>, NROWS> s2;
/*
j=0
do k=1,NN
i1=ibest+(k-1)*NDOWNSPS
csymb=cmplx(0.0,0.0)
if( i1.ge.0 .and. i1+(NDOWNSPS-1) .le. NP2-1 ) csymb=cd0(i1:i1+(NDOWNSPS-1))
call four2a(csymb,NDOWNSPS,1,-1,1)
s2(0:7,k)=abs(csymb(1:8))/1e3
enddo
*/
for (int k = 0; k < NN; ++k)
{
// Calculate the starting index for the current symbol.
int const i1 = ibest + k * Mode::NDOWNSPS;
csymb.fill(ZERO);
if (i1 >= 0 && i1 + Mode::NDOWNSPS <= NP2)
{
std::copy(cd0.begin() + i1,
cd0.begin() + i1 + Mode::NDOWNSPS,
csymb.begin());
}
fftwf_execute(plans[Plan::CS]);
// Normalize and take the magnitude of the first 8 points.
for (int i = 0; i < NROWS; ++i)
{
s2[i][k] = std::abs(csymb[i]) / 1000.0f;
}
}
// Sync quality check using Costas tone patterns.
int nsync = 0;
for (std::size_t costas = 0; costas < Costas.size(); ++costas)
{
auto const offset = costas * 36;
for (std::size_t column = 0; column < 7; ++column)
{
// Find the row containing the maximum value in the
// current column.
auto const max_row = std::distance(
s2.begin(),
std::max_element(s2.begin(),
s2.end(),
[index = offset + column]
(auto const & rowA,
auto const & rowB)
{
return rowA[index] < rowB[index];
}));
// Check if the max row matches the Costas pattern.
if (Costas[costas][column] == max_row) ++nsync;
}
}
// If the sync quality isn't at least 7, this one's a loser.
if (nsync <= 6) return std::nullopt;
if (syncStats)
{
emitEvent(JS8::Event::SyncCandidate{Mode::NSUBMODE, f1, xdt, nsync});
}
std::array<std::array<float, ND>, NROWS> s1;
// Fill s1 from s2, excluding the Costas arrays.
for (int row = 0; row < NROWS; ++row)
{
std::copy(s2[row].begin() + 7, s2[row].begin() + 36, s1[row].begin());
std::copy(s2[row].begin() + 43, s2[row].begin() + 72, s1[row].begin() + 29);
}
// Flatten s1 into a single 1D array and find the median.
auto const median = [&s1]()
{
constexpr std::size_t size = NROWS * ND;
constexpr std::size_t nth = size / 2 - 1;
std::vector<float> s1flat;
s1flat.reserve(size);
for (auto const & row : s1)
{
s1flat.insert(s1flat.end(),
row.begin(),
row.end());
}
std::nth_element(s1flat.begin(),
s1flat.begin() + nth,
s1flat.end());
return s1flat[nth];
}();
// Normalize s1 by dividing each element by the median value.
for (auto & row : s1)
{
for (auto & value : row)
{
value /= median;
}
}
// Temporary variables for metrics
std::array<float, 3 * ND> llr0 = {};
std::array<float, 3 * ND> llr1 = {};
// Compute metrics for each row in `s1`
for (int j = 0; j < ND; ++j)
{
int const i1 = 3 * j; // First column (matches Fortran's i1)
int const i2 = 3 * j + 1; // Second column (matches Fortran's i2)
int const i4 = 3 * j + 2; // Third column (matches Fortran's i4)
std::array<float, NROWS> ps;
for (int i = 0; i < NROWS; ++i) ps[i] = s1[i][j];
// Assign to `bmeta` in column order, with correct values
llr0[i1] = std::max({ps[4], ps[5], ps[6], ps[7]}) - std::max({ps[0], ps[1], ps[2], ps[3]}); // r4
llr0[i2] = std::max({ps[2], ps[3], ps[6], ps[7]}) - std::max({ps[0], ps[1], ps[4], ps[5]}); // r2
llr0[i4] = std::max({ps[1], ps[3], ps[5], ps[7]}) - std::max({ps[0], ps[2], ps[4], ps[6]}); // r1
for (auto & x : ps) x = std::log(x + 1e-32f);
// Assign to `bmetb` in column order, with correct values
llr1[i1] = std::max({ps[4], ps[5], ps[6], ps[7]}) - std::max({ps[0], ps[1], ps[2], ps[3]}); // r4
llr1[i2] = std::max({ps[2], ps[3], ps[6], ps[7]}) - std::max({ps[0], ps[1], ps[4], ps[5]}); // r2
llr1[i4] = std::max({ps[1], ps[3], ps[5], ps[7]}) - std::max({ps[0], ps[2], ps[4], ps[6]}); // r1
}
auto const normalizeLLR = [](auto & llr)
{
float sum = 0.0f;
float sum_of_squares = 0.0f;
for (auto const value : llr)
{
sum += value;
sum_of_squares += value * value;
}
float const llrav = sum / llr.size();
float const llr2av = sum_of_squares / llr.size();
float const variance = llr2av - llrav * llrav;
float const llrsig = std::sqrt(variance > 0.0f ? variance : llr2av);
for (float & val : llr) val = (val / llrsig) * 2.83f;
};
// Normalize and process metrics
normalizeLLR(llr0);
normalizeLLR(llr1);
std::array<int8_t, K> decoded;
std::array<int8_t, N> cw;
// Loop over decoding passes
for (int ipass = 1; ipass <= 4; ++ipass)
{
// LLR 0 used on passes 1, 3, and 4; LLR 1 used on pass 2.
auto const & llr = ipass == 2 ? llr1 : llr0;
// Zero the first 24 bytes of LLR 0 on the third pass;
// the first 48 bytes of LLR 0 on the fourth pass;
if (ipass == 3) std::fill(llr0.begin(), llr0.begin() + 24, 0.0f);
else if (ipass == 4) std::fill(llr0.begin() + 24, llr0.begin() + 48, 0.0f);
// Decode using belief propagation.
nharderrors = bpdecode174(llr, decoded, cw);
dmin = 0.0f;
if (ndepth >= 3 && nharderrors < 0) {
int ndeep = 3;
if (std::abs(nfqso - f1) <= napwid) {
if ((ipass == 3 || ipass == 4) && !nagain) {
ndeep = 3;
} else {
ndeep = 4;
}
}
if (nagain) {
ndeep = 5;
}
nharderrors = osd174(llr, ndeep, decoded, cw, dmin);
}
xsnr = -99.0f;
// Check for all-zero codeword
if (std::all_of(cw.begin(), cw.end(), [](int x) { return x == 0; }))
{
continue;
}
if (nharderrors >= 0 && nharderrors + dmin < 60.0f &&
!(sync < 2.0f && nharderrors > 35) &&
!(ipass > 2 && nharderrors > 39) &&
!(ipass == 4 && nharderrors > 30))
{
if (checkCRC12(decoded))
{
if (syncStats)
{
emitEvent(JS8::Event::SyncDecode{Mode::NSUBMODE, f1, xdt2});
}
auto message = extractmessage174(decoded);
int const i3bit = 4 * decoded[72]
+ 2 * decoded[73]
+ decoded[74];
std::array<int, NN> itone;
JS8::encode(i3bit, Costas, message.data(), itone.data());
// Subtract signal if needed.
if (lsubtract) subtractjs8(genjs8refsig(itone, f1), xdt2);
float xsig = 0.0f;
float xnoi = 0.0f;
for (int i = 0; i < NN; ++i)
{
xsig += std::pow(s2[ itone[i] ][i], 2); // Signal power
xnoi += std::pow(s2[(itone[i] + 4) % 7][i], 2); // Noise power
}
xsnr = 10.0f * std::log10((xnoi > 0.0f &&
xnoi < xsig) ? xsig / xnoi - 1.0f
: 0.001f) - 27.0f;
if (!nagain)
{
float const x = xsig / xbase - 1.0f;
float const x2 = (x > 1.259e-10f)
? 10.0f * std::log10(x)
: -99.0f;
xsnr = x2 - 32.0f;
}
if (xsnr < -28.0f) xsnr = -28.0f;
return std::make_optional<Decode>(i3bit, message);
}
}
else
{
nharderrors = -1;
}
}
return std::nullopt;
}
// Compute noise baseline. Important to note that the Fortran version
// used up to 1000 lower envelope points for the polynomial determination
// here, which caused some oddities when the matrix was ill-conditioned.
//
// I'm trying an alternate approach based on Chebyshev nodes.
//
// Inputs: 1. savg
// 2. Closed range of savg defined by [ia, ib]
// Outputs: 1. savg normalized to dB scale
// 2. sbase
void
baselinejs8(int const ia,
int const ib)
{
// Convert savg from power scale to db scale.
for (auto i = ia; i <= ib; ++i) savg[i] = 10.0f * std::log10(savg[i]);
// Data referenced in savg is defined by the closed range [ia, ib];
auto const data = savg.begin() + ia;
std::size_t const size = ib - ia + 1;
// Loop invariants; sentinel one past the end of the range, and
// the number of points in each of the arms on either side of a
// node.
auto const end = data + size;
auto const arm = size / (2 * BASELINE_NODES.size());
// Collect lower envelope points; use Chebyshev node interpolants
// to reduce Runge's phenomenon oscillations.
for (std::size_t i = 0; i < BASELINE_NODES.size(); ++i)
{
auto const node = size * BASELINE_NODES[i];
auto const base = data + static_cast<int>(std::round(node));
auto span = std::vector<float>(std::clamp(base - arm, data, end),
std::clamp(base + arm, data, end));
auto const n = span.size() * BASELINE_SAMPLE / 100;
std::nth_element(span.begin(), span.begin() + n, span.end());
p.row(i) << node, span[n];
}
// Extract x and y values from points and prepare the Vandermonde
// matrix, initializing the first column with 1 (x^0); remaining
// columns are filled with the Schur product.
Eigen::VectorXd x = p.col(0);
Eigen::VectorXd y = p.col(1);
V.col(0).setOnes();
for (Eigen::Index i = 1; i < V.cols(); ++i)
{
V.col(i) = V.col(i - 1).cwiseProduct(x);
}
// Solve the least squares problem for polynomial coefficients;
// evaluate the polynomial and create the baseline.
c = V.colPivHouseholderQr().solve(y);
sbase.fill(0.0f);
for (std::size_t i = 0; i < size; ++i) sbase[ia + i] = evaluate(i) + 0.65f;
}
// Extracted from the downsampling process; this step is part of the
// frequency-domain filtering process for downsampling the JS8 signal.
// After the FFT, the resulting frequency-domain data (ds_cx) can be
// manipulated (e.g., band-pass filtered or shifted). Subsequent inverse
// FFT operations convert the filtered data back to the time domain at
// a lower sample rate, achieving the desired downsampling.
void
computeBasebandFFT()
{
// ds_dx is an array of complex<float>; we're going to do an in-place
// FFT, so we'll interpret the first half of the array as if they were
// floats, which they are.
float * fftw_real = reinterpret_cast<float *>(ds_cx.data());
// Copy in data and zero-pad any remainder; not all modes will have
// a remainder.
std::copy(dd.begin(), dd.end(), fftw_real);
std::fill(fftw_real + dd.size(), fftw_real + Mode::NDFFT1, 0.0f);
fftwf_execute(plans[Plan::BB]);
}
// This function extracts a narrow frequency band around the target frequency f0,
// applies tapering to reduce spectral artifacts, aligns the signal to the center
// frequency, performs an inverse FFT to convert the data back into the time domain,
// and normalizes the result for further processing in the JS8 decoding pipeline.
void
js8_downsample(float const f0)
{
// Frequency band extraction; identifies a narrow frequency band around the
// target frequency (f0) based on a predefined range (8.5 baud above and 1.5
// baud below). The indices of this range in the frequency-domain representation
// (ds_cx) are calculated (ib and it), and the relevant frequency-domain samples
// are extracted into cd0.
constexpr float DF = 12000.0f / Mode::NDFFT1;
constexpr float BAUD = 12000.0f / Mode::NSPS;
float const ft = f0 + 8.5f * BAUD;
float const fb = f0 - 1.5f * BAUD;
int const i0 = static_cast<int>(std::round(f0 / DF));
int const it = std::min( static_cast<int>(std::round(ft / DF)), Mode::NDFFT1 / 2);
int const ib = std::max(0, static_cast<int>(std::round(fb / DF)));
std::size_t const NDD_SIZE = Mode::NDD + 1;
std::size_t const RANGE_SIZE = it - ib + 1;
std::fill_n(cd0.begin(), Mode::NDFFT2, ZERO);
std::copy(ds_cx.begin() + ib,
ds_cx.begin() + ib + RANGE_SIZE,
cd0.begin());
// Tapering is applied to smooth the edges of the frequency band, reducing
// spectral leakage during the inverse FFT. Reversed taper at the beginning,
// normal taper at the end.
auto const head = cd0.begin();
auto const tail = cd0.begin() + RANGE_SIZE;
std::transform(head, head + NDD_SIZE, Taper[0].begin(), head, std::multiplies<>());
std::transform(tail - NDD_SIZE, tail, Taper[1].begin(), tail - NDD_SIZE, std::multiplies<>());
// The extracted frequency band is aligned to the center of the frequency domain
// representation (i0 - ib) via a cyclic shift using std::rotate. This centers
// the desired signal.
std::rotate(cd0.begin(), cd0.begin() + (i0 - ib), cd0.begin() + Mode::NDFFT2);
// An inverse FFT is performed on the frequency-domain data (cd0) to transform it
// back into the time domain, effectively yielding a downsampled, time-domain signal
// focused on the extracted narrow frequency band.
fftwf_execute(plans[Plan::DS]);
// The resulting time-domain samples are normalized by a factor derived from the
// input and output FFT sizes (Mode::NDFFT1 and Mode::NDFFT2), ensuring consistency
// in the signal’s amplitude.
float const factor = 1.0f / std::sqrt(static_cast<float>(Mode::NDFFT1) * Mode::NDFFT2);
std::transform(cd0.begin(),
cd0.end(),
cd0.begin(),
[factor](auto & value) { return value * factor; });
}
// Evaluate the synchronization power of signal segments, ranks potential candidates, and
// extracts the most promising ones for further decoding.
//
// Detailed Steps:
//
// 1. Compute Symbol Spectra:
//
// - The signal is processed in overlapping segments, with each segment multiplied by
// a Nuttall window to reduce spectral leakage.
// - An FFT is performed on each windowed segment to obtain the frequency-domain
// representation.
// - The power spectrum of each segment is computed, and the average spectrum is
// accumulated across segments.
//
// 2. Filter Edge Adjustments:
//
// - Adjusts the frequency bounds (nfa and nfb) to ensure the analysis remains
// within valid and meaningful regions of the signal.
//
// 3. Baseline Computation:
//
// - The average spectrum is converted to a dB scale.
// - Baseline is computed to distinguish significant signal components from
// background noise.
//
// 4. Synchronization Metric Calculation:
//
// - For each frequency bin in the specified range, evaluates synchronization
// power using a Costas waveform.
// - Sync metric is computed over the index range, considering all combinations
// of Costas patterns.
// - The maximum sync value and its corresponding offset are recorded for each
// frequency bin.
//
// 5. Normalization:
//
// - The sync values are normalized to the 40th percentile value using a ranked
// index. This ensures a consistent scaling across different signals and noise
// levels.
//
// 6. Candidate Extraction:
//
// - Candidates with a strong sync metric (above a defined threshold) are extracted.
// - Near-duplicate candidates of lesser synchronization power, based on frequency
// proximity, are eliminated.
//
// 7. Output:
//
// - Returns a vector of the most promising signal candidates, sorted by their
// synchronization power. It's expected that these will be re-sorted by the
// caller into a desirable order, but synchronization power order facilitates
// debugging this function.
std::vector<Sync>
syncjs8(int nfa,
int nfb)
{
// Compute symbol spectra
savg.fill(0.0f);
for (int j = 0; j < Mode::NHSYM; ++j)
{
int const ia = j * Mode::NSTEP;
int const ib = ia + Mode::NFFT1;
if (ib > Mode::NMAX) break;
std::transform(dd.begin() + ia,
dd.begin() + ib,
nuttal.begin(),
reinterpret_cast<float *>(sd.data()),
std::multiplies<float>{});
fftwf_execute(plans[Plan::SD]);
// Compute power spectrum
for (int i = 0; i < Mode::NSPS; ++i)
{
auto const power = std::norm(sd[i]);
s[i][j] = power;
savg[i] += power;
}
}
// Filter edge sanity measures
int const nwin = nfb - nfa;
if (nfa < 100)
{
nfa = 100;
if (nwin < 100) nfb = nfa + nwin;
}
if (nfb > 4910)
{
nfb = 4910;
if (nwin < 100) nfa = nfb - nwin;
}
auto const ia = std::max(0, static_cast<int>(std::round(nfa / Mode::DF)));
auto const ib = static_cast<int>(std::round(nfb / Mode::DF));
// Convert average spectrum from power to db scale and compute
// baseline.
baselinejs8(ia, ib);
// Compute and populate the sync index.
sync.clear();
for (int i = ia; i <= ib; ++i)
{
float max_value = -std::numeric_limits<float>::infinity();
int max_index = -Mode::JZ;
for (int j = -Mode::JZ; j <= Mode::JZ; ++j)
{
std::array<std::array<float, 3>, 2> t{};
for (int p = 0; p < 3; ++p)
{
for (int n = 0; n < 7; ++n)
{
int const offset = j + Mode::JSTRT + NSSY * n + p * 36 * NSSY;
if (offset >= 0 && offset < Mode::NHSYM)
{
// Accumulate Costas pattern contributions.
t[0][p] += s[i + NFOS * Costas[p][n]][offset];
// Accumulate sum over all frequencies for this block.
for (int freq = 0; freq < 7; ++freq)
{
t[1][p] += s[i + NFOS * freq][offset];
}
}
}
}
// Compute sync metric over the index range. We are at the moment
// maintaining the Fortran summation methodology for compatibility
// testing; there are more efficient ways to do this, but IEEE 754
// addition is a touchy thing, so we'll need to ensure that any
// changes don't negatively affect result precision.
auto const compute_sync = [&t](int start, int end)
{
float tx = 0.0f;
float t0 = 0.0f;
for (int i = start; i <= end; ++i)
{
tx += t[0][i];
t0 += t[1][i];
}
return tx / ((t0 - tx) / 6.0f);
};
if (auto const sync_value = std::max({
compute_sync(0, 2),
compute_sync(0, 1),
compute_sync(1, 2)
}); sync_value > max_value)
{
max_value = sync_value;
max_index = j;
}
}
sync.emplace(Mode::DF * i,
Mode::TSTEP * (max_index + 0.5f),
max_value);
}
// If we found nothing, we're done here.
if (sync.empty()) return {};
// Access the sync indices.
auto & freqIndex = sync.get<Tag::Freq>();
auto & rankIndex = sync.get<Tag::Rank>();
auto & syncIndex = sync.get<Tag::Sync>();
// Normalize to the 40th percentile using the frequency index,
// which is stable under sync value mutation. One thing to note
// here is that the Fortran version didn't seem to reliably
// calculate the 40th percentile rank; sometimes high, other
// times low, infrequently actually the 40th percentile value.
// This method should be perfectly accurate in all cases.
auto const normalize =
[
sync = rankIndex.nth(rankIndex.size() * 4 / 10)->sync
]
(Sync & entry)
{
entry.sync /= sync;
};
for (auto it = freqIndex.begin();
it != freqIndex.end();
++it)
{
freqIndex.modify(it, normalize);
}
// Extract candidates.
std::vector<Sync> candidates;
for (auto it = syncIndex.begin();
it != syncIndex.end() && candidates.size() < NMAXCAND;
it = syncIndex.begin())
{
// Stop iteration if below threshold or invalid; as the
// index is sorted by value, any subsequent entries will
// also be below the threshold or invalid.
if (it->sync < ASYNCMIN || std::isnan(it->sync)) break;
// Good value, relatively strong; save the candidate.
candidates.push_back(*it);
// Remove the candidate and any near-duplicates based
// on frequency. This invalidates `it`, so we reset it
// to the index begin in the loop increment condition.
freqIndex.erase(
freqIndex.lower_bound(it->freq - Mode::AZ),
freqIndex.upper_bound(it->freq + Mode::AZ));
}
normalizeS();
return candidates;
}
// Here due to it being done in the Fortran, but `s` is never referenced
// beyond `syncjs8` so unless the mainline is looking at this via shared
// memory, not sure that we need it.
void
normalizeS()
{
float maxVal = std::numeric_limits<float>::lowest();
for (auto const & row : s)
{
maxVal = std::max(maxVal, *std::max_element(row.begin(), row.end()));
}
float const factor = 20.0f / maxVal;
for (auto & row : s)
{
for (auto & value : row) value *= factor;
}
}
// Returns the total synchronization power, which is a measure of how well
// the signal aligns with the Costas sequence after accounting for the
// frequency adjustment. Used to identify the best alignment for further
// decoding.
float
syncjs8d(int const i0,
float const delf)
{
constexpr float BASE_DPHI = TAU * (1.0f / (12000.0f / Mode::NDOWN));
// If delta frequency is non-zero, compute the frequency
// adjustment array, otherwise, use what'll be an identity
// transfrom when multiplied.
std::array<std::complex<float>, Mode::NDOWNSPS> freqAdjust;
if (delf != 0.0f)
{
float const dphi = BASE_DPHI * delf;
float phi = 0.0f;
// std::fmod() is almost like Fortran's mod(), but not quite;
// Since delf can be negative, we must ensure that phi stays
// within [0, TAU), which Fortran's mod() handles by itself.
for (int i = 0; i < Mode::NDOWNSPS; ++i)
{
freqAdjust[i] = std::polar(1.0f, phi);
if (phi = std::fmod(phi + dphi, TAU);
phi < 0.0f)
{
phi += TAU;
}
}
}
else
{
freqAdjust.fill(std::complex<float>{1.0f, 0.0f});
}
// Compute sync power by looping over the Costas indices for
// each of the 3 Costas blocks, accumulating as we go.
float sync = 0.0f;
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 7; ++j)
{
if (auto const offset = 36 * i * Mode::NDOWNSPS
+ i0 + j * Mode::NDOWNSPS; offset >= 0 &&
offset + Mode::NDOWNSPS <= Mode::NP2)
{
sync += std::norm(
std::transform_reduce(
freqAdjust.begin(), // Range start
freqAdjust.end(), // Range end
cd0.begin() + offset, // Data start
std::complex<float>{}, // Initial reduction value
std::plus<>{}, // Reduction by accumulation
[&](auto const & fa, // Conjugate and multiply
auto const & cd)
{
return cd * std::conj(fa * csyncs[i][j][&fa - &freqAdjust[0]]);
}
));
}
}
}
return sync;
}
// Generate a reference signal, based on the provided tone sequence and
// base frequency. The output is a vector of complex values representing
// the signal in the time domain.
std::vector<std::complex<float>>
genjs8refsig(std::array<int, NN> const & itone,
float const f0)
{
// Precompute the base frequency contribution; full circle in
// radians, multipled by the base frequency, multiplied by the
// sampling interval, i.e., the time step between samples, which
// results in the base frequency phase increment. Start the
// phase accumulator off at zero.
float const BFPI = TAU * f0 * (1.0f / 12000.0f);
auto phi = 0.0f;
std::vector<std::complex<float>> cref;
cref.reserve(NN * Mode::NSPS);
for (int i = 0; i < NN; ++i)
{
// Compute phase increment for the tone; frequency offset is
// determined by the tone value.
float const dphi = BFPI + TAU * static_cast<float>(itone[i]) / Mode::NSPS;
// Iterate over the samples per symbol to generate the time
// domain signal.
for (std::size_t is = 0; is < Mode::NSPS; ++is)
{
cref.push_back(std::polar(1.0f, phi));
phi = std::fmod(phi + dphi, TAU);
}
}
return cref;
}
// Subtract a JS8 signal
//
// Measured signal : dd(t) = a(t)cos(2*pi*f0*t+theta(t))
// Reference signal : cref(t) = exp( j*(2*pi*f0*t+phi(t)) )
// Complex amp : cfilt(t) = LPF[ dd(t)*CONJG(cref(t)) ]
// Subtract : dd(t) = dd(t) - 2*REAL{cref*cfilt}
//
// Important to note that dt can be negative here.
void
subtractjs8(std::vector<std::complex<float>> const & cref,
float const dt)
{
auto const nstart = static_cast<int>(dt * 12000.0f);
std::size_t const cref_start = (nstart < 0) ? static_cast<std::size_t>(-nstart) : 0;
std::size_t const dd_start = (nstart > 0) ? static_cast<std::size_t>( nstart) : 0;
auto const size = std::min(cref.size() - cref_start, dd.size() - dd_start);
// Populate complex filter with the conjugate of the reference signal.
for (std::size_t i = 0; i < size; ++i)
{
cfilt[i] = dd[dd_start + i] * std::conj(cref[cref_start + i]);
}
// Zero-fill the remainder, if any.
std::fill(cfilt.begin() + size, cfilt.end(), ZERO);
// FFT to the frequency domain.
fftwf_execute(plans[Plan::CF]);
// Apply the filter in the frequency domain.
std::transform(cfilt.begin(),
cfilt.end(),
filter.begin(),
cfilt.begin(),
std::multiplies<>());
// Inverse FFT to return to the time domain.
fftwf_execute(plans[Plan::CB]);
// Subtract the reconstructed signal.
for (std::size_t i = 0; i < size; ++i)
{
dd[dd_start + i] -= 2.0f * std::real(cfilt[i] * cref[cref_start + i]);
}
}
public:
// Constructor
explicit Decoder(JS8::Event::Emitter emitter)
: emitEvent(emitter)
{
// Intialize the Nuttal window. In theory, we can do this as a
// constexpr function at compile time, but doing so yield results
// slightly different than the Fortran version did, so for sanity
// while testing, we'll opt for consistency. IEEE 754 is always a
// bit brittle.
constexpr float a0 = 0.3635819f;
constexpr float a1 = -0.4891775f;
constexpr float a2 = 0.1365995f;
constexpr float a3 = -0.0106411f;
// Computed Pi constant to match the Fortran version; we could
// probably use M_PI here, but for the moment, matching Fortran
// exactly.
float const pi = 4.0f * std::atan(1.0f);
float sum = 0.0f;
for (std::size_t i = 0; i < nuttal.size(); ++i)
{
float value = a0;
float value_c = 0.0f; // Compensation for lost low-order bits
// Naive summation here will exhibit substantial precision loss
// relative to the Fortran version; we use Kahan summation to
// compensate, which should provide identical results to Fortran.
auto const kahan_add = [&](float const term)
{
float const y = term - value_c;
float const t = value + y;
value_c = (t - value) - y;
value = t;
};
kahan_add(a1 * std::cos(2 * pi * i / nuttal.size()));
kahan_add(a2 * std::cos(4 * pi * i / nuttal.size()));
kahan_add(a3 * std::cos(6 * pi * i / nuttal.size()));
nuttal[i] = value;
sum += value;
}
// Normalize the Nuttal window.
for (auto & value : nuttal) value = value / sum * nuttal.size() / 300.0f;
// Initialize Costas waveforms.
for (int i = 0; i < 7; ++i)
{
float const dphia = TAU * Costas[0][i] / Mode::NDOWNSPS;
float const dphib = TAU * Costas[1][i] / Mode::NDOWNSPS;
float const dphic = TAU * Costas[2][i] / Mode::NDOWNSPS;
float phia = 0.0f;
float phib = 0.0f;
float phic = 0.0f;
for (int j = 0; j < Mode::NDOWNSPS; ++j)
{
csyncs[0][i][j] = std::polar(1.0f, phia);
csyncs[1][i][j] = std::polar(1.0f, phib);
csyncs[2][i][j] = std::polar(1.0f, phic);
phia = std::fmod(phia + dphia, TAU);
phib = std::fmod(phib + dphib, TAU);
phic = std::fmod(phic + dphic, TAU);
}
}
// First-time filter creation
std::vector<float> window(NFILT + 1);
sum = 0.0f;
// Compute the Hann-like window
for (int j = -NFILT / 2; j <= NFILT / 2; ++j)
{
float const value = std::pow(std::cos(M_PI * j / NFILT), 2);
window[j + NFILT / 2] = value;
sum += value;
}
// Normalize the window.
std::transform(window.begin(),
window.end(),
window.begin(),
[sum](float val) { return val / sum; });
// Populate the first and last portions of filter with the window.
for (std::size_t i = 0; i < NFILT / 2; ++i)
{
filter[i] = std::complex<float>{window[i ], 0.0f};
filter[i + Mode::NMAX - NFILT] = std::complex<float>{window[i + NFILT / 2], 0.0f};
}
// Explicitly zero the middle portion.
std::fill(filter.begin() + NFILT / 2,
filter.begin() + Mode::NMAX - NFILT / 2,
ZERO);
// Apply FFT to the filter coefficients.
fftwf_plan fftw_plan;
{
std::lock_guard<std::mutex> lock(fftw_mutex);
fftw_plan = fftwf_plan_dft_1d(Mode::NMAX,
reinterpret_cast<fftwf_complex *>(filter.data()),
reinterpret_cast<fftwf_complex *>(filter.data()),
FFTW_FORWARD,
FFTW_ESTIMATE_PATIENT);
if (!fftw_plan)
{
throw std::runtime_error("Failed to create FFT plan");
}
}
fftwf_execute(fftw_plan);
{
std::lock_guard<std::mutex> lock(fftw_mutex);
fftwf_destroy_plan(fftw_plan);
}
std::transform(filter.begin(),
filter.end(),
filter.begin(),
[factor = 1.0f / Mode::NMAX](std::complex<float> val)
{
return val * factor;
});
// The rest of our FFT plans are always the same size and operate on the
// same data, so we can reuse them as long as we're alive.
std::lock_guard<std::mutex> lock(fftw_mutex);
plans[Plan::DS] = fftwf_plan_dft_1d(Mode::NDFFT2,
reinterpret_cast<fftwf_complex *>(cd0.data()),
reinterpret_cast<fftwf_complex *>(cd0.data()),
FFTW_BACKWARD,
FFTW_ESTIMATE_PATIENT);
plans[Plan::BB] = fftwf_plan_dft_r2c_1d(Mode::NDFFT1,
reinterpret_cast<float *>(ds_cx.data()),
reinterpret_cast<fftwf_complex *>(ds_cx.data()),
FFTW_ESTIMATE_PATIENT);
plans[Plan::CF] = fftwf_plan_dft_1d(Mode::NMAX,
reinterpret_cast<fftwf_complex *>(cfilt.data()),
reinterpret_cast<fftwf_complex *>(cfilt.data()),
FFTW_FORWARD,
FFTW_ESTIMATE_PATIENT);
plans[Plan::CB] = fftwf_plan_dft_1d(Mode::NMAX,
reinterpret_cast<fftwf_complex *>(cfilt.data()),
reinterpret_cast<fftwf_complex *>(cfilt.data()),
FFTW_BACKWARD,
FFTW_ESTIMATE_PATIENT);
plans[Plan::SD] = fftwf_plan_dft_r2c_1d(Mode::NFFT1,
reinterpret_cast<float *>(sd.data()),
reinterpret_cast<fftwf_complex *>(sd.data()),
FFTW_ESTIMATE_PATIENT);
plans[Plan::CS] = fftwf_plan_dft_1d(Mode::NDOWNSPS,
reinterpret_cast<fftwf_complex *>(csymb.data()),
reinterpret_cast<fftwf_complex *>(csymb.data()),
FFTW_FORWARD,
FFTW_ESTIMATE_PATIENT);
for (auto plan : plans)
{
if (!plan) throw std::runtime_error("Failed to create FFT plan");
}
}
// Destructor
~Decoder()
{
std::lock_guard<std::mutex> lock(fftw_mutex);
for (auto plan : plans)
{
if (plan) fftwf_destroy_plan(plan);
}
}
// Decode entry point.
//
// XXX still working on this.
int
decode(const std::vector<int16_t> & iwave,
int const nutc,
int const nfqso,
int const nfa,
int const nfb,
int const ndepth,
bool const nagain,
float const napwid,
bool const syncStats,
int const kpos,
int const ksz)
{
// Copy the relevant frames for decoding
int pos = std::max(0, kpos);
int sz = std::max(0, ksz);
assert(sz <= Mode::NMAX);
if (syncStats) emitEvent(JS8::Event::SyncStart{pos, sz});
auto const ddCopy = [](auto const begin,
auto const end,
auto const to)
{
std::transform(begin, end, to, [](auto const value)
{
return static_cast<float>(value);
});
};
dd.fill(0.0f);
if ((MAX_BUFFER_SIZE - pos) < sz)
{
// Wrap case; split into two parts.
int const firstsize = MAX_BUFFER_SIZE - pos;
int const secondsize = sz - firstsize;
ddCopy(iwave.begin() + pos, iwave.begin() + pos + firstsize, dd.begin());
ddCopy(iwave.begin(), iwave.begin() + secondsize, dd.begin() + firstsize);
}
else
{
// Non-wrapping case; copy directly.
ddCopy(iwave.begin() + pos, iwave.begin() + pos + sz, dd.begin());
}
int const ifa = nagain ? nfqso - 10 : nfa;
int const ifb = nagain ? nfqso + 10 : nfb;
int const npass = calculateNPass(ndepth);
Decode::Map decodes;
for (int ipass = 1; ipass <= npass; ++ipass)
{
auto candidates = syncjs8(ifa, ifb);
if (candidates.empty()) continue; // XXX probably incorrect
// Sort candidates by proximity to nfqso and frequency.
std::sort(candidates.begin(),
candidates.end(),
[nfqso](auto const & a,
auto const & b)
{
auto const a_dist = std::abs(a.freq - nfqso);
auto const b_dist = std::abs(b.freq - nfqso);
if (a_dist < 10.0f && b_dist >= 10.0f) return true;
if (b_dist < 10.0f && a_dist >= 10.0f) return false;
return std::tie(a_dist, a.freq) <
std::tie(b_dist, b.freq);
});
computeBasebandFFT();
bool new_decodes = false;
bool lsubtract = (ipass == 1 && ndepth != 1) || (ipass > 1 && ipass < 4);
for (auto [f1, xdt, sync] : candidates)
{
float xsnr = 0.0f;
float dmin = 0.0f;
int nharderrors = -1;
if (auto decode = js8dec(syncStats,
nfqso,
ndepth,
napwid,
lsubtract,
nagain,
f1,
xdt,
nharderrors,
dmin,
xsnr))
{
int const nsnr = std::round(xsnr);
// If this message is new, or it's a duplicate, but it's got a better
// SNR than what we had before, then it's interesting to us.
if (auto [iter, inserted] = decodes.try_emplace(std::move(*decode), nsnr);
inserted || iter->second < nsnr)
{
new_decodes = true;
// Update the SNR if this is an improved decode.
if (!inserted) iter->second = nsnr;
// Trigger callback for new or improved decodes.
emitEvent(JS8::Event::Decoded{nutc,
nsnr,
xdt - Mode::ASTART,
f1,
iter->first.data,
iter->first.type,
1.0f - (nharderrors + dmin) / 60.0f,
Mode::NSUBMODE});
}
}
}
// If no new decodes occurred during this pass, terminate early.
if (!new_decodes) break;
}
return decodes.size();
}
};
// Explicit template class instantiations; avoids compiler complaints
// about unused variables.
template class Decoder<ModeA>;
template class Decoder<ModeB>;
template class Decoder<ModeC>;
template class Decoder<ModeE>;
template class Decoder<ModeI>;
}
/******************************************************************************/
// Worker
/******************************************************************************/
namespace JS8
{
class Worker : public QObject
{
Q_OBJECT
public:
explicit Worker(QObject *parent = nullptr)
: QObject(parent)
, decoderA([this](Event::Variant const & event) { decodeEvent(event); })
, decoderB([this](Event::Variant const & event) { decodeEvent(event); })
, decoderC([this](Event::Variant const & event) { decodeEvent(event); })
, decoderE([this](Event::Variant const & event) { decodeEvent(event); })
, decoderI([this](Event::Variant const & event) { decodeEvent(event); })
{}
public slots:
void decode();
signals:
void decodeEvent(Event::Variant const &);
private:
::Decoder<ModeA> decoderA;
::Decoder<ModeB> decoderB;
::Decoder<ModeC> decoderC;
::Decoder<ModeE> decoderE;
::Decoder<ModeI> decoderI;
struct dec_data the_data; // XXX to ensure a clean picture for now
};
void
Worker::decode()
{
the_data = dec_data; // XXX remove for production
int decodes = 0;
emit decodeEvent(JS8::Event::DecodeStarted{the_data.params.nsubmode,
the_data.params.nsubmodes});
std::vector<std::int16_t> data = {std::begin(the_data.d2), std::end(the_data.d2)};
if (the_data.params.nsubmode == 8 || (the_data.params.nsubmodes & 16) == 16)
{
decodes += decoderI.decode(data,
the_data.params.nutc,
the_data.params.nfqso,
the_data.params.nfa,
the_data.params.nfb,
the_data.params.ndepth,
the_data.params.nagain,
the_data.params.napwid,
the_data.params.syncStats,
the_data.params.kposI,
the_data.params.kszI);
}
if (the_data.params.nsubmode == 4 || (the_data.params.nsubmodes & 8) == 8)
{
decodes += decoderE.decode(data,
the_data.params.nutc,
the_data.params.nfqso,
the_data.params.nfa,
the_data.params.nfb,
the_data.params.ndepth,
the_data.params.nagain,
the_data.params.napwid,
the_data.params.syncStats,
the_data.params.kposE,
the_data.params.kszE);
}
if (the_data.params.nsubmode == 2 || (the_data.params.nsubmodes & 4) == 4)
{
decodes += decoderC.decode(data,
the_data.params.nutc,
the_data.params.nfqso,
the_data.params.nfa,
the_data.params.nfb,
the_data.params.ndepth,
the_data.params.nagain,
the_data.params.napwid,
the_data.params.syncStats,
the_data.params.kposC,
the_data.params.kszC);
}
if (the_data.params.nsubmode == 1 || (the_data.params.nsubmodes & 2) == 2)
{
decodes += decoderB.decode(data,
the_data.params.nutc,
the_data.params.nfqso,
the_data.params.nfa,
the_data.params.nfb,
the_data.params.ndepth,
the_data.params.nagain,
the_data.params.napwid,
the_data.params.syncStats,
the_data.params.kposB,
the_data.params.kszB);
}
if (the_data.params.nsubmode == 0 || (the_data.params.nsubmodes & 1) == 1)
{
decodes += decoderA.decode(data,
the_data.params.nutc,
the_data.params.nfqso,
the_data.params.nfa,
the_data.params.nfb,
the_data.params.ndepth,
the_data.params.nagain,
the_data.params.napwid,
the_data.params.syncStats,
the_data.params.kposA,
the_data.params.kszA);
}
emit decodeEvent(JS8::Event::DecodeFinished{decodes});
}
}
/******************************************************************************/
// Public Interface - Decoding
/******************************************************************************/
#include "JS8.moc"
namespace JS8
{
Decoder::Decoder(QObject * parent)
: QObject(parent)
, m_worker(new Worker())
{
m_worker->moveToThread(&m_thread);
// QObject::connect(&m_thread, &QThread::finished, m_worker.data(), &QObject::deleteLater);
QObject::connect(m_worker.data(), &Worker::decodeEvent, this, &Decoder::decodeEvent);
}
Decoder::~Decoder() = default;
void
Decoder::start(QThread::Priority priority)
{
m_thread.start(priority);
}
void
Decoder::quit()
{
m_thread.quit();
}
bool
Decoder::wait()
{
return m_thread.wait();
}
void
Decoder::decode()
{
QMetaObject::invokeMethod(m_worker.data(), "decode", Qt::QueuedConnection);
}
}
/******************************************************************************/
// Public Interface - Encoding
/******************************************************************************/
namespace JS8
{
// Port of the Fortran `genjs8` subroutine; from the 12 bytes of `message`,
// construct an 87-bit JS8 message and encode it into tones. Costas array
// to use supplied by the caller, as is the type of message, indicated by
// the lower 3 bits of `type`.
void
encode(int const type,
Costas::Array const & costas,
const char * const message,
int * const tones)
{
// Our initial goal here is an 87-bit message, for which a std::bitset
// would be the obvious choice, but we've got to compute a checksum of
// the first 75 bits; thus, an array instead.
//
// Message structure:
//
// +----------+----------+----------+
// | | | 72 bits | 12 6-bit words
// | | +==========+
// | | 87 bits | 3 bits | Frame type
// | 11 bytes | +==========+
// | | | 12 bits | 12-bit BE checksum
// | |----------+==========+
// | | 1 bit | 1 bit | Leftover bit in array
// +----------+----------+==========+
std::array<std::uint8_t, 11> bytes = {};
// Convert the 12 characters we've been handed to 6-bit words and pack
// them into the byte array, 4 characters, 24 bits at a time, into the
// 9 bytes [0,8], 72 bits total. Throws if handed an invalid character.
for (int i = 0, j = 0; i < 12; i += 4, j += 3)
{
std::uint32_t words = (alphabetWord(message[i ]) << 18) |
(alphabetWord(message[i + 1]) << 12) |
(alphabetWord(message[i + 2]) << 6) |
alphabetWord(message[i + 3]);
bytes[j ] = words >> 16;
bytes[j + 1] = words >> 8;
bytes[j + 2] = words;
}
// The bottom 3 bits of type are the frame type; these go into the
// next 3 bits in the byte array, i.e., the first 3 bits of byte 9,
// after which we'll be at 75 bits in total.
bytes[9] = (type & 0b111) << 5;
// We now need to compute the augmented CRC-12 of the complete
// byte array, including the trailing zero bits that we've not
// set yet.
auto const crc = CRC12(bytes);
// That CRC needs to occupy the next 12 bits of the array, i.e.,
// the final 5 bits of byte 9, and the first 7 bits of byte 10.
bytes[9] |= (crc >> 7) & 0x1F;
bytes[10] = (crc & 0x7F) << 1;
// That's it for our 87-bit message; we're now going to turn it
// into two blocks of 29 3-bit words, which will in turn become
// tones, the first block being parity for the second, bracketed
// by the Costas arrays.
//
// Output structure:
//
// +----------+----------+
// | | 7 bytes | Costas array A
// | +==========+
// | | 29 bytes | Parity data
// | +==========+
// | 79 bytes | 7 bytes | Costas array B
// | +==========+
// | | 29 bytes | Output data
// | +==========+
// | | 7 bytes | Costas array C
// +----------+==========+
auto costasData = tones;
auto parityData = tones + 7;
auto outputData = tones + 43;
// Output the 3 Costas arrays at offsets 0, 36, and 72.
for (auto const & array : costas)
{
std::copy(array.begin(), array.end(), costasData);
costasData += 36;
}
// Our 87 bits are going to be morphed into two sets of 29 3-bit
// words, the first one parity for the second; we're going to do
// this in parallel.
std::size_t outputBits = 0;
std::size_t outputByte = 0;
std::uint8_t outputMask = 0x80;
std::uint8_t outputWord = 0;
std::uint8_t parityWord = 0;
for (std::size_t i = 0; i < 87; ++i)
{
// Compute parity for the current bit; inputs for parity computation
// are the corresponding parity matrix row and each bit in the message;
// the parity matrix row, referenced by `i`, contains 87 boolean values.
// Each `true` value defines a message bit that must be summed, modulo
// 2, to produce the parity check bit for the bit we're working on now.
//
// In short, if the parity matrix bit `(i, j)` and the message bit `j`
// are both set, then we add 1 to the parity bits accumulator. If, after
// processing all message bits the accumulated result is odd, then the
// parity bit should be set for the current bit.
std::size_t parityBits = 0;
std::size_t parityByte = 0;
std::uint8_t parityMask = 0x80;
for (std::size_t j = 0; j < 87; ++j)
{
parityBits += parity(i, j) && (bytes[parityByte] & parityMask);
parityMask = (parityMask == 1) ? (++parityByte, 0x80) : (parityMask >> 1);
}
// Accumulate the parity and output bits; this is the point at which
// we perform the modulo 2 operation on the summed parity bits.
parityWord = (parityWord << 1) | (parityBits & 1);
outputWord = (outputWord << 1) | ((bytes[outputByte] & outputMask) != 0);
outputMask = (outputMask == 1) ? (++outputByte, 0x80) : (outputMask >> 1);
// If we're at a 3-bit boundary, output the words and reset.
if (++outputBits == 3)
{
*parityData++ = parityWord;
*outputData++ = outputWord;
parityWord = 0;
outputWord = 0;
outputBits = 0;
}
}
}
}
/******************************************************************************/
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