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codec2/src/mpdecode_core.c

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/*
FILE...: mpdecode_core.c
AUTHOR.: Matthew C. Valenti, Rohit Iyer Seshadri, David Rowe
CREATED: Sep 2016
C-callable core functions moved from MpDecode.c, so they can be used for
Octave and C programs.
*/
#include "mpdecode_core.h"
#include <assert.h>
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#ifndef USE_ORIGINAL_PHI0
#include "phi0.h"
#endif
#include "debug_alloc.h"
#ifdef __EMBEDDED__
#include "machdep.h"
#endif
#define QPSK_CONSTELLATION_SIZE 4
#define QPSK_BITS_PER_SYMBOL 2
/* QPSK constellation for symbol likelihood calculations */
static COMP S_matrix[] = {
{1.0f, 0.0f}, {0.0f, 1.0f}, {0.0f, -1.0f}, {-1.0f, 0.0f}};
// c_nodes will be an array of NumberParityBits of struct c_node
// Each c_node contains an array of <degree> c_sub_node elements
// This structure reduces the indexing calclations in SumProduct()
struct c_sub_node { // Order is important here to keep total size small.
uint16_t index; // Values from H_rows (except last 2 entries)
uint16_t socket; // The socket number at the v_node
float message; // modified during operation!
};
struct c_node {
int degree; // A count of elements in the following arrays
struct c_sub_node *subs;
};
// v_nodes will be an array of CodeLength of struct v_node
struct v_sub_node {
uint16_t index; // the index of a c_node it is connected to
// Filled with values from H_cols (except last 2 entries)
uint16_t socket; // socket number at the c_node
float message; // Loaded with input data
// modified during operation!
uint8_t sign; // 1 if input is negative
// modified during operation!
};
struct v_node {
int degree; // A count of ???
float initial_value;
struct v_sub_node *subs;
};
void encode(struct LDPC *ldpc, unsigned char ibits[], unsigned char pbits[]) {
unsigned int p, i, tmp, par, prev = 0;
int ind;
uint16_t *H_rows = ldpc->H_rows;
for (p = 0; p < ldpc->NumberParityBits; p++) {
par = 0;
for (i = 0; i < ldpc->max_row_weight; i++) {
ind = H_rows[p + i * ldpc->NumberParityBits];
if (ind) par = par + ibits[ind - 1];
}
tmp = par + prev;
tmp &= 1; // only retain the lsb
prev = tmp;
pbits[p] = tmp;
}
}
#ifdef USE_ORIGINAL_PHI0
/* Phi function */
static float phi0(float x) {
float z;
if (x > 10)
return (0);
else if (x < 9.08e-5)
return (10);
else if (x > 9)
return (1.6881e-4);
/* return( 1.4970e-004 ); */
else if (x > 8)
return (4.5887e-4);
/* return( 4.0694e-004 ); */
else if (x > 7)
return (1.2473e-3);
/* return( 1.1062e-003 ); */
else if (x > 6)
return (3.3906e-3);
/* return( 3.0069e-003 ); */
else if (x > 5)
return (9.2168e-3);
/* return( 8.1736e-003 ); */
else {
z = (float)exp(x);
return ((float)log((z + 1) / (z - 1)));
}
}
#endif
/* Values for linear approximation (DecoderType=5) */
#define AJIAN -0.24904163195436
#define TJIAN 2.50681740420944
/* The linear-log-MAP algorithm */
static float max_star0(float delta1, float delta2) {
register float diff;
diff = delta2 - delta1;
if (diff > TJIAN)
return (delta2);
else if (diff < -TJIAN)
return (delta1);
else if (diff > 0)
return (delta2 + AJIAN * (diff - TJIAN));
else
return (delta1 - AJIAN * (diff + TJIAN));
}
void init_c_v_nodes(struct c_node *c_nodes, int shift, int NumberParityBits,
int max_row_weight, uint16_t *H_rows, int H1,
int CodeLength, struct v_node *v_nodes, int NumberRowsHcols,
uint16_t *H_cols, int max_col_weight, int dec_type,
float *input) {
int i, j, k, count, cnt, c_index, v_index;
/* first determine the degree of each c-node */
if (shift == 0) {
for (i = 0; i < NumberParityBits; i++) {
count = 0;
for (j = 0; j < max_row_weight; j++) {
if (H_rows[i + j * NumberParityBits] > 0) {
count++;
}
}
c_nodes[i].degree = count;
if (H1) {
if (i == 0) {
c_nodes[i].degree = count + 1;
} else {
c_nodes[i].degree = count + 2;
}
}
}
} else {
cnt = 0;
for (i = 0; i < (NumberParityBits / shift); i++) {
for (k = 0; k < shift; k++) {
count = 0;
for (j = 0; j < max_row_weight; j++) {
if (H_rows[cnt + j * NumberParityBits] > 0) {
count++;
}
}
c_nodes[cnt].degree = count;
if ((i == 0) || (i == (NumberParityBits / shift) - 1)) {
c_nodes[cnt].degree = count + 1;
} else {
c_nodes[cnt].degree = count + 2;
}
cnt++;
}
}
}
if (H1) {
if (shift == 0) {
for (i = 0; i < NumberParityBits; i++) {
// Allocate sub nodes
c_nodes[i].subs = CALLOC(c_nodes[i].degree, sizeof(struct c_sub_node));
assert(c_nodes[i].subs);
// Populate sub nodes
for (j = 0; j < c_nodes[i].degree - 2; j++) {
c_nodes[i].subs[j].index = (H_rows[i + j * NumberParityBits] - 1);
}
j = c_nodes[i].degree - 2;
if (i == 0) {
c_nodes[i].subs[j].index = (H_rows[i + j * NumberParityBits] - 1);
} else {
c_nodes[i].subs[j].index = (CodeLength - NumberParityBits) + i - 1;
}
j = c_nodes[i].degree - 1;
c_nodes[i].subs[j].index = (CodeLength - NumberParityBits) + i;
}
}
if (shift > 0) {
cnt = 0;
for (i = 0; i < (NumberParityBits / shift); i++) {
for (k = 0; k < shift; k++) {
// Allocate sub nodes
c_nodes[cnt].subs =
CALLOC(c_nodes[cnt].degree, sizeof(struct c_sub_node));
assert(c_nodes[cnt].subs);
// Populate sub nodes
for (j = 0; j < c_nodes[cnt].degree - 2; j++) {
c_nodes[cnt].subs[j].index =
(H_rows[cnt + j * NumberParityBits] - 1);
}
j = c_nodes[cnt].degree - 2;
if ((i == 0) || (i == (NumberParityBits / shift - 1))) {
c_nodes[cnt].subs[j].index =
(H_rows[cnt + j * NumberParityBits] - 1);
} else {
c_nodes[cnt].subs[j].index =
(CodeLength - NumberParityBits) + k + shift * (i);
}
j = c_nodes[cnt].degree - 1;
c_nodes[cnt].subs[j].index =
(CodeLength - NumberParityBits) + k + shift * (i + 1);
if (i == (NumberParityBits / shift - 1)) {
c_nodes[cnt].subs[j].index =
(CodeLength - NumberParityBits) + k + shift * (i);
}
cnt++;
}
}
}
} else {
for (i = 0; i < NumberParityBits; i++) {
// Allocate sub nodes
c_nodes[i].subs = CALLOC(c_nodes[i].degree, sizeof(struct c_sub_node));
assert(c_nodes[i].subs);
// Populate sub nodes
for (j = 0; j < c_nodes[i].degree; j++) {
c_nodes[i].subs[j].index = (H_rows[i + j * NumberParityBits] - 1);
}
}
}
/* determine degree of each v-node */
for (i = 0; i < (CodeLength - NumberParityBits + shift); i++) {
count = 0;
for (j = 0; j < max_col_weight; j++) {
if (H_cols[i + j * NumberRowsHcols] > 0) {
count++;
}
}
v_nodes[i].degree = count;
}
for (i = CodeLength - NumberParityBits + shift; i < CodeLength; i++) {
count = 0;
if (H1) {
if (i != CodeLength - 1) {
v_nodes[i].degree = 2;
} else {
v_nodes[i].degree = 1;
}
} else {
for (j = 0; j < max_col_weight; j++) {
if (H_cols[i + j * NumberRowsHcols] > 0) {
count++;
}
}
v_nodes[i].degree = count;
}
}
if (shift > 0) {
v_nodes[CodeLength - 1].degree = v_nodes[CodeLength - 1].degree + 1;
}
/* set up v_nodes */
for (i = 0; i < CodeLength; i++) {
// Allocate sub nodes
v_nodes[i].subs = CALLOC(v_nodes[i].degree, sizeof(struct v_sub_node));
assert(v_nodes[i].subs);
// Populate sub nodes
/* index tells which c-nodes this v-node is connected to */
v_nodes[i].initial_value = input[i];
count = 0;
for (j = 0; j < v_nodes[i].degree; j++) {
if ((H1) && (i >= CodeLength - NumberParityBits + shift)) {
v_nodes[i].subs[j].index =
i - (CodeLength - NumberParityBits + shift) + count;
if (shift == 0) {
count = count + 1;
} else {
count = count + shift;
}
} else {
v_nodes[i].subs[j].index = (H_cols[i + j * NumberRowsHcols] - 1);
}
/* search the connected c-node for the proper message value */
for (c_index = 0; c_index < c_nodes[v_nodes[i].subs[j].index].degree;
c_index++)
if (c_nodes[v_nodes[i].subs[j].index].subs[c_index].index == i) {
v_nodes[i].subs[j].socket = c_index;
break;
}
/* initialize v-node with received LLR */
if (dec_type == 1)
v_nodes[i].subs[j].message = fabs(input[i]);
else
v_nodes[i].subs[j].message = phi0(fabs(input[i]));
if (input[i] < 0) v_nodes[i].subs[j].sign = 1;
}
}
/* now finish setting up the c_nodes */
for (i = 0; i < NumberParityBits; i++) {
/* index tells which v-nodes this c-node is connected to */
for (j = 0; j < c_nodes[i].degree; j++) {
/* search the connected v-node for the proper message value */
for (v_index = 0; v_index < v_nodes[c_nodes[i].subs[j].index].degree;
v_index++)
if (v_nodes[c_nodes[i].subs[j].index].subs[v_index].index == i) {
c_nodes[i].subs[j].socket = v_index;
break;
}
}
}
}
///////////////////////////////////////
/* function for doing the MP decoding */
// Returns the iteration count
int SumProduct(int *parityCheckCount, char DecodedBits[],
struct c_node c_nodes[], struct v_node v_nodes[], int CodeLength,
int NumberParityBits, int max_iter, float r_scale_factor,
float q_scale_factor, int data[]) {
int result;
int bitErrors;
int i, j, iter;
float phi_sum;
int sign;
float temp_sum;
float Qi;
int ssum;
result = max_iter;
for (iter = 0; iter < max_iter; iter++) {
for (i = 0; i < CodeLength; i++) DecodedBits[i] = 0; // Clear each pass!
bitErrors = 0;
/* update r */
ssum = 0;
for (j = 0; j < NumberParityBits; j++) {
sign = v_nodes[c_nodes[j].subs[0].index]
.subs[c_nodes[j].subs[0].socket]
.sign;
phi_sum = v_nodes[c_nodes[j].subs[0].index]
.subs[c_nodes[j].subs[0].socket]
.message;
for (i = 1; i < c_nodes[j].degree; i++) {
// Compiler should optomize this but write the best we can to start
// from.
struct c_sub_node *cp = &c_nodes[j].subs[i];
struct v_sub_node *vp = &v_nodes[cp->index].subs[cp->socket];
phi_sum += vp->message;
sign ^= vp->sign;
}
if (sign == 0) ssum++;
for (i = 0; i < c_nodes[j].degree; i++) {
struct c_sub_node *cp = &c_nodes[j].subs[i];
struct v_sub_node *vp = &v_nodes[cp->index].subs[cp->socket];
if (sign ^ vp->sign) {
cp->message = -phi0(phi_sum - vp->message); // *r_scale_factor;
} else
cp->message = phi0(phi_sum - vp->message); // *r_scale_factor;
}
}
/* update q */
for (i = 0; i < CodeLength; i++) {
/* first compute the LLR */
Qi = v_nodes[i].initial_value;
for (j = 0; j < v_nodes[i].degree; j++) {
struct v_sub_node *vp = &v_nodes[i].subs[j];
Qi += c_nodes[vp->index].subs[vp->socket].message;
}
/* make hard decision */
if (Qi < 0) {
DecodedBits[i] = 1;
}
/* now subtract to get the extrinsic information */
for (j = 0; j < v_nodes[i].degree; j++) {
struct v_sub_node *vp = &v_nodes[i].subs[j];
temp_sum = Qi - c_nodes[vp->index].subs[vp->socket].message;
vp->message = phi0(fabs(temp_sum)); // *q_scale_factor;
if (temp_sum > 0)
vp->sign = 0;
else
vp->sign = 1;
}
}
/* count data bit errors, assuming that it is systematic */
for (i = 0; i < CodeLength - NumberParityBits; i++)
if (DecodedBits[i] != data[i]) bitErrors++;
/* Halt if zero errors */
if (bitErrors == 0) {
result = iter + 1;
break;
}
// count the number of PC satisfied and exit if all OK
*parityCheckCount = ssum;
if (ssum == NumberParityBits) {
result = iter + 1;
break;
}
}
return (result);
}
/* Convenience function to call LDPC decoder from C programs */
int run_ldpc_decoder(struct LDPC *ldpc, uint8_t out_char[], float input[],
int *parityCheckCount) {
int max_iter, dec_type;
float q_scale_factor, r_scale_factor;
int max_row_weight, max_col_weight;
int CodeLength, NumberParityBits, NumberRowsHcols, shift, H1;
int i;
struct c_node *c_nodes;
struct v_node *v_nodes;
/* default values */
max_iter = ldpc->max_iter;
dec_type = ldpc->dec_type;
q_scale_factor = ldpc->q_scale_factor;
r_scale_factor = ldpc->r_scale_factor;
CodeLength = ldpc->CodeLength; /* length of entire codeword */
NumberParityBits = ldpc->NumberParityBits;
NumberRowsHcols = ldpc->NumberRowsHcols;
char *DecodedBits = CALLOC(CodeLength, sizeof(char));
assert(DecodedBits);
/* derive some parameters */
shift = (NumberParityBits + NumberRowsHcols) - CodeLength;
if (NumberRowsHcols == CodeLength) {
H1 = 0;
shift = 0;
} else {
H1 = 1;
}
max_row_weight = ldpc->max_row_weight;
max_col_weight = ldpc->max_col_weight;
/* initialize c-node and v-node structures */
c_nodes = CALLOC(NumberParityBits, sizeof(struct c_node));
assert(c_nodes);
v_nodes = CALLOC(CodeLength, sizeof(struct v_node));
assert(v_nodes);
init_c_v_nodes(c_nodes, shift, NumberParityBits, max_row_weight, ldpc->H_rows,
H1, CodeLength, v_nodes, NumberRowsHcols, ldpc->H_cols,
max_col_weight, dec_type, input);
int DataLength = CodeLength - NumberParityBits;
int *data_int = CALLOC(DataLength, sizeof(int));
/* need to clear these on each call */
for (i = 0; i < CodeLength; i++) DecodedBits[i] = 0;
/* Call function to do the actual decoding */
int iter = SumProduct(parityCheckCount, DecodedBits, c_nodes, v_nodes,
CodeLength, NumberParityBits, max_iter, r_scale_factor,
q_scale_factor, data_int);
for (i = 0; i < CodeLength; i++) out_char[i] = DecodedBits[i];
/* Clean up memory */
FREE(DecodedBits);
FREE(data_int);
for (i = 0; i < NumberParityBits; i++) FREE(c_nodes[i].subs);
FREE(c_nodes);
for (i = 0; i < CodeLength; i++) FREE(v_nodes[i].subs);
FREE(v_nodes);
return iter;
}
void sd_to_llr(float llr[], float sd[], int n) {
double sum, mean, sign, sumsq, estvar, estEsN0, x;
int i;
/* convert SD samples to LLRs -------------------------------*/
sum = 0.0;
for (i = 0; i < n; i++) sum += fabs(sd[i]);
mean = sum / n;
/* find variance from +/-1 symbol position */
sum = sumsq = 0.0;
for (i = 0; i < n; i++) {
sign = (sd[i] > 0.0L) - (sd[i] < 0.0L);
x = ((double)sd[i] / mean - sign);
sum += x;
sumsq += x * x;
}
estvar = (n * sumsq - sum * sum) / (n * (n - 1));
// fprintf(stderr, "mean: %f var: %f\n", mean, estvar);
estEsN0 = 1.0 / (2.0L * estvar + 1E-3);
for (i = 0; i < n; i++) llr[i] = 4.0L * estEsN0 * sd[i];
}
/*
Determine symbol likelihood from received QPSK symbols.
Notes:
1) We assume fading[] is real, it is also possible to compute
with complex fading, see CML library Demod2D.c source code.
2) Using floats instead of doubles, for stm32.
Testing shows good BERs with floats.
*/
void Demod2D(float symbol_likelihood[], /* output, M*number_symbols */
COMP r[], /* received QPSK symbols, number_symbols */
COMP S_matrix[], /* constellation of size M */
float EsNo,
float fading[], /* real fading values, number_symbols */
float mean_amp, int number_symbols) {
int M = QPSK_CONSTELLATION_SIZE;
int i, j;
float tempsr, tempsi, Er, Ei;
/* determine output */
for (i = 0; i < number_symbols; i++) { /* go through each received symbol */
for (j = 0; j < M; j++) { /* each postulated symbol */
tempsr = fading[i] * S_matrix[j].real / mean_amp;
tempsi = fading[i] * S_matrix[j].imag / mean_amp;
Er = r[i].real / mean_amp - tempsr;
Ei = r[i].imag / mean_amp - tempsi;
symbol_likelihood[i * M + j] = -EsNo * (Er * Er + Ei * Ei);
// printf("symbol_likelihood[%d][%d] = %f\n",
// i,j,symbol_likelihood[i*M+j]);
}
// exit(0);
}
}
void Somap(float bit_likelihood[], /* number_bits, bps*number_symbols */
float symbol_likelihood[], /* M*number_symbols */
int M, /* constellation size */
int bps, /* bits per symbol */
int number_symbols) {
int n, i, j, k, mask;
float num[bps], den[bps];
float metric;
for (n = 0; n < number_symbols; n++) { /* loop over symbols */
for (k = 0; k < bps; k++) {
/* initialize */
num[k] = -1000000;
den[k] = -1000000;
}
for (i = 0; i < M; i++) {
metric =
symbol_likelihood[n * M + i]; /* channel metric for this symbol */
mask = 1 << (bps - 1);
for (j = 0; j < bps; j++) {
mask = mask >> 1;
}
mask = 1 << (bps - 1);
for (k = 0; k < bps; k++) { /* loop over bits */
if (mask & i) {
/* this bit is a one */
num[k] = max_star0(num[k], metric);
} else {
/* this bit is a zero */
den[k] = max_star0(den[k], metric);
}
mask = mask >> 1;
}
}
for (k = 0; k < bps; k++) {
bit_likelihood[bps * n + k] = num[k] - den[k];
}
}
}
void symbols_to_llrs(float llr[], COMP rx_qpsk_symbols[], float rx_amps[],
float EsNo, float mean_amp, int nsyms) {
int i;
float symbol_likelihood[nsyms * QPSK_CONSTELLATION_SIZE];
float bit_likelihood[nsyms * QPSK_BITS_PER_SYMBOL];
Demod2D(symbol_likelihood, rx_qpsk_symbols, S_matrix, EsNo, rx_amps, mean_amp,
nsyms);
Somap(bit_likelihood, symbol_likelihood, QPSK_CONSTELLATION_SIZE,
QPSK_BITS_PER_SYMBOL, nsyms);
for (i = 0; i < nsyms * QPSK_BITS_PER_SYMBOL; i++) {
llr[i] = -bit_likelihood[i];
}
}
/*
Description: Transforms M-dimensional FSK symbols into ML symbol
log-likelihoods
The calling syntax is:
[output] = FskDemod( input, EsNo, [csi_flag], [fade_coef] )
Where:
output = M by N matrix of symbol log-likelihoods
input = M by N matrix of (complex) matched filter outputs
EsNo = the symbol SNR (in linear, not dB, units)
csi_flag = 0 for coherent reception (default)
1 for noncoherent reception w/ perfect amplitude estimates
2 for noncoherent reception without amplitude estimates
fade_coef = 1 by N matrix of (complex) fading coefficients (defaults
to all-ones, i.e. AWGN)
Copyright (C) 2006, Matthew C. Valenti
Last updated on May 6, 2006
Function DemodFSK is part of the Iterative Solutions
Coded Modulation Library. The Iterative Solutions Coded Modulation
Library is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 2.1 of the License,
or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
/* the logI_0 function */
static float logbesseli0(float x) {
if (x < 1)
return (0.226 * x * x + 0.0125 * x - 0.0012);
else if (x < 2)
return (0.1245 * x * x + 0.2177 * x - 0.108);
else if (x < 5)
return (0.0288 * x * x + 0.6314 * x - 0.5645);
else if (x < 20)
return (0.002 * x * x + 0.9048 * x - 1.2997);
else
return (0.9867 * x - 2.2053);
}
/* Function that does the demodulation (can be used in stand-alone C) */
static void FskDemod(float out[], float yr[], float v_est, float SNR, int M,
int number_symbols) {
int i, j;
float y_envelope, scale_factor;
scale_factor = 2 * SNR;
for (i = 0; i < number_symbols; i++) {
for (j = 0; j < M; j++) {
y_envelope = sqrt(yr[j * number_symbols + i] *
yr[j * number_symbols + i] / (v_est * v_est));
out[i * M + j] = logbesseli0(scale_factor * y_envelope);
}
}
}
void fsk_rx_filt_to_llrs(float llr[], float rx_filt[], float v_est,
float SNRest, int M, int nsyms) {
int i;
int bps = log2(M);
float symbol_likelihood[M * nsyms];
float bit_likelihood[bps * nsyms];
FskDemod(symbol_likelihood, rx_filt, v_est, SNRest, M, nsyms);
Somap(bit_likelihood, symbol_likelihood, M, bps, nsyms);
for (i = 0; i < bps * nsyms; i++) {
llr[i] = -bit_likelihood[i];
}
}
void ldpc_print_info(struct LDPC *ldpc) {
fprintf(stderr, "ldpc->max_iter = %d\n", ldpc->max_iter);
fprintf(stderr, "ldpc->dec_type = %d\n", ldpc->dec_type);
fprintf(stderr, "ldpc->q_scale_factor = %d\n", ldpc->q_scale_factor);
fprintf(stderr, "ldpc->r_scale_factor = %d\n", ldpc->r_scale_factor);
fprintf(stderr, "ldpc->CodeLength = %d\n", ldpc->CodeLength);
fprintf(stderr, "ldpc->NumberParityBits = %d\n", ldpc->NumberParityBits);
fprintf(stderr, "ldpc->NumberRowsHcols = %d\n", ldpc->NumberRowsHcols);
fprintf(stderr, "ldpc->max_row_weight = %d\n", ldpc->max_row_weight);
fprintf(stderr, "ldpc->max_col_weight = %d\n", ldpc->max_col_weight);
fprintf(stderr, "ldpc->data_bits_per_frame = %d\n",
ldpc->data_bits_per_frame);
fprintf(stderr, "ldpc->coded_bits_per_frame = %d\n",
ldpc->coded_bits_per_frame);
}
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