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#include <stdint.h>
#include <unistd.h>
#include <stdbool.h>
#include <math.h>
#include <stdio.h>
void gausselimination(size_t n, size_t k, int8_t *A, int8_t *b);
void inner_logbp(
size_t m, size_t n,
size_t bits_count, size_t nodes_count, const uint32_t bits_values[], const uint32_t nodes_values[],
int8_t Lc[],
float Lq[], float Lr[],
unsigned int n_iter,
float L_posteriori_out[]);
//decode(384, 6, 8, ...)
int decode(size_t n, size_t nodes_count, size_t bits_count, uint32_t bits[], int8_t y[], int8_t out[], unsigned int maxiter) {
const size_t m = n * nodes_count / bits_count;
float Lq[m*n];
float Lr[m*n];
float L_posteriori[n];
/* Calculate column bit positions from row bit positions */
int32_t bits_transposed[nodes_count * n];
for (size_t i=0; i<nodes_count * n; i++)
bits_transposed[i] = -1;
for (size_t i=0; i<m; i++) {
for (size_t j=0; j<bits_count; j++) {
int32_t *base = bits_transposed + bits[i*bits_count + j] * nodes_count;
for (; *base != -1; base++)
;
*base = i;
}
}
/*
printf("Row positions: [");
for (size_t i=0; i<m*bits_count; i++) {
if (i)
printf(", ");
if (i%32 == 0)
printf("\n ");
printf("%4d", bits[i]);
}
printf("\n]\n");
printf("Column positions: [");
for (size_t i=0; i<n*nodes_count; i++) {
if (i)
printf(", ");
if (i%32 == 0)
printf("\n ");
printf("%4d", bits_transposed[i]);
}
printf("\n]\n");
*/
/* Run iterative optimization algorithm */
for (unsigned int n_iter=0; n_iter<maxiter; n_iter++) {
inner_logbp(m, n, bits_count, nodes_count, bits, (uint32_t*)bits_transposed, y, Lq, Lr, n_iter, L_posteriori);
/*
float *arrs[3] = {Lq, Lr, L_posteriori};
const char *names[3] = {"Lq", "Lr", "L_posteriori"};
size_t lens[3] = {m*n, m*n, n};
const size_t head_tail = 10;
for (int j=0; j<3; j++) {
printf("%s=[", names[j]);
bool ellipsis = false;
const int w = 16;
for (size_t i=0; i<lens[j]; i++) {
if (lens[j] > 1000 && i/w > head_tail && i/w < m*n/w-head_tail) {
if (!ellipsis) {
ellipsis = true;
printf("\n ...");
}
continue;
}
if (i)
printf(", ");
if (i%w == 0)
printf("\n ");
float outf = arrs[j][i];
char *s = outf < 0 ? "\033[91m" : (outf > 0 ? "\033[92m" : "\033[94m");
printf("%s% 012.6g\033[38;5;240m", s, outf);
}
printf("\n]\n");
}
*/
for (size_t i=0; i<n; i++)
out[i] = L_posteriori[i] <= 0.0f;
for (size_t i=0; i<m; i++) {
bool sum = 0;
for (size_t j=0; j<bits_count; j++)
sum ^= out[bits[i*bits_count + j]];
if (sum)
continue;
}
fflush(stdout);
return n_iter;
}
fflush(stdout);
return -1;
}
/* Perform inner ext LogBP solver */
void inner_logbp(
size_t m, size_t n,
size_t bits_count, size_t nodes_count, uint32_t const bits_values[], const uint32_t nodes_values[],
int8_t Lc[],
float Lq[], float Lr[],
unsigned int n_iter,
float L_posteriori_out[]) {
/*
printf("Input data: [");
for (size_t i=0; i<n; i++) {
if (i)
printf(", ");
if (i%32 == 0)
printf("\n ");
printf("%4d", Lc[i]);
}
printf("\n]\n");
*/
/* step 1 : Horizontal */
unsigned int bits_counter = 0;
for (size_t i=0; i<m; i++) {
//printf("=== i=%zu\n", i);
for (size_t p=bits_counter; p<bits_counter+bits_count; p++) {
size_t j = bits_values[p];
//printf("\033[38;5;240mj=%04zd ", j);
float x = 1;
if (n_iter == 0) {
for (size_t q=bits_counter; q<bits_counter+bits_count; q++) {
if (bits_values[q] != j) {
//int lcv = Lc[bits_values[q]];
//char *s = lcv < 0 ? "\033[91m" : (lcv > 0 ? "\033[92m" : "\033[94m");
//printf("nij=%04u Lc=%s%3d\033[38;5;240m ", bits_values[q], s, lcv);
x *= tanhf(0.5f * Lc[bits_values[q]]);
}
}
} else {
for (size_t q=bits_counter; q<bits_counter+bits_count; q++) {
if (bits_values[q] != j)
x *= tanhf(0.5f * Lq[i*n + bits_values[q]]);
}
}
//printf("\n==== i=%03zd p=%01zd x=%08f\n", i, p-bits_counter, x);
float num = 1 + x;
float denom = 1 - x;
if (num == 0)
Lr[i*n + j] = -1.0f;
else if (denom == 0)
Lr[i*n + j] = 1.0f;
else
Lr[i*n + j] = logf(num/denom);
}
bits_counter += bits_count;
}
/* step 2 : Vertical */
unsigned int nodes_counter = 0;
for (size_t j=0; j<n; j++) {
for (size_t p=bits_counter; p<nodes_counter+nodes_count; p++) {
size_t i = nodes_values[p];
Lq[i*n + j] = Lc[j];
for (size_t q=bits_counter; q<nodes_counter+nodes_count; q++) {
if (nodes_values[q] != i)
Lq[i*n + j] += Lr[nodes_values[q]*n + j];
}
}
nodes_counter += nodes_count;
}
/* LLR a posteriori */
nodes_counter = 0;
for (size_t j=0; j<n; j++) {
float sum = 0;
for (size_t k=bits_counter; k<nodes_counter+nodes_count; k++)
sum += Lr[nodes_values[k]*n + j];
nodes_counter += nodes_count;
L_posteriori_out[j] = Lc[j] + sum;
}
}
/* Compute the original (k) bit message from a (n) bit codeword x.
*
* tG: (n, k)-matrix
* x: (n)-vector
* out: (k)-vector
*/
void get_message(size_t n, size_t k, int8_t *tG, int8_t *x, int8_t *out) {
gausselimination(n, k, tG, x);
out[k - 1] = x[k - 1];
for (ssize_t i=k-2; i>=0; i--) {
out[i] = x[i];
uint8_t sum = 0;
for (size_t j=i+1; j<k; j++)
sum ^= tG[i*k + j] * out[j];
out[i] = !!(out[i] - sum);
}
}
/* Solve linear system in Z/2Z via Gauss Gauss elimination.
*
* A: (n, k)-matrix
* b: (n)-vector
*/
void gausselimination(size_t n, size_t k, int8_t *A, int8_t *b) {
ssize_t d = k<n ? k : n;
for (ssize_t j=0; j<d; j++) {
ssize_t pivot = -1;
for (size_t i=j; i<n; i++) {
if (A[i*k + j]) {
pivot = i;
break;
}
}
if (pivot == -1)
continue;
if (pivot != j) {
for (size_t i=0; i<k; i++) {
int8_t tmp = A[j*k + i];
A[j*k + i] = A[pivot*k + i];
A[pivot*k + i] = tmp;
}
int8_t tmp = b[j];
b[j] = b[pivot];
b[pivot] = tmp;
}
for (size_t i=j+1; i<n; i++) {
if (A[i*k + j]) {
for (size_t p=0; p<k; p++)
A[i*k + p] = !!(A[i*k + p] - A[j*k + p]);
b[i] = !!(b[i] - b[j]);
}
}
}
}
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