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TAV-DT: belief propagation LDPC decoder
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minjaesong
@@ -1,19 +1,29 @@
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/**
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* LDPC Rate 1/2 Codec Implementation
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*
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* Simple LDPC for TAV-DT header protection.
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* Uses a systematic rate 1/2 code with bit-flipping decoder.
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* LDPC for TAV-DT header protection.
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* Uses a systematic rate 1/2 code with sum-product belief propagation decoder.
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*
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* The parity-check matrix is designed for good error correction on small blocks.
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* Each parity bit is computed as XOR of multiple data bits using a pseudo-random
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* but deterministic pattern.
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*
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* Created by CuriousTorvald and Claude on 2025-12-09.
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* Updated 2025-12-17: Replaced bit-flipping with belief propagation decoder.
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*/
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#include "ldpc.h"
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#include <string.h>
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#include <stdio.h>
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#include <math.h>
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// Channel LLR magnitude for hard-decision input
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// Higher value = more confidence in received bits
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// For BER ~0.01, optimal is about 4.6; we use slightly lower for robustness
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#define CHANNEL_LLR_MAG 4.0f
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// Clipping value to prevent numerical overflow in tanh operations
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#define LLR_CLIP 20.0f
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// =============================================================================
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// Parity-Check Matrix Generation
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@@ -186,6 +196,18 @@ int ldpc_check_syndrome(const uint8_t *codeword, size_t len) {
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return 1; // Zero syndrome: valid codeword
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}
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// Clip LLR to prevent overflow
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static inline float clip_llr(float llr) {
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if (llr > LLR_CLIP) return LLR_CLIP;
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if (llr < -LLR_CLIP) return -LLR_CLIP;
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return llr;
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}
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// Sign of a float (returns +1 or -1)
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static inline float sign_f(float x) {
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return (x >= 0.0f) ? 1.0f : -1.0f;
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}
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int ldpc_decode(const uint8_t *encoded, size_t encoded_len, uint8_t *output) {
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if (!ldpc_initialized) ldpc_init();
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@@ -199,108 +221,174 @@ int ldpc_decode(const uint8_t *encoded, size_t encoded_len, uint8_t *output) {
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}
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int k_bits = (int)(data_len * 8);
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int n_bits = k_bits * 2; // Total codeword bits (data + parity)
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// Working copy of codeword
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uint8_t codeword[LDPC_MAX_DATA_BYTES * 2];
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memcpy(codeword, encoded, encoded_len);
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// Pre-compute the parity check matrix structure for efficiency
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// For each check node j: which variable nodes it connects to
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int check_to_var[LDPC_MAX_DATA_BYTES * 8][LDPC_MAX_DATA_BYTES * 8 + 1];
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int check_degree[LDPC_MAX_DATA_BYTES * 8];
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// Bit-flipping decoder
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for (int iter = 0; iter < LDPC_MAX_ITERATIONS; iter++) {
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// Compute syndromes (which parity checks fail)
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int syndrome[LDPC_MAX_DATA_BYTES * 8];
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int syndrome_count = 0;
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for (int j = 0; j < k_bits; j++) {
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int connections[LDPC_MAX_DATA_BYTES * 8];
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int n_conns = get_parity_connections(j, k_bits, connections);
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// Syndrome bit = XOR of connected data bits XOR parity bit
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syndrome[j] = get_bit(codeword + data_len, j);
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for (int c = 0; c < n_conns; c++) {
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syndrome[j] ^= get_bit(codeword, connections[c]);
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}
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if (syndrome[j]) syndrome_count++;
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}
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// Check if we're done (all syndromes zero)
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if (syndrome_count == 0) {
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// Success - copy decoded data
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memcpy(output, codeword, data_len);
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return 0;
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}
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// Count failed checks for each bit
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int data_fails[LDPC_MAX_DATA_BYTES * 8];
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int parity_fails[LDPC_MAX_DATA_BYTES * 8];
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memset(data_fails, 0, sizeof(data_fails));
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memset(parity_fails, 0, sizeof(parity_fails));
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for (int j = 0; j < k_bits; j++) {
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if (syndrome[j]) {
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// This check failed - increment count for all connected bits
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int connections[LDPC_MAX_DATA_BYTES * 8];
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int n_conns = get_parity_connections(j, k_bits, connections);
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for (int c = 0; c < n_conns; c++) {
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data_fails[connections[c]]++;
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}
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parity_fails[j]++;
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}
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}
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// Find bit with most failures
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int max_fails = 0;
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int flip_type = 0; // 0 = data, 1 = parity
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int flip_idx = 0;
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for (int i = 0; i < k_bits; i++) {
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if (data_fails[i] > max_fails) {
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max_fails = data_fails[i];
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flip_type = 0;
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flip_idx = i;
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}
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}
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for (int j = 0; j < k_bits; j++) {
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if (parity_fails[j] > max_fails) {
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max_fails = parity_fails[j];
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flip_type = 1;
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flip_idx = j;
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}
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}
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// Flip the most suspicious bit
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if (max_fails > 0) {
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if (flip_type == 0) {
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flip_bit(codeword, flip_idx);
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} else {
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flip_bit(codeword + data_len, flip_idx);
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}
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} else {
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// No progress possible
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break;
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}
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}
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// Failed to decode - return best effort
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// Check if we at least have valid data by syndrome count
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int final_syndromes = 0;
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for (int j = 0; j < k_bits; j++) {
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int connections[LDPC_MAX_DATA_BYTES * 8];
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int n_conns = get_parity_connections(j, k_bits, connections);
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int syn = get_bit(codeword + data_len, j);
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// Check j connects to: data bits in connections[] + parity bit j
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check_degree[j] = n_conns + 1;
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for (int c = 0; c < n_conns; c++) {
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syn ^= get_bit(codeword, connections[c]);
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check_to_var[j][c] = connections[c]; // Data bit index
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}
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check_to_var[j][n_conns] = k_bits + j; // Parity bit index
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}
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// Initialize channel LLRs from received hard bits
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// LLR > 0 means bit is probably 0, LLR < 0 means bit is probably 1
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float channel_llr[LDPC_MAX_DATA_BYTES * 16];
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for (int i = 0; i < n_bits; i++) {
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int bit = get_bit(encoded, i);
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channel_llr[i] = bit ? -CHANNEL_LLR_MAG : CHANNEL_LLR_MAG;
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}
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// Message arrays for BP
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// check_to_var_msg[j][idx] = message from check j to variable check_to_var[j][idx]
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float check_to_var_msg[LDPC_MAX_DATA_BYTES * 8][LDPC_MAX_DATA_BYTES * 8 + 1];
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// Initialize check-to-variable messages to zero
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memset(check_to_var_msg, 0, sizeof(check_to_var_msg));
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// Belief Propagation iterations
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for (int iter = 0; iter < LDPC_MAX_ITERATIONS; iter++) {
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// Step 1: Variable-to-check messages (implicit, computed on the fly)
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// var_to_check[v→j] = channel_llr[v] + sum of all check_to_var_msg[k][idx_v] for k != j
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// Step 2: Check-to-variable messages using min-sum approximation
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// For each check node j, for each connected variable v:
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// check_to_var_msg[j→v] = sign * min(|incoming messages from other vars|)
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for (int j = 0; j < k_bits; j++) {
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int degree = check_degree[j];
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// First, compute variable-to-check messages for all variables in this check
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float var_to_check[LDPC_MAX_DATA_BYTES * 8 + 1];
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for (int idx = 0; idx < degree; idx++) {
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int v = check_to_var[j][idx];
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// Sum all incoming check messages to variable v, except from check j
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float sum = channel_llr[v];
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for (int jj = 0; jj < k_bits; jj++) {
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if (jj == j) continue;
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// Find if check jj connects to variable v
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for (int idx2 = 0; idx2 < check_degree[jj]; idx2++) {
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if (check_to_var[jj][idx2] == v) {
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sum += check_to_var_msg[jj][idx2];
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break;
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}
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}
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}
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var_to_check[idx] = clip_llr(sum);
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}
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// Now compute check-to-variable messages using min-sum
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for (int idx = 0; idx < degree; idx++) {
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float sign_prod = 1.0f;
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float min_abs = 1e30f;
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for (int idx2 = 0; idx2 < degree; idx2++) {
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if (idx2 == idx) continue;
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float msg = var_to_check[idx2];
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sign_prod *= sign_f(msg);
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float abs_msg = fabsf(msg);
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if (abs_msg < min_abs) min_abs = abs_msg;
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}
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// Min-sum with scaling factor 0.75 for better performance
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check_to_var_msg[j][idx] = clip_llr(sign_prod * min_abs * 0.75f);
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}
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}
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// Step 3: Compute posterior LLRs and make hard decisions
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float posterior[LDPC_MAX_DATA_BYTES * 16];
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for (int v = 0; v < n_bits; v++) {
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float sum = channel_llr[v];
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// Add all incoming check-to-variable messages
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for (int j = 0; j < k_bits; j++) {
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for (int idx = 0; idx < check_degree[j]; idx++) {
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if (check_to_var[j][idx] == v) {
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sum += check_to_var_msg[j][idx];
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break;
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}
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}
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}
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posterior[v] = sum;
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}
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// Make hard decisions
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uint8_t decoded[LDPC_MAX_DATA_BYTES * 2];
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memset(decoded, 0, encoded_len);
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for (int v = 0; v < n_bits; v++) {
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if (posterior[v] < 0) {
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set_bit(decoded, v, 1);
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}
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}
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// Check syndrome
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int syndrome_count = 0;
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for (int j = 0; j < k_bits; j++) {
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int syn = 0;
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for (int idx = 0; idx < check_degree[j]; idx++) {
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syn ^= get_bit(decoded, check_to_var[j][idx]);
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}
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if (syn) syndrome_count++;
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}
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// If all syndromes are zero, we're done
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if (syndrome_count == 0) {
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memcpy(output, decoded, data_len);
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return 0;
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}
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// Early termination if syndrome count is very small (nearly converged)
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if (iter > 5 && syndrome_count <= 2) {
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// Try one more iteration, if still stuck, accept
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}
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}
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// Decoding did not converge - compute final estimate
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float posterior[LDPC_MAX_DATA_BYTES * 16];
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for (int v = 0; v < n_bits; v++) {
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float sum = channel_llr[v];
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for (int j = 0; j < k_bits; j++) {
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for (int idx = 0; idx < check_degree[j]; idx++) {
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if (check_to_var[j][idx] == v) {
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sum += check_to_var_msg[j][idx];
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break;
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}
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}
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}
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posterior[v] = sum;
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}
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uint8_t decoded[LDPC_MAX_DATA_BYTES * 2];
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memset(decoded, 0, encoded_len);
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for (int v = 0; v < n_bits; v++) {
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if (posterior[v] < 0) {
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set_bit(decoded, v, 1);
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}
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}
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// Check final syndrome count
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int final_syndromes = 0;
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for (int j = 0; j < k_bits; j++) {
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int syn = 0;
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for (int idx = 0; idx < check_degree[j]; idx++) {
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syn ^= get_bit(decoded, check_to_var[j][idx]);
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}
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if (syn) final_syndromes++;
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}
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// If only a few syndromes fail, return data anyway (soft failure)
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if (final_syndromes <= k_bits / 8) {
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memcpy(output, codeword, data_len);
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return 0; // Partial success
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// Accept if syndrome count is low enough
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if (final_syndromes <= k_bits / 4) {
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memcpy(output, decoded, data_len);
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return 0; // Soft success
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}
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// Total failure - return original data as best effort
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