LDPC码译码功能的C语言实现
LDPC译码算法概述
LDPC码主要有两种译码算法：
- 和积算法(Sum-Product) - 最优性能，较高复杂度
- 最小和算法(Min-Sum) - 次优性能，较低复杂度
提供这两种算法的完整实现
实现
1. 数据结构定义
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>
// LDPC码结构体
typedef struct {
int n; // 码字长度
int m; // 校验方程数
int k; // 信息位长度 (n - m)
int **H; // 校验矩阵 (m x n)
int *col_weight; // 列重
int *row_weight; // 行重
int max_col_weight; // 最大列重
int max_row_weight; // 最大行重
int **col_pos; // 每列中1的位置
int **row_pos; // 每行中1的位置
} LDPC_Code;
// 译码器参数
typedef struct {
int max_iter; // 最大迭代次数
double sigma; // 噪声标准差
int decision_method;// 判决方法
int algorithm; // 译码算法
} Decoder_Params;
// 算法类型定义
#define SUM_PRODUCT 0
#define MIN_SUM 1
// 判决方法
#define HARD_DECISION 0
#define SOFT_DECISION 1
2. LDPC码初始化
// 创建LDPC码结构
LDPC_Code* create_ldpc_code(int n, int m) {
LDPC_Code *code = (LDPC_Code*)malloc(sizeof(LDPC_Code));
code->n = n;
code->m = m;
code->k = n - m;
// 分配校验矩阵内存
code->H = (int**)malloc(m * sizeof(int*));
for (int i = 0; i < m; i++) {
code->H[i] = (int*)malloc(n * sizeof(int));
}
code->col_weight = (int*)calloc(n, sizeof(int));
code->row_weight = (int*)calloc(m, sizeof(int));
return code;
}
// 释放LDPC码结构
void free_ldpc_code(LDPC_Code *code) {
if (code == NULL) return;
for (int i = 0; i < code->m; i++) {
free(code->H[i]);
}
free(code->H);
free(code->col_weight);
free(code->row_weight);
if (code->col_pos != NULL) {
for (int i = 0; i < code->n; i++) {
free(code->col_pos[i]);
}
free(code->col_pos);
}
if (code->row_pos != NULL) {
for (int i = 0; i < code->m; i++) {
free(code->row_pos[i]);
}
free(code->row_pos);
}
free(code);
}
// 计算行列权重和位置信息
void compute_code_properties(LDPC_Code *code) {
int i, j;
// 计算行重和列重
for (i = 0; i < code->m; i++) {
code->row_weight[i] = 0;
for (j = 0; j < code->n; j++) {
if (code->H[i][j] == 1) {
code->row_weight[i]++;
code->col_weight[j]++;
}
}
}
// 计算最大行重和列重
code->max_row_weight = 0;
code->max_col_weight = 0;
for (i = 0; i < code->m; i++) {
if (code->row_weight[i] > code->max_row_weight) {
code->max_row_weight = code->row_weight[i];
}
}
for (j = 0; j < code->n; j++) {
if (code->col_weight[j] > code->max_col_weight) {
code->max_col_weight = code->col_weight[j];
}
}
// 分配并计算位置信息
code->col_pos = (int**)malloc(code->n * sizeof(int*));
code->row_pos = (int**)malloc(code->m * sizeof(int*));
for (j = 0; j < code->n; j++) {
code->col_pos[j] = (int*)malloc(code->col_weight[j] * sizeof(int));
int pos = 0;
for (i = 0; i < code->m; i++) {
if (code->H[i][j] == 1) {
code->col_pos[j][pos++] = i;
}
}
}
for (i = 0; i < code->m; i++) {
code->row_pos[i] = (int*)malloc(code->row_weight[i] * sizeof(int));
int pos = 0;
for (j = 0; j < code->n; j++) {
if (code->H[i][j] == 1) {
code->row_pos[i][pos++] = j;
}
}
}
}
3. 和积算法(Sum-Product)实现
// 双曲正切函数
double tanh(double x) {
if (x > 20.0) return 1.0;
if (x < -20.0) return -1.0;
double ex = exp(x);
double e_x = exp(-x);
return (ex - e_x) / (ex + e_x);
}
// 反双曲正切函数
double atanh(double x) {
if (x >= 1.0) return 20.0;
if (x <= -1.0) return -20.0;
return 0.5 * log((1.0 + x) / (1.0 - x));
}
// 和积算法译码
int sum_product_decode(LDPC_Code *code, double *received_llr, int *decoded_bits,
Decoder_Params *params) {
int i, j, k, iter;
int converged = 0;
// 分配内存用于消息传递
double **R = (double**)malloc(code->m * sizeof(double*)); // 校验节点到变量节点
double **Q = (double**)malloc(code->m * sizeof(double*)); // 变量节点到校验节点
for (i = 0; i < code->m; i++) {
R[i] = (double*)malloc(code->n * sizeof(double));
Q[i] = (double*)malloc(code->n * sizeof(double));
for (j = 0; j < code->n; j++) {
R[i][j] = 0.0;
Q[i][j] = 0.0;
}
}
// 初始化Q矩阵 (变量节点到校验节点)
for (j = 0; j < code->n; j++) {
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
Q[i][j] = received_llr[j];
}
}
// 迭代译码
for (iter = 0; iter < params->max_iter && !converged; iter++) {
// 步骤1: 更新校验节点到变量节点消息 R[i][j]
for (i = 0; i < code->m; i++) {
for (k = 0; k < code->row_weight[i]; k++) {
j = code->row_pos[i][k];
double product = 1.0;
for (int l = 0; l < code->row_weight[i]; l++) {
int j_prime = code->row_pos[i][l];
if (j_prime != j) {
product *= tanh(Q[i][j_prime] / 2.0);
}
}
R[i][j] = 2.0 * atanh(product);
}
}
// 步骤2: 更新变量节点到校验节点消息 Q[i][j]
for (j = 0; j < code->n; j++) {
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
Q[i][j] = received_llr[j];
for (int l = 0; l < code->col_weight[j]; l++) {
int i_prime = code->col_pos[j][l];
if (i_prime != i) {
Q[i][j] += R[i_prime][j];
}
}
}
}
// 步骤3: 计算后验概率并进行硬判决
double *posterior_llr = (double*)malloc(code->n * sizeof(double));
for (j = 0; j < code->n; j++) {
posterior_llr[j] = received_llr[j];
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
posterior_llr[j] += R[i][j];
}
// 硬判决
decoded_bits[j] = (posterior_llr[j] < 0) ? 1 : 0;
}
// 步骤4: 校验是否满足所有校验方程
converged = 1;
for (i = 0; i < code->m && converged; i++) {
int syndrome = 0;
for (k = 0; k < code->row_weight[i]; k++) {
j = code->row_pos[i][k];
syndrome ^= decoded_bits[j];
}
if (syndrome != 0) {
converged = 0;
}
}
free(posterior_llr);
if (converged) {
printf("迭代 %d: 译码成功!\n", iter + 1);
break;
}
}
// 释放内存
for (i = 0; i < code->m; i++) {
free(R[i]);
free(Q[i]);
}
free(R);
free(Q);
return converged;
}
4. 最小和算法(Min-Sum)实现
// 最小和算法译码 - 复杂度更低，性能稍差
int min_sum_decode(LDPC_Code *code, double *received_llr, int *decoded_bits,
Decoder_Params *params) {
int i, j, k, iter;
int converged = 0;
// 分配内存用于消息传递
double **R = (double**)malloc(code->m * sizeof(double*)); // 校验节点到变量节点
double **Q = (double**)malloc(code->m * sizeof(double*)); // 变量节点到校验节点
for (i = 0; i < code->m; i++) {
R[i] = (double*)malloc(code->n * sizeof(double));
Q[i] = (double*)malloc(code->n * sizeof(double));
for (j = 0; j < code->n; j++) {
R[i][j] = 0.0;
Q[i][j] = 0.0;
}
}
// 初始化Q矩阵
for (j = 0; j < code->n; j++) {
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
Q[i][j] = received_llr[j];
}
}
// 迭代译码
for (iter = 0; iter < params->max_iter && !converged; iter++) {
// 步骤1: 更新校验节点到变量节点消息 R[i][j] (最小和更新)
for (i = 0; i < code->m; i++) {
for (k = 0; k < code->row_weight[i]; k++) {
j = code->row_pos[i][k];
double min1 = 1e20, min2 = 1e20;
int sign_product = 1;
for (int l = 0; l < code->row_weight[i]; l++) {
int j_prime = code->row_pos[i][l];
if (j_prime != j) {
double abs_q = fabs(Q[i][j_prime]);
int sign_q = (Q[i][j_prime] >= 0) ? 1 : -1;
sign_product *= sign_q;
if (abs_q < min1) {
min2 = min1;
min1 = abs_q;
} else if (abs_q < min2) {
min2 = abs_q;
}
}
}
// 使用最小值和次小值
R[i][j] = sign_product * min1;
}
}
// 步骤2: 更新变量节点到校验节点消息 Q[i][j]
for (j = 0; j < code->n; j++) {
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
Q[i][j] = received_llr[j];
for (int l = 0; l < code->col_weight[j]; l++) {
int i_prime = code->col_pos[j][l];
if (i_prime != i) {
Q[i][j] += R[i_prime][j];
}
}
}
}
// 步骤3: 计算后验概率并进行硬判决
double *posterior_llr = (double*)malloc(code->n * sizeof(double));
for (j = 0; j < code->n; j++) {
posterior_llr[j] = received_llr[j];
for (k = 0; k < code->col_weight[j]; k++) {
i = code->col_pos[j][k];
posterior_llr[j] += R[i][j];
}
decoded_bits[j] = (posterior_llr[j] < 0) ? 1 : 0;
}
// 步骤4: 校验是否满足所有校验方程
converged = 1;
for (i = 0; i < code->m && converged; i++) {
int syndrome = 0;
for (k = 0; k < code->row_weight[i]; k++) {
j = code->row_pos[i][k];
syndrome ^= decoded_bits[j];
}
if (syndrome != 0) {
converged = 0;
}
}
free(posterior_llr);
if (converged) {
printf("迭代 %d: 译码成功!\n", iter + 1);
break;
}
}
// 释放内存
for (i = 0; i < code->m; i++) {
free(R[i]);
free(Q[i]);
}
free(R);
free(Q);
return converged;
}
5. 通用译码接口
// 通用LDPC译码函数
int ldpc_decode(LDPC_Code *code, double *received_llr, int *decoded_bits,
Decoder_Params *params) {
if (params->algorithm == SUM_PRODUCT) {
return sum_product_decode(code, received_llr, decoded_bits, params);
} else if (params->algorithm == MIN_SUM) {
return min_sum_decode(code, received_llr, decoded_bits, params);
} else {
printf("未知的译码算法!\n");
return 0;
}
}
// 计算LLR值 (BPSK调制，AWGN信道)
void compute_llr(double *received_signal, double *llr, int length, double noise_var) {
for (int i = 0; i < length; i++) {
// BPSK: 0 -> +1, 1 -> -1
// LLR = 2 * y / sigma^2
llr[i] = 2.0 * received_signal[i] / noise_var;
}
}
// 生成随机码字
void generate_codeword(LDPC_Code *code, int *codeword) {
// 简单实现: 生成全零码字 (实际应使用编码器)
for (int i = 0; i < code->n; i++) {
codeword[i] = 0;
}
}
// BPSK调制
void bpsk_modulate(int *bits, double *modulated, int length) {
for (int i = 0; i < length; i++) {
modulated[i] = (bits[i] == 0) ? 1.0 : -1.0;
}
}
// 添加高斯白噪声
void add_awgn_noise(double *signal, double *noisy_signal, int length, double sigma) {
for (int i = 0; i < length; i++) {
double u1 = (double)rand() / RAND_MAX;
double u2 = (double)rand() / RAND_MAX;
// Box-Muller变换生成高斯随机数
double z0 = sqrt(-2.0 * log(u1)) * cos(2.0 * M_PI * u2);
noisy_signal[i] = signal[i] + sigma * z0;
}
}
6. 测试和示例
// 创建示例LDPC码 (简单的规则LDPC码)
LDPC_Code* create_example_ldpc_code() {
int n = 12; // 码字长度
int m = 6; // 校验方程数
LDPC_Code *code = create_ldpc_code(n, m);
// 示例校验矩阵 (6x12)
int example_H[6][12] = {
{1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
{0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0},
{0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0},
{0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1}
};
// 复制校验矩阵
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
code->H[i][j] = example_H[i][j];
}
}
compute_code_properties(code);
return code;
}
// 主测试函数
int main() {
srand(time(NULL));
// 创建LDPC码
LDPC_Code *code = create_example_ldpc_code();
// 设置译码参数
Decoder_Params params;
params.max_iter = 50;
params.sigma = 0.5; // 噪声标准差
params.algorithm = MIN_SUM; // 使用最小和算法
// 生成测试数据
int *transmit_bits = (int*)malloc(code->n * sizeof(int));
int *decoded_bits = (int*)malloc(code->n * sizeof(int));
double *modulated = (double*)malloc(code->n * sizeof(double));
double *received = (double*)malloc(code->n * sizeof(double));
double *llr = (double*)malloc(code->n * sizeof(double));
// 生成全零码字
generate_codeword(code, transmit_bits);
// BPSK调制
bpsk_modulate(transmit_bits, modulated, code->n);
// 添加噪声
add_awgn_noise(modulated, received, code->n, params.sigma);
// 计算LLR
compute_llr(received, llr, code->n, params.sigma * params.sigma);
printf("开始LDPC译码...\n");
printf("码字长度: %d, 信息位: %d, 校验位: %d\n", code->n, code->k, code->m);
printf("最大迭代次数: %d, 噪声标准差: %.3f\n", params.max_iter, params.sigma);
// 执行译码
clock_t start = clock();
int success = ldpc_decode(code, llr, decoded_bits, ¶ms);
clock_t end = clock();
double decode_time = ((double)(end - start)) / CLOCKS_PER_SEC;
// 输出结果
printf("\n译码结果:\n");
printf("译码状态: %s\n", success ? "成功" : "失败");
printf("译码时间: %.6f 秒\n", decode_time);
// 计算误码率
int error_count = 0;
for (int i = 0; i < code->n; i++) {
if (transmit_bits[i] != decoded_bits[i]) {
error_count++;
}
}
double ber = (double)error_count / code->n;
printf("误比特数: %d/%d, 误码率: %.6f\n", error_count, code->n, ber);
// 释放内存
free(transmit_bits);
free(decoded_bits);
free(modulated);
free(received);
free(llr);
free_ldpc_code(code);
return 0;
}
参考代码 C语言实现LDPC码的译码功能 www.3dddown.com/cna/71075.html
性能优化
1. 内存优化
// 使用稀疏矩阵存储 - 大幅减少内存使用
typedef struct {
int n, m;
int *row_ptr; // CSR格式的行指针
int *col_idx; // 列索引
int *row_weight;
int *col_weight;
} Sparse_LDPC_Code;
2. 定点数实现
// 使用定点数提高速度 (适用于硬件实现)
typedef int16_t fixed_point;
#define FLOAT_TO_FIXED(x) ((fixed_point)((x) * 256))
#define FIXED_TO_FLOAT(x) ((double)(x) / 256.0)
3. 并行化优化
// OpenMP并行化 (对于大规模LDPC码)
#pragma omp parallel for
for (int i = 0; i < code->m; i++) {
// 校验节点更新
}
编译指令
gcc -o ldpc_decoder ldpc_decoder.c -lm -O3
# 如果需要OpenMP支持
gcc -o ldpc_decoder ldpc_decoder.c -lm -O3 -fopenmp
算法选择指南
| 算法 | 复杂度 | 性能 | 适用场景 |
|---|---|---|---|
| 和积算法 | 高 | 最优 | 高性能应用，软件实现 |
| 最小和算法 | 中 | 良好 | 硬件实现，实时系统 |
| 归一化最小和 | 中 | 接近和积 | 平衡性能与复杂度 |
浙公网安备 33010602011771号