#include <stdio.h>
#include <conio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#define MM 8 /* RS code over GF(2**8) */
#define KK 239 /* Number of information symbols */
#define NN 255 /* Total codeword length */
#define TT 8 /* Error correction capability */
int alpha_to[NN + 1]; /* Exponent to element mapping */
int index_of[NN + 1]; /* Element to exponent mapping */
int gg[NN - KK + 1]; /* Generator polynomial */
int recd[NN]; /* Received codeword */
int err_flag; /* Error flag */
int data[KK], bb[NN - KK]; /* Data and parity symbols */
/* GF multiplication */
int gf_mult(int a, int b) {
if (a == 0 || b == 0) return 0;
return alpha_to[(index_of[a] + index_of[b]) % NN];
}
/* GF inverse */
int gf_inv(int a) {
if (a == 0) return 0;
return alpha_to[(NN - index_of[a]) % NN];
}
/* Generate GF(2^8) */
void generate_gf() {
int pp[9] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 }; /* Primitive polynomial */
register int i, mask = 1;
alpha_to[MM] = 0;
for (i = 0; i < MM; i++) {
alpha_to[i] = mask;
index_of[alpha_to[i]] = i;
if (pp[i] != 0) alpha_to[MM] ^= mask;
mask <<= 1;
}
index_of[alpha_to[MM]] = MM;
mask >>= 1;
for (i = MM + 1; i < NN; i++) {
if (alpha_to[i - 1] >= mask)
alpha_to[i] = alpha_to[MM] ^ ((alpha_to[i - 1] ^ mask) << 1);
else
alpha_to[i] = alpha_to[i - 1] << 1;
index_of[alpha_to[i]] = i;
}
index_of[0] = -1;
}
/* Generate generator polynomial */
void gen_poly() {
register int i, j;
gg[0] = 2; /* α^1 */
gg[1] = 1; /* g(x) = x + α^1 */
for (i = 2; i <= NN - KK; i++) {
gg[i] = 1;
for (j = i - 1; j > 0; j--) {
if (gg[j] != 0)
gg[j] = gg[j - 1] ^ alpha_to[(index_of[gg[j]] + i) % NN];
else
gg[j] = gg[j - 1];
}
gg[0] = alpha_to[(index_of[gg[0]] + i) % NN];
}
/* Convert to index form */
for (i = 0; i <= NN - KK; i++)
gg[i] = index_of[gg[i]];
}
/* RS encoding */
void encode_rs() {
register int i, j;
int feedback;
for (i = 0; i < NN - KK; i++) bb[i] = 0;
for (i = KK - 1; i >= 0; i--) {
feedback = index_of[data[i] ^ bb[NN - KK - 1]];
if (feedback != -1) {
for (j = NN - KK - 1; j > 0; j--) {
if (gg[j] != -1)
bb[j] = bb[j - 1] ^ alpha_to[(gg[j] + feedback) % NN];
else
bb[j] = bb[j - 1];
}
bb[0] = alpha_to[(gg[0] + feedback) % NN];
}
else {
for (j = NN - KK - 1; j > 0; j--)
bb[j] = bb[j - 1];
bb[0] = 0;
}
}
}
/* Compute polynomial degree */
int poly_degree(int poly[], int len) {
int deg = -1;
for (int i = len - 1; i >= 0; i--) {
if (poly[i] != 0) {
deg = i;
break;
}
}
return deg;
}
/* Polynomial multiplication with mod x^limit */
void poly_mult(int a[], int a_deg, int b[], int b_deg, int result[], int limit) {
for (int i = 0; i < limit; i++) result[i] = 0;
for (int i = 0; i <= a_deg; i++) {
if (a[i] != 0) {
for (int j = 0; j <= b_deg && i + j < limit; j++) {
if (b[j] != 0) {
result[i + j] ^= gf_mult(a[i], b[j]);
}
}
}
}
}
/* Copy polynomial */
void copy_poly(int src[], int dest[], int len) {
for (int i = 0; i < len; i++) {
dest[i] = src[i];
}
}
/* RS decoding with Euclidean algorithm */
void decode_rs() {
int s[NN - KK + 1]; /* Syndrome values */
int root[TT], loc[TT], err[NN];
int erasures[2 * TT]; /* Erasure positions */
int erasure_count = 0; /* Number of erasures */
int syn_error = 0; /* Syndrome error flag */
register int i, j;
/* Erasure detection */
for (i = 0; i < NN; i++) {
if (recd[i] == -1 && erasure_count < 2 * TT) {
erasures[erasure_count++] = i;
}
}
/* Syndrome calculation */
for (i = 1; i <= NN - KK; i++) {
s[i] = 0;
for (j = 0; j < NN; j++) {
if (recd[j] == -1) continue;
if (recd[j] != 0) {
int exp = (index_of[recd[j]] + i * j) % NN;
if (exp < 0) exp += NN;
s[i] ^= alpha_to[exp];
}
}
if (s[i] != 0) syn_error = 1;
s[i] = (s[i] == 0) ? -1 : index_of[s[i]];
}
if (syn_error || erasure_count > 0) {
err_flag = 1;
/* Allocate memory for polynomials */
int gamma[NN - KK + 1] = { 0 }; /* Erasure locator polynomial */
int T[NN - KK] = { 0 }; /* Modified syndrome polynomial */
int max_deg = 2 * (NN - KK) + 1; /* 33 */
int R0[65] = { 0 };
int R1[65] = { 0 };
int V0[65] = { 0 };
int V1[65] = { 0 };
int lambda[NN - KK + 1] = { 0 };/* Error locator polynomial */
int omega[NN - KK] = { 0 }; /* Error evaluator polynomial */
/* Initialize gamma = 1 (erasure locator polynomial) */
gamma[0] = 1;
if (erasure_count > 0) {
for (i = 0; i < erasure_count; i++) {
int Xi = alpha_to[erasures[i] % NN];
int tmp[NN - KK + 1] = { 0 };
tmp[0] = gamma[0];
for (j = 1; j <= NN - KK; j++) {
tmp[j] = gamma[j] ^ gf_mult(Xi, gamma[j - 1]);
}
for (j = 0; j <= NN - KK; j++) {
gamma[j] = tmp[j];
}
}
}
/* Convert syndrome to polynomial form */
int S_poly[NN - KK];
for (i = 0; i < NN - KK; i++) {
if (s[i + 1] == -1) {
S_poly[i] = 0;
}
else {
S_poly[i] = alpha_to[s[i + 1]];
}
}
/* Compute modified syndrome T(x) = S(x) * gamma(x) mod x^(2t) */
int gamma_deg = poly_degree(gamma, NN - KK + 1);
poly_mult(S_poly, NN - KK - 1, gamma, gamma_deg, T, NN - KK);
/* Initialize Euclidean algorithm */
R0[NN - KK] = 1; /* R0 = x^(2t) */
int deg_R0 = NN - KK; /* Degree of x^(2t) */
for (i = 0; i < NN - KK; i++) {
R1[i] = T[i];
}
int deg_R1 = poly_degree(R1, max_deg);
V1[0] = 1; /* V1 = 1 */
int deg_V0 = -1; /* V0 = 0 */
int deg_V1 = 0; /* Degree of V1 is 0 */
int v_max = (NN - KK - erasure_count) / 2; /* Max errors correctable */
/* Euclidean algorithm iteration */
while (deg_R1 != -1 && deg_R1 >= v_max) {
if (deg_R0 < deg_R1) {
/* Swap R0 and R1 */
int temp_deg = deg_R0;
deg_R0 = deg_R1;
deg_R1 = temp_deg;
int temp_R[65];
copy_poly(R0, temp_R, max_deg);
copy_poly(R1, R0, max_deg);
copy_poly(temp_R, R1, max_deg);
/* Swap V0 and V1 */
temp_deg = deg_V0;
deg_V0 = deg_V1;
deg_V1 = temp_deg;
int temp_V[65];
copy_poly(V0, temp_V, max_deg);
copy_poly(V1, V0, max_deg);
copy_poly(temp_V, V1, max_deg);
}
int shift = deg_R0 - deg_R1;
int factor = gf_mult(R0[deg_R0], gf_inv(R1[deg_R1]));
/* Update R0: R0 = R0 + factor * x^shift * R1 */
for (i = 0; i <= deg_R1; i++) {
if (R1[i] != 0 && i + shift < max_deg) {
R0[i + shift] ^= gf_mult(factor, R1[i]);
}
}
deg_R0 = poly_degree(R0, max_deg);
/* Update V0: V0 = V0 + factor * x^shift * V1 */
for (i = 0; i <= deg_V1; i++) {
if (V1[i] != 0 && i + shift < max_deg) {
if (i + shift < max_deg) {
V0[i + shift] ^= gf_mult(factor, V1[i]);
}
}
}
deg_V0 = poly_degree(V0, max_deg);
}
/* Error locator polynomial = V1 (lambda) */
for (i = 0; i <= deg_V1; i++) {
lambda[i] = V1[i];
}
int deg_lambda = deg_V1;
/* Error evaluator polynomial = R1 (omega) */
for (i = 0; i <= deg_R1; i++) {
omega[i] = R1[i];
}
int deg_omega = deg_R1;
/* Compute total error locator (gamma * lambda) */
int total_loc[2 * TT + 1] = { 0 };
poly_mult(gamma, gamma_deg, lambda, deg_lambda, total_loc, 2 * TT + 1);
int deg_total = poly_degree(total_loc, 2 * TT + 1);
/* Find roots of total_loc (Chien search) */
int count = 0;
for (int pos = 0; pos < NN; pos++) {
int Xi_inv = alpha_to[(NN - pos) % NN];
int sum = total_loc[0]; /* Evaluate polynomial at alpha^(-pos) */
int Xi_power = Xi_inv;
for (i = 1; i <= deg_total; i++) {
if (total_loc[i] != 0) {
sum ^= gf_mult(total_loc[i], Xi_power);
}
Xi_power = gf_mult(Xi_power, Xi_inv);
}
if (sum == 0) {
loc[count] = pos;
root[count] = Xi_inv; /* alpha^(-pos) */
count++;
if (count > deg_total) break; /* Stop if found more roots than degree */
}
}
if (count != deg_total || deg_total == -1) {
err_flag = 2; /* Too many errors or no roots found */
}
else {
/* Initialize error array */
for (i = 0; i < NN; i++) {
err[i] = 0;
if (recd[i] == -1) recd[i] = 0;
}
/* Forney algorithm for error values */
for (i = 0; i < count; i++) {
int pos = loc[i];
int Xi = root[i]; /* alpha^(-pos) */
/* Compute numerator (omega(Xi)) */
int num = 0;
int Xi_power = 1;
for (j = 0; j <= deg_omega; j++) {
if (omega[j] != 0) {
num ^= gf_mult(omega[j], Xi_power);
}
Xi_power = gf_mult(Xi_power, Xi);
}
/* Compute denominator (lambda'(Xi)) */
int denom = 0;
for (j = 1; j <= deg_total; j += 2) { /* Only odd powers */
if (total_loc[j] != 0) {
/* Derivative term: j * loc[j] * Xi^(j-1) */
int deriv = gf_mult(total_loc[j], alpha_to[(j - 1) * index_of[Xi] % NN]);
denom ^= deriv;
}
}
if (denom != 0) {
int err_val = gf_mult(num, gf_inv(denom));
recd[pos] ^= err_val;
}
else {
err_flag = 2;
break;
}
}
}
}
else {
err_flag = 0; /* No errors */
}
}
/* Print hex array */
void print_hex_array(int arr[], int start, int count) {
for (int i = 0; i < count; i++) {
printf("%02X ", arr[start + i]);
}
printf("\n");
}
int main() {
int acterr_num, err_pos[TT];
srand((unsigned)time(NULL));
generate_gf();
gen_poly();
do {
printf("\nReed-Solomon (255,239) 解码测试\n");
printf("最大纠错能力: %d 个错误\n", TT);
printf("输入注入错误数量(0-%d): ", TT);
scanf_s("%d", &acterr_num);
if (acterr_num > TT) {
printf("错误数量超过纠错能力!\n");
continue;
}
/* 生成随机数据 */
for (int i = 0; i < KK; i++)
data[i] = rand() % (NN + 1);
/* 编码 */
encode_rs();
/* 构建码字 */
for (int i = 0; i < NN - KK; i++)
recd[i] = bb[i];
for (int i = NN - KK; i < NN; i++)
recd[i] = data[i - (NN - KK)];
/* 保存原始码字 */
int recd_copy[NN];
for (int i = 0; i < NN; i++)
recd_copy[i] = recd[i];
/* 显示原始数据 */
printf("\n原始数据(前10个符号):\n");
print_hex_array(recd, NN - KK, 10);
/* 手动输入错误位置 */
if (acterr_num > 0) {
printf("输入错误位置(0-%d):\n", NN - 1);
for (int i = 0; i < acterr_num; i++) {
printf("错误 %d 位置: ", i + 1);
scanf_s("%d", &err_pos[i]);
if (err_pos[i] < 0 || err_pos[i] >= NN) {
printf("位置无效!\n");
i--;
continue;
}
}
}
/* 注入错误 */
printf("\n注入%d个错误...\n", acterr_num);
for (int i = 0; i < acterr_num; i++) {
int err_val = 1 + rand() % (NN - 1); // 非零错误值
int original = recd[err_pos[i]];
recd[err_pos[i]] ^= err_val;
printf(" 位置 %d: %02X → %02X (错误值 = %02X)\n",
err_pos[i], original, recd[err_pos[i]], err_val);
}
/* 解码 */
decode_rs();
/* 显示解码结果 */
printf("\n状态: ");
switch (err_flag) {
case 0: printf("未检测到错误"); break;
case 1: printf("错误纠正成功"); break;
case 2: printf("错误超出能力"); break;
default: printf("未知状态");
}
printf("\n\n解码后数据(前10个符号):\n");
print_hex_array(recd, NN - KK, 10);
printf("原始数据(前10个符号):\n");
print_hex_array(recd_copy, NN - KK, 10);
/* 验证结果 */
int errors = 0;
for (int i = NN - KK; i < NN; i++) {
if (recd[i] != recd_copy[i]) {
printf("位置 %d: 原始值=%02X, 解码值=%02X\n",
i, recd_copy[i], recd[i]);
errors++;
}
}
if (errors == 0) {
printf("\n验证: 所有数据符号与原始一致!\n");
}
else {
printf("\n验证: %d个数据符号与原始不同\n", errors);
}
printf("\n按ESC退出，其他键继续...");
} while (_getch() != 27);
return 0;
}
最新发布
本文深入探讨了Linux环境下rand()函数在不同形式除法操作中产生的数值特性，对比分析了Windows与Linux的RAND_MAX差异，并揭示了其背后的数学原理。
扫一扫
886
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
