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Copy pathReedSolomon_ErrorCorrection_Mode225223.cpp
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ReedSolomon_ErrorCorrection_Mode225223.cpp
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////////////////////////////////////////////////////////////////////////////////
// //
// Reed-Solomon (255,223) encoding/decoding //
// Derived from the software by Phil Karn //
// Copyright 2002 Phil Karn, KA9Q //
// May be used under the terms of the GNU General Public License (GPL) //
// //
////////////////////////////////////////////////////////////////////////////////
#include <string.h>
typedef unsigned char uchar;
typedef unsigned int uint;
uchar alpha[] = {
0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
0x87, 0x89, 0x95, 0xad, 0xdd, 0x3d, 0x7a, 0xf4,
0x6f, 0xde, 0x3b, 0x76, 0xec, 0x5f, 0xbe, 0xfb,
0x71, 0xe2, 0x43, 0x86, 0x8b, 0x91, 0xa5, 0xcd,
0x1d, 0x3a, 0x74, 0xe8, 0x57, 0xae, 0xdb, 0x31,
0x62, 0xc4, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0x67,
0xce, 0x1b, 0x36, 0x6c, 0xd8, 0x37, 0x6e, 0xdc,
0x3f, 0x7e, 0xfc, 0x7f, 0xfe, 0x7b, 0xf6, 0x6b,
0xd6, 0x2b, 0x56, 0xac, 0xdf, 0x39, 0x72, 0xe4,
0x4f, 0x9e, 0xbb, 0xf1, 0x65, 0xca, 0x13, 0x26,
0x4c, 0x98, 0xb7, 0xe9, 0x55, 0xaa, 0xd3, 0x21,
0x42, 0x84, 0x8f, 0x99, 0xb5, 0xed, 0x5d, 0xba,
0xf3, 0x61, 0xc2, 0x03, 0x06, 0x0c, 0x18, 0x30,
0x60, 0xc0, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0,
0x47, 0x8e, 0x9b, 0xb1, 0xe5, 0x4d, 0x9a, 0xb3,
0xe1, 0x45, 0x8a, 0x93, 0xa1, 0xc5, 0x0d, 0x1a,
0x34, 0x68, 0xd0, 0x27, 0x4e, 0x9c, 0xbf, 0xf9,
0x75, 0xea, 0x53, 0xa6, 0xcb, 0x11, 0x22, 0x44,
0x88, 0x97, 0xa9, 0xd5, 0x2d, 0x5a, 0xb4, 0xef,
0x59, 0xb2, 0xe3, 0x41, 0x82, 0x83, 0x81, 0x85,
0x8d, 0x9d, 0xbd, 0xfd, 0x7d, 0xfa, 0x73, 0xe6,
0x4b, 0x96, 0xab, 0xd1, 0x25, 0x4a, 0x94, 0xaf,
0xd9, 0x35, 0x6a, 0xd4, 0x2f, 0x5e, 0xbc, 0xff,
0x79, 0xf2, 0x63, 0xc6, 0x0b, 0x16, 0x2c, 0x58,
0xb0, 0xe7, 0x49, 0x92, 0xa3, 0xc1, 0x05, 0x0a,
0x14, 0x28, 0x50, 0xa0, 0xc7, 0x09, 0x12, 0x24,
0x48, 0x90, 0xa7, 0xc9, 0x15, 0x2a, 0x54, 0xa8,
0xd7, 0x29, 0x52, 0xa4, 0xcf, 0x19, 0x32, 0x64,
0xc8, 0x17, 0x2e, 0x5c, 0xb8, 0xf7, 0x69, 0xd2,
0x23, 0x46, 0x8c, 0x9f, 0xb9, 0xf5, 0x6d, 0xda,
0x33, 0x66, 0xcc, 0x1f, 0x3e, 0x7c, 0xf8, 0x77,
0xee, 0x5b, 0xb6, 0xeb, 0x51, 0xa2, 0xc3, 0x00
};
uchar index[] = {
255, 0, 1, 99, 2, 198, 100, 106,
3, 205, 199, 188, 101, 126, 107, 42,
4, 141, 206, 78, 200, 212, 189, 225,
102, 221, 127, 49, 108, 32, 43, 243,
5, 87, 142, 232, 207, 172, 79, 131,
201, 217, 213, 65, 190, 148, 226, 180,
103, 39, 222, 240, 128, 177, 50, 53,
109, 69, 33, 18, 44, 13, 244, 56,
6, 155, 88, 26, 143, 121, 233, 112,
208, 194, 173, 168, 80, 117, 132, 72,
202, 252, 218, 138, 214, 84, 66, 36,
191, 152, 149, 249, 227, 94, 181, 21,
104, 97, 40, 186, 223, 76, 241, 47,
129, 230, 178, 63, 51, 238, 54, 16,
110, 24, 70, 166, 34, 136, 19, 247,
45, 184, 14, 61, 245, 164, 57, 59,
7, 158, 156, 157, 89, 159, 27, 8,
144, 9, 122, 28, 234, 160, 113, 90,
209, 29, 195, 123, 174, 10, 169, 145,
81, 91, 118, 114, 133, 161, 73, 235,
203, 124, 253, 196, 219, 30, 139, 210,
215, 146, 85, 170, 67, 11, 37, 175,
192, 115, 153, 119, 150, 92, 250, 82,
228, 236, 95, 74, 182, 162, 22, 134,
105, 197, 98, 254, 41, 125, 187, 204,
224, 211, 77, 140, 242, 31, 48, 220,
130, 171, 231, 86, 179, 147, 64, 216,
52, 176, 239, 38, 55, 12, 17, 68,
111, 120, 25, 154, 71, 116, 167, 193,
35, 83, 137, 251, 20, 93, 248, 151,
46, 75, 185, 96, 15, 237, 62, 229,
246, 135, 165, 23, 58, 163, 60, 183
};
uchar poly[] = {
0, 249, 59, 66, 4, 43, 126, 251,
97, 30, 3, 213, 50, 66, 170, 5,
24, 5, 170, 66, 50, 213, 3, 30,
97, 251, 126, 43, 4, 66, 59, 249,
0
};
void Encode8(uchar *data,uchar *bb,int pad) {
int i,j;
uchar feedback;
memset(bb,0,32);
for (i=0; i<223-pad; i++) {
feedback=index[data[i]^bb[0]];
if (feedback!=255) {
for (j=1; j<32; j++) {
bb[j]^=alpha[(feedback+poly[32-j])%255];
};
};
memmove(bb,bb+1,31);
if (feedback!=255)
bb[31]=alpha[(feedback+poly[0])%255];
else
bb[31]=0;
;
};
};
int Decode8(uchar *data,int *eras_pos,int no_eras,int pad) {
int i,j,r,k,deg_lambda,el,deg_omega;
int syn_error,count;
uchar u,q,tmp,num1,num2,den,discr_r;
uchar lambda[33],s[32],b[33],t[33],omega[33];
uchar root[32],reg[33],loc[32];
for (i=0; i<32; i++)
s[i]=data[0];
for (j=1; j<255-pad; j++) {
for (i=0; i<32; i++) {
if (s[i]==0)
s[i]=data[j];
else
s[i]=data[j]^alpha[(index[s[i]]+(112+i)*11)%255];
;
};
};
syn_error=0;
for (i=0; i<32; i++) {
syn_error|=s[i];
s[i]=index[s[i]]; };
if (syn_error==0) {
count=0; goto finish; };
memset(lambda+1,0,32);
lambda[0]=1;
if (no_eras>0) {
lambda[1]=alpha[(11*(254-eras_pos[0]))%255];
for (i=1; i<no_eras; i++) {
u=(uchar)((11*(254-eras_pos[i]))%255);
for (j=i+1; j>0; j--) {
tmp=index[lambda[j-1]];
if (tmp!=255) lambda[j]^=alpha[(u+tmp)%255];
};
};
};
for (i=0; i<33; i++)
b[i]=index[lambda[i]];
r=el=no_eras;
while (++r<=32) {
discr_r=0;
for (i=0; i<r; i++) {
if ((lambda[i]!=0) && (s[r-i-1]!=255)) {
discr_r^=alpha[(index[lambda[i]]+s[r-i-1])%255];
};
};
discr_r=index[discr_r];
if (discr_r==255) {
memmove(b+1,b,32);
b[0]=255; }
else {
t[0]=lambda[0];
for (i=0; i<32; i++) {
if (b[i]!=255)
t[i+1]=lambda[i+1]^alpha[(discr_r+b[i])%255];
else
t[i+1]=lambda[i+1];
;
};
if (2*el<=r+no_eras-1) {
el=r+no_eras-el;
for (i=0; i<=32; i++)
b[i]=(uchar)(lambda[i]==0?255:(index[lambda[i]]-discr_r+255)%255);
; }
else {
memmove(b+1,b,32);
b[0]=255; };
memcpy(lambda,t,33);
};
};
deg_lambda=0;
for (i=0; i<33; i++) {
lambda[i]=index[lambda[i]];
if (lambda[i]!=255) deg_lambda=i; };
memcpy(reg+1,lambda+1,32);
count=0;
for (i=1,k=115; i<=255; i++,k=(k+116)%255) {
q=1;
for (j=deg_lambda; j>0; j--) {
if (reg[j]!=255) {
reg[j]=(uchar)((reg[j]+j)%255);
q^=alpha[reg[j]];
};
};
if (q!=0) continue;
root[count]=(uchar)i;
loc[count]=(uchar)k;
if (++count==deg_lambda) break;
};
if (deg_lambda!=count) {
count=-1;
goto finish; };
deg_omega=deg_lambda-1;
for (i=0; i<=deg_omega; i++ ) {
tmp=0;
for (j=i; j>=0; j--) {
if ((s[i-j]!=255) && (lambda[j]!=255)) {
tmp^=alpha[(s[i-j]+lambda[j])%255];
};
};
omega[i]=index[tmp];
};
for (j=count-1; j>=0; j--) {
num1=0;
for (i=deg_omega; i>=0; i--) {
if (omega[i]!=255) {
num1^=alpha[(omega[i]+i*root[j])%255];
};
};
num2=alpha[(root[j]*111+255)%255];
den=0;
for (i=(deg_lambda<31?deg_lambda:31) & ~1; i>=0; i-=2) {
if (lambda[i+1]!=255) {
den^=alpha[(lambda[i+1]+i*root[j])%255];
};
};
if (num1!=0 && loc[j]>=pad) {
data[loc[j]-pad]^=alpha[(index[num1]+index[num2]+255-index[den])%255];
};
};
finish:
if (eras_pos!=NULL) {
for (i=0; i<count; i++) eras_pos[i]=loc[i]; };
return count;
};