kopia lustrzana https://github.com/rs1729/RS
ECC: Reed-Solomon RS(223,32)-CCSDS
Zilog80
rodzic
761777e1d7
commit
e8b5e774be
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@ -10,8 +10,14 @@
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Vaisala RS92, RS41:
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RS(255, 231), t=12
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f=X^8+X^4+X^3+X^2+1, b=0
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g(X) = (X-alpha^0)...(X-alpha^(2t-1))
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LMS6:
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RS(255, 223), t=16 (CCSDS)
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f=X^8+X^7+X^2+X+1, b=112
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g(X) = (X-(alpha^11)^112)...(X-(alpha^11)^(112+2t-1))
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Meisei:
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bin.BCH(63, 51), t=2
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g(X) = (X^6+X+1)(X^6+X^4+X^2+X+1)
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@ -66,6 +72,10 @@ static GF_t GF256RS = { 0x11D, // RS-GF(2^8): X^8 + X^4 + X^3 + X^2 + 1 : 0x11D
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256, // 2^8
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0x02 }; // generator: alpha = X
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static GF_t GF256RSccsds = { 0x187, // RS-GF(2^8): X^8 + X^7 + X^2 + X + 1 : 0x187
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256, // 2^8
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0x02 }; // generator: alpha = X
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static GF_t GF64BCH = { 0x43, // BCH-GF(2^6): X^6 + X + 1 : 0x43
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64, // 2^6
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0x02 }; // generator: alpha = X
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@ -85,12 +95,14 @@ typedef struct {
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ui8_t R; // RS: R=2t, BCH: R<=mt
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ui8_t K; // K=N-R
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ui8_t b;
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ui8_t p; ui8_t ip; // p*ip = 1 mod N
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ui8_t g[MAX_DEG+1]; // ohne g[] eventuell als init_return
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} RS_t;
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static RS_t RS256 = { 255, 12, 24, 231, 0, {0}};
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static RS_t BCH64 = { 63, 2, 12, 51, 1, {0}};
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static RS_t RS256 = { 255, 12, 24, 231, 0, 1, 1, {0}};
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static RS_t RS256ccsds = { 255, 16, 32, 223, 112, 11, 116, {0}};
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static RS_t BCH64 = { 63, 2, 12, 51, 1, 1, 1, {0}};
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static GF_t GF;
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@ -627,7 +639,7 @@ int era_sigma(int n, ui8_t era_pos[], ui8_t *sigma) {
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sig[0] = 1;
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Xa[0] = 1;
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for (i = 0; i < n; i++) { // n <= 2*RS.t
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a_i = exp_a[era_pos[i] % (GF.ord-1)];
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a_i = exp_a[(RS.p*era_pos[i]) % (GF.ord-1)];
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Xa[1] = a_i; // Xalp[0..1]: (1-alpha^(j_)X)
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poly_mul(sig, Xa, sig);
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}
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@ -642,9 +654,9 @@ int syndromes(ui8_t cw[], ui8_t *S) {
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int i, errors = 0;
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ui8_t a_i;
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// syndromes: e_j=S(alpha^(b+i))
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// syndromes: e_j=S((alpha^p)^(b+i)) (wie in g(X))
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for (i = 0; i < 2*RS.t; i++) {
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a_i = exp_a[(RS.b+i) % (GF.ord-1)]; // alpha^(b+i)
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a_i = exp_a[(RS.p*(RS.b+i)) % (GF.ord-1)]; // (alpha^p)^(b+i)
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S[i] = poly_eval(cw, a_i);
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if (S[i]) errors = 1;
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}
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@ -718,7 +730,7 @@ int rs_init_RS255() {
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GF = GF256RS;
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check_gen = GF_genTab( GF, exp_a, log_a);
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RS = RS256; // N=255, t=12, b=0
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RS = RS256; // N=255, t=12, b=0, p=1
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for (i = 0; i <= MAX_DEG; i++) RS.g[i] = 0;
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for (i = 0; i <= MAX_DEG; i++) Xalp[i] = 0;
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@ -733,6 +745,55 @@ int rs_init_RS255() {
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return check_gen;
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}
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int rs_init_RS255ccsds() {
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int i, check_gen;
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ui8_t Xalp[MAX_DEG+1];
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GF = GF256RSccsds;
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check_gen = GF_genTab( GF, exp_a, log_a);
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RS = RS256ccsds; // N=255, t=16, b=112, p=11
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for (i = 0; i <= MAX_DEG; i++) RS.g[i] = 0;
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for (i = 0; i <= MAX_DEG; i++) Xalp[i] = 0;
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// beta=alpha^p primitive root of g(X)
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// beta^ip=alpha // N=255, p=11 -> ip=116
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for (i = 1; i < GF.ord-1; i++) {
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if ( (RS.p * i) % (GF.ord-1) == 1 ) {
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RS.ip = i;
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break;
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}
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}
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// g(X)=(X-(alpha^p)^b)...(X-(alpha^p)^(b+2t-1)), b=112
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RS.g[0] = 0x01;
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Xalp[1] = 0x01; // X
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for (i = 0; i < 2*RS.t; i++) {
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Xalp[0] = exp_a[(RS.p*(RS.b+i)) % (GF.ord-1)]; // Xalp[0..1]: X - (alpha^p)^(b+i)
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poly_mul(RS.g, Xalp, RS.g);
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}
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/*
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RS.g[ 0] = RS.g[32] = exp_a[0];
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RS.g[ 1] = RS.g[31] = exp_a[249];
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RS.g[ 2] = RS.g[30] = exp_a[59];
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RS.g[ 3] = RS.g[29] = exp_a[66];
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RS.g[ 4] = RS.g[28] = exp_a[4];
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RS.g[ 5] = RS.g[27] = exp_a[43];
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RS.g[ 6] = RS.g[26] = exp_a[126];
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RS.g[ 7] = RS.g[25] = exp_a[251];
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RS.g[ 8] = RS.g[24] = exp_a[97];
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RS.g[ 9] = RS.g[23] = exp_a[30];
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RS.g[10] = RS.g[22] = exp_a[3];
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RS.g[11] = RS.g[21] = exp_a[213];
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RS.g[12] = RS.g[20] = exp_a[50];
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RS.g[13] = RS.g[19] = exp_a[66];
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RS.g[14] = RS.g[18] = exp_a[170];
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RS.g[15] = RS.g[17] = exp_a[5];
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RS.g[16] = exp_a[24];
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*/
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return check_gen;
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}
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int rs_init_BCH64() {
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int i, check_gen;
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@ -761,7 +822,7 @@ int rs_encode(ui8_t cw[]) {
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return 0;
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}
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// 2*Errors + Erasure <= 2*RS.t
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// 2*Errors + Erasure <= 2*t
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int rs_decode_ErrEra(ui8_t cw[], int nera, ui8_t era_pos[],
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ui8_t *err_pos, ui8_t *err_val) {
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ui8_t x, gamma;
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@ -793,7 +854,7 @@ int rs_decode_ErrEra(ui8_t cw[], int nera, ui8_t era_pos[],
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if (nera > 0) {
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era_sigma(nera, era_pos, sigma);
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poly_mul(sigma, S, S);
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for (i = 2*RS.t; i <= MAX_DEG; i++) S[i] = 0; // S = sig*S mod x^12
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for (i = 2*RS.t; i <= MAX_DEG; i++) S[i] = 0; // S = sig*S mod x^2t
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}
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if (errera)
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@ -823,7 +884,8 @@ int rs_decode_ErrEra(ui8_t cw[], int nera, ui8_t era_pos[],
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x = (ui8_t)i; // roll-over
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if (poly_eval(sigLam, x) == 0) { // Lambda(x)=0 fuer x in erasures[] moeglich
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// error location index
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err_pos[nerr] = log_a[GF_inv(x)];
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ui8_t x1 = GF_inv(x);
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err_pos[nerr] = (log_a[x1]*RS.ip) % (GF.ord-1);
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// error value; bin-BCH: err_val=1
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err_val[nerr] = forney(x, Omega, sigLam);
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//err_val[nerr] == 0, wenn era_val[pos]=0, d.h. cw[pos] schon korrekt
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@ -832,7 +894,7 @@ int rs_decode_ErrEra(ui8_t cw[], int nera, ui8_t era_pos[],
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if (nerr >= deg_sigLam) break;
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}
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// 2*Errors + Erasure <= 2*RS.t
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// 2*Errors + Erasure <= 2*t
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if (nerr < deg_sigLam) errera = -1; // uncorrectable errors
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else {
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errera = nerr;
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@ -843,7 +905,7 @@ int rs_decode_ErrEra(ui8_t cw[], int nera, ui8_t era_pos[],
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return errera;
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}
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// Errors <= RS.t
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// Errors <= t
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int rs_decode(ui8_t cw[], ui8_t *err_pos, ui8_t *err_val) {
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ui8_t tmp[1] = {0};
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return rs_decode_ErrEra(cw, 0, tmp, err_pos, err_val);
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