diff options
Diffstat (limited to 'lib/fec')
| -rw-r--r-- | lib/fec/LICENSE | 502 | ||||
| -rw-r--r-- | lib/fec/README.md | 12 | ||||
| -rw-r--r-- | lib/fec/char.h | 24 | ||||
| -rw-r--r-- | lib/fec/decode_rs.h | 298 | ||||
| -rw-r--r-- | lib/fec/decode_rs_char.c | 22 | ||||
| -rw-r--r-- | lib/fec/encode_rs.h | 58 | ||||
| -rw-r--r-- | lib/fec/encode_rs_char.c | 15 | ||||
| -rw-r--r-- | lib/fec/fec.h | 30 | ||||
| -rw-r--r-- | lib/fec/init_rs.h | 104 | ||||
| -rw-r--r-- | lib/fec/init_rs_char.c | 35 | ||||
| -rw-r--r-- | lib/fec/rs-common.h | 26 |
11 files changed, 1126 insertions, 0 deletions
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Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the + library `Frob' (a library for tweaking knobs) written by James Random Hacker. + + {signature of Ty Coon}, 1 April 1990 + Ty Coon, President of Vice + +That's all there is to it! diff --git a/lib/fec/README.md b/lib/fec/README.md new file mode 100644 index 0000000..a44d28d --- /dev/null +++ b/lib/fec/README.md @@ -0,0 +1,12 @@ +FEC routines from KA9Q's libfec +=============================== + +This folder contains part of the libfec library by KA9Q. Only the +char-sized Reed-Solomon encoder and decoder is here. + +The files have been copied from the libfec fork at +https://github.com/Opendigitalradio/ka9q-fec + +Original code is at http://www.ka9q.net/code/fec/ + +All files in this folder are licenced under the LGPL v2.1, please see LICENCE diff --git a/lib/fec/char.h b/lib/fec/char.h new file mode 100644 index 0000000..25efd65 --- /dev/null +++ b/lib/fec/char.h @@ -0,0 +1,24 @@ +/* Stuff specific to the 8-bit symbol version of the general purpose RS codecs + * + * Copyright 2003, Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ +typedef unsigned char data_t; + +#define MODNN(x) modnn(rs,x) + +#define MM (rs->mm) +#define NN (rs->nn) +#define ALPHA_TO (rs->alpha_to) +#define INDEX_OF (rs->index_of) +#define GENPOLY (rs->genpoly) +#define NROOTS (rs->nroots) +#define FCR (rs->fcr) +#define PRIM (rs->prim) +#define IPRIM (rs->iprim) +#define PAD (rs->pad) +#define A0 (NN) + + + + diff --git a/lib/fec/decode_rs.h b/lib/fec/decode_rs.h new file mode 100644 index 0000000..647b885 --- /dev/null +++ b/lib/fec/decode_rs.h @@ -0,0 +1,298 @@ +/* The guts of the Reed-Solomon decoder, meant to be #included + * into a function body with the following typedefs, macros and variables supplied + * according to the code parameters: + + * data_t - a typedef for the data symbol + * data_t data[] - array of NN data and parity symbols to be corrected in place + * retval - an integer lvalue into which the decoder's return code is written + * NROOTS - the number of roots in the RS code generator polynomial, + * which is the same as the number of parity symbols in a block. + Integer variable or literal. + * NN - the total number of symbols in a RS block. Integer variable or literal. + * PAD - the number of pad symbols in a block. Integer variable or literal. + * ALPHA_TO - The address of an array of NN elements to convert Galois field + * elements in index (log) form to polynomial form. Read only. + * INDEX_OF - The address of an array of NN elements to convert Galois field + * elements in polynomial form to index (log) form. Read only. + * MODNN - a function to reduce its argument modulo NN. May be inline or a macro. + * FCR - An integer literal or variable specifying the first consecutive root of the + * Reed-Solomon generator polynomial. Integer variable or literal. + * PRIM - The primitive root of the generator poly. Integer variable or literal. + * DEBUG - If set to 1 or more, do various internal consistency checking. Leave this + * undefined for production code + + * The memset(), memmove(), and memcpy() functions are used. The appropriate header + * file declaring these functions (usually <string.h>) must be included by the calling + * program. + */ + + +#if !defined(NROOTS) +#error "NROOTS not defined" +#endif + +#if !defined(NN) +#error "NN not defined" +#endif + +#if !defined(PAD) +#error "PAD not defined" +#endif + +#if !defined(ALPHA_TO) +#error "ALPHA_TO not defined" +#endif + +#if !defined(INDEX_OF) +#error "INDEX_OF not defined" +#endif + +#if !defined(MODNN) +#error "MODNN not defined" +#endif + +#if !defined(FCR) +#error "FCR not defined" +#endif + +#if !defined(PRIM) +#error "PRIM not defined" +#endif + +#if !defined(NULL) +#define NULL ((void *)0) +#endif + +#undef MIN +#define MIN(a,b) ((a) < (b) ? (a) : (b)) +#undef A0 +#define A0 (NN) + +{ + int deg_lambda, el, deg_omega; + int i, j, r,k; + data_t u,q,tmp,num1,num2,den,discr_r; + data_t lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly + * and syndrome poly */ + data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1]; + data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS]; + int syn_error, count; + + /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */ + for(i=0;i<NROOTS;i++) + s[i] = data[0]; + + for(j=1;j<NN-PAD;j++){ + for(i=0;i<NROOTS;i++){ + if(s[i] == 0){ + s[i] = data[j]; + } else { + s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)]; + } + } + } + + /* Convert syndromes to index form, checking for nonzero condition */ + syn_error = 0; + for(i=0;i<NROOTS;i++){ + syn_error |= s[i]; + s[i] = INDEX_OF[s[i]]; + } + + if (!syn_error) { + /* if syndrome is zero, data[] is a codeword and there are no + * errors to correct. So return data[] unmodified + */ + count = 0; + goto finish; + } + memset(&lambda[1],0,NROOTS*sizeof(lambda[0])); + lambda[0] = 1; + + if (no_eras > 0) { + /* Init lambda to be the erasure locator polynomial */ + lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))]; + for (i = 1; i < no_eras; i++) { + u = MODNN(PRIM*(NN-1-eras_pos[i])); + for (j = i+1; j > 0; j--) { + tmp = INDEX_OF[lambda[j - 1]]; + if(tmp != A0) + lambda[j] ^= ALPHA_TO[MODNN(u + tmp)]; + } + } + +#if DEBUG >= 1 + /* Test code that verifies the erasure locator polynomial just constructed + Needed only for decoder debugging. */ + + /* find roots of the erasure location polynomial */ + for(i=1;i<=no_eras;i++) + reg[i] = INDEX_OF[lambda[i]]; + + count = 0; + for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) { + q = 1; + for (j = 1; j <= no_eras; j++) + if (reg[j] != A0) { + reg[j] = MODNN(reg[j] + j); + q ^= ALPHA_TO[reg[j]]; + } + if (q != 0) + continue; + /* store root and error location number indices */ + root[count] = i; + loc[count] = k; + count++; + } + if (count != no_eras) { + fprintf(stderr, "count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras); + count = -1; + goto finish; + } +#if DEBUG >= 2 + fprintf(stderr, "\n Erasure positions as determined by roots of Eras Loc Poly:\n"); + for (i = 0; i < count; i++) + fprintf(stderr, "%d ", loc[i]); + fprintf(stderr, "\n"); +#endif +#endif + } + for(i=0;i<NROOTS+1;i++) + b[i] = INDEX_OF[lambda[i]]; + + /* + * Begin Berlekamp-Massey algorithm to determine error+erasure + * locator polynomial + */ + r = no_eras; + el = no_eras; + while (++r <= NROOTS) { /* r is the step number */ + /* Compute discrepancy at the r-th step in poly-form */ + discr_r = 0; + for (i = 0; i < r; i++){ + if ((lambda[i] != 0) && (s[r-i-1] != A0)) { + discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])]; + } + } + discr_r = INDEX_OF[discr_r]; /* Index form */ + if (discr_r == A0) { + /* 2 lines below: B(x) <-- x*B(x) */ + memmove(&b[1],b,NROOTS*sizeof(b[0])); + b[0] = A0; + } else { + /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */ + t[0] = lambda[0]; + for (i = 0 ; i < NROOTS; i++) { + if(b[i] != A0) + t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(discr_r + b[i])]; + else + t[i+1] = lambda[i+1]; + } + if (2 * el <= r + no_eras - 1) { + el = r + no_eras - el; + /* + * 2 lines below: B(x) <-- inv(discr_r) * + * lambda(x) + */ + for (i = 0; i <= NROOTS; i++) + b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN); + } else { + /* 2 lines below: B(x) <-- x*B(x) */ + memmove(&b[1],b,NROOTS*sizeof(b[0])); + b[0] = A0; + } + memcpy(lambda,t,(NROOTS+1)*sizeof(t[0])); + } + } + + /* Convert lambda to index form and compute deg(lambda(x)) */ + deg_lambda = 0; + for(i=0;i<NROOTS+1;i++){ + lambda[i] = INDEX_OF[lambda[i]]; + if(lambda[i] != A0) + deg_lambda = i; + } + /* Find roots of the error+erasure locator polynomial by Chien search */ + memcpy(®[1],&lambda[1],NROOTS*sizeof(reg[0])); + count = 0; /* Number of roots of lambda(x) */ + for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) { + q = 1; /* lambda[0] is always 0 */ + for (j = deg_lambda; j > 0; j--){ + if (reg[j] != A0) { + reg[j] = MODNN(reg[j] + j); + q ^= ALPHA_TO[reg[j]]; + } + } + if (q != 0) + continue; /* Not a root */ + /* store root (index-form) and error location number */ +#if DEBUG>=2 + fprintf(stderr, "count %d root %d loc %d\n",count,i,k); +#endif + root[count] = i; + loc[count] = k; + /* If we've already found max possible roots, + * abort the search to save time + */ + if(++count == deg_lambda) + break; + } + if (deg_lambda != count) { + /* + * deg(lambda) unequal to number of roots => uncorrectable + * error detected + */ + count = -1; + goto finish; + } + /* + * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo + * x**NROOTS). in index form. Also find deg(omega). + */ + deg_omega = deg_lambda-1; + for (i = 0; i <= deg_omega;i++){ + tmp = 0; + for(j=i;j >= 0; j--){ + if ((s[i - j] != A0) && (lambda[j] != A0)) + tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])]; + } + omega[i] = INDEX_OF[tmp]; + } + + /* + * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = + * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form + */ + for (j = count-1; j >=0; j--) { + num1 = 0; + for (i = deg_omega; i >= 0; i--) { + if (omega[i] != A0) + num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])]; + } + num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)]; + den = 0; + + /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */ + for (i = MIN(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) { + if(lambda[i+1] != A0) + den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])]; + } +#if DEBUG >= 1 + if (den == 0) { + fprintf(stderr, "\n ERROR: denominator = 0\n"); + count = -1; + goto finish; + } +#endif + /* Apply error to data */ + if (num1 != 0 && loc[j] >= PAD) { + data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])]; + } + } + finish: + if(eras_pos != NULL){ + for(i=0;i<count;i++) + eras_pos[i] = loc[i]; + } + retval = count; +} diff --git a/lib/fec/decode_rs_char.c b/lib/fec/decode_rs_char.c new file mode 100644 index 0000000..7105233 --- /dev/null +++ b/lib/fec/decode_rs_char.c @@ -0,0 +1,22 @@ +/* General purpose Reed-Solomon decoder for 8-bit symbols or less + * Copyright 2003 Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ + +#ifdef DEBUG +#include <stdio.h> +#endif + +#include <string.h> + +#include "char.h" +#include "rs-common.h" + +int decode_rs_char(void *p, data_t *data, int *eras_pos, int no_eras){ + int retval; + struct rs *rs = (struct rs *)p; + +#include "decode_rs.h" + + return retval; +} diff --git a/lib/fec/encode_rs.h b/lib/fec/encode_rs.h new file mode 100644 index 0000000..2c157f9 --- /dev/null +++ b/lib/fec/encode_rs.h @@ -0,0 +1,58 @@ +/* The guts of the Reed-Solomon encoder, meant to be #included + * into a function body with the following typedefs, macros and variables supplied + * according to the code parameters: + + * data_t - a typedef for the data symbol + * data_t data[] - array of NN-NROOTS-PAD and type data_t to be encoded + * data_t parity[] - an array of NROOTS and type data_t to be written with parity symbols + * NROOTS - the number of roots in the RS code generator polynomial, + * which is the same as the number of parity symbols in a block. + Integer variable or literal. + * + * NN - the total number of symbols in a RS block. Integer variable or literal. + * PAD - the number of pad symbols in a block. Integer variable or literal. + * ALPHA_TO - The address of an array of NN elements to convert Galois field + * elements in index (log) form to polynomial form. Read only. + * INDEX_OF - The address of an array of NN elements to convert Galois field + * elements in polynomial form to index (log) form. Read only. + * MODNN - a function to reduce its argument modulo NN. May be inline or a macro. + * GENPOLY - an array of NROOTS+1 elements containing the generator polynomial in index form + + * The memset() and memmove() functions are used. The appropriate header + * file declaring these functions (usually <string.h>) must be included by the calling + * program. + + * Copyright 2004, Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ + + +#undef A0 +#define A0 (NN) /* Special reserved value encoding zero in index form */ + +{ + int i, j; + data_t feedback; + + memset(parity,0,NROOTS*sizeof(data_t)); + + for(i=0;i<NN-NROOTS-PAD;i++){ + feedback = INDEX_OF[data[i] ^ parity[0]]; + if(feedback != A0){ /* feedback term is non-zero */ +#ifdef UNNORMALIZED + /* This line is unnecessary when GENPOLY[NROOTS] is unity, as it must + * always be for the polynomials constructed by init_rs() + */ + feedback = MODNN(NN - GENPOLY[NROOTS] + feedback); +#endif + for(j=1;j<NROOTS;j++) + parity[j] ^= ALPHA_TO[MODNN(feedback + GENPOLY[NROOTS-j])]; + } + /* Shift */ + memmove(&parity[0],&parity[1],sizeof(data_t)*(NROOTS-1)); + if(feedback != A0) + parity[NROOTS-1] = ALPHA_TO[MODNN(feedback + GENPOLY[0])]; + else + parity[NROOTS-1] = 0; + } +} diff --git a/lib/fec/encode_rs_char.c b/lib/fec/encode_rs_char.c new file mode 100644 index 0000000..a9bf2b8 --- /dev/null +++ b/lib/fec/encode_rs_char.c @@ -0,0 +1,15 @@ +/* Reed-Solomon encoder + * Copyright 2002, Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ +#include <string.h> + +#include "char.h" +#include "rs-common.h" + +void encode_rs_char(void *p,data_t *data, data_t *parity){ + struct rs *rs = (struct rs *)p; + +#include "encode_rs.h" + +} diff --git a/lib/fec/fec.h b/lib/fec/fec.h new file mode 100644 index 0000000..0d1bae1 --- /dev/null +++ b/lib/fec/fec.h @@ -0,0 +1,30 @@ +/* Main header for reduced libfec. + * + * The FEC code in this folder is + * Copyright 2003 Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ + +#pragma once + +#include <stdlib.h> + +#include "char.h" +#include "rs-common.h" + +/* Initialize a Reed-Solomon codec + * symsize = symbol size, bits + * gfpoly = Field generator polynomial coefficients + * fcr = first root of RS code generator polynomial, index form + * prim = primitive element to generate polynomial roots + * nroots = RS code generator polynomial degree (number of roots) + * pad = padding bytes at front of shortened block + */ +void *init_rs_char(int symsize,int gfpoly,int fcr,int prim,int nroots,int pad); + +int decode_rs_char(void *p, data_t *data, int *eras_pos, int no_eras); + +void encode_rs_char(void *p,data_t *data, data_t *parity); + +void free_rs_char(void *p); + diff --git a/lib/fec/init_rs.h b/lib/fec/init_rs.h new file mode 100644 index 0000000..a5e8b4a --- /dev/null +++ b/lib/fec/init_rs.h @@ -0,0 +1,104 @@ +/* Common code for intializing a Reed-Solomon control block (char or int symbols) + * Copyright 2004 Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ + +{ + int i, j, sr,root,iprim; + + rs = NULL; + /* Check parameter ranges */ + if(symsize < 0 || symsize > 8*sizeof(data_t)){ + goto done; + } + + if(fcr < 0 || fcr >= (1<<symsize)) + goto done; + if(prim <= 0 || prim >= (1<<symsize)) + goto done; + if(nroots < 0 || nroots >= (1<<symsize)) + goto done; /* Can't have more roots than symbol values! */ + if(pad < 0 || pad >= ((1<<symsize) -1 - nroots)) + goto done; /* Too much padding */ + + rs = (struct rs *)calloc(1,sizeof(struct rs)); + if(rs == NULL) + goto done; + + rs->mm = symsize; + rs->nn = (1<<symsize)-1; + rs->pad = pad; + + rs->alpha_to = (data_t *)malloc(sizeof(data_t)*(rs->nn+1)); + if(rs->alpha_to == NULL){ + free(rs); + rs = NULL; + goto done; + } + rs->index_of = (data_t *)malloc(sizeof(data_t)*(rs->nn+1)); + if(rs->index_of == NULL){ + free(rs->alpha_to); + free(rs); + rs = NULL; + goto done; + } + + /* Generate Galois field lookup tables */ + rs->index_of[0] = A0; /* log(zero) = -inf */ + rs->alpha_to[A0] = 0; /* alpha**-inf = 0 */ + sr = 1; + for(i=0;i<rs->nn;i++){ + rs->index_of[sr] = i; + rs->alpha_to[i] = sr; + sr <<= 1; + if(sr & (1<<symsize)) + sr ^= gfpoly; + sr &= rs->nn; + } + if(sr != 1){ + /* field generator polynomial is not primitive! */ + free(rs->alpha_to); + free(rs->index_of); + free(rs); + rs = NULL; + goto done; + } + + /* Form RS code generator polynomial from its roots */ + rs->genpoly = (data_t *)malloc(sizeof(data_t)*(nroots+1)); + if(rs->genpoly == NULL){ + free(rs->alpha_to); + free(rs->index_of); + free(rs); + rs = NULL; + goto done; + } + rs->fcr = fcr; + rs->prim = prim; + rs->nroots = nroots; + + /* Find prim-th root of 1, used in decoding */ + for(iprim=1;(iprim % prim) != 0;iprim += rs->nn) + ; + rs->iprim = iprim / prim; + + rs->genpoly[0] = 1; + for (i = 0,root=fcr*prim; i < nroots; i++,root += prim) { + rs->genpoly[i+1] = 1; + + /* Multiply rs->genpoly[] by @**(root + x) */ + for (j = i; j > 0; j--){ + if (rs->genpoly[j] != 0) + rs->genpoly[j] = rs->genpoly[j-1] ^ rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[j]] + root)]; + else + rs->genpoly[j] = rs->genpoly[j-1]; + } + /* rs->genpoly[0] can never be zero */ + rs->genpoly[0] = rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[0]] + root)]; + } + /* convert rs->genpoly[] to index form for quicker encoding */ + for (i = 0; i <= nroots; i++) + rs->genpoly[i] = rs->index_of[rs->genpoly[i]]; + done:; + +} diff --git a/lib/fec/init_rs_char.c b/lib/fec/init_rs_char.c new file mode 100644 index 0000000..a51099a --- /dev/null +++ b/lib/fec/init_rs_char.c @@ -0,0 +1,35 @@ +/* Initialize a RS codec + * + * Copyright 2002 Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ +#include <stdlib.h> + +#include "char.h" +#include "rs-common.h" + +void free_rs_char(void *p){ + struct rs *rs = (struct rs *)p; + + free(rs->alpha_to); + free(rs->index_of); + free(rs->genpoly); + free(rs); +} + +/* Initialize a Reed-Solomon codec + * symsize = symbol size, bits + * gfpoly = Field generator polynomial coefficients + * fcr = first root of RS code generator polynomial, index form + * prim = primitive element to generate polynomial roots + * nroots = RS code generator polynomial degree (number of roots) + * pad = padding bytes at front of shortened block + */ +void *init_rs_char(int symsize,int gfpoly,int fcr,int prim, + int nroots,int pad){ + struct rs *rs; + +#include "init_rs.h" + + return rs; +} diff --git a/lib/fec/rs-common.h b/lib/fec/rs-common.h new file mode 100644 index 0000000..e64eb39 --- /dev/null +++ b/lib/fec/rs-common.h @@ -0,0 +1,26 @@ +/* Stuff common to all the general-purpose Reed-Solomon codecs + * Copyright 2004 Phil Karn, KA9Q + * May be used under the terms of the GNU Lesser General Public License (LGPL) + */ + +/* Reed-Solomon codec control block */ +struct rs { + int mm; /* Bits per symbol */ + int nn; /* Symbols per block (= (1<<mm)-1) */ + data_t *alpha_to; /* log lookup table */ + data_t *index_of; /* Antilog lookup table */ + data_t *genpoly; /* Generator polynomial */ + int nroots; /* Number of generator roots = number of parity symbols */ + int fcr; /* First consecutive root, index form */ + int prim; /* Primitive element, index form */ + int iprim; /* prim-th root of 1, index form */ + int pad; /* Padding bytes in shortened block */ +}; + +static inline int modnn(struct rs *rs,int x){ + while (x >= rs->nn) { + x -= rs->nn; + x = (x >> rs->mm) + (x & rs->nn); + } + return x; +} |