REED-SOLOMON(3)

NAME
init_rs_int, encode_rs_int, decode_rs_int, free_rs_int, init_rs_char, encode_rs_char, decode_rs_char, free_rs_char, encode_rs_8, decode_rs_8, encode_rs_ccsds, decode_rs_ccsds - Reed-Solomon encoding/decoding

SYNOPSIS
#include "fec.h"

void *init_rs_int(int symsize,int gfpoly,int fcr,int prim,
     int nroots,int pad);

void encode_rs_int(void *rs,int *data,int *parity);

int decode_rs_int(void *rs,int *data,int *eras_pos,int no_eras);

void free_rs_int(void *rs);

void *init_rs_char(int symsize,int gfpoly,int fcr,int prim,
     int nroots,int pad);

void encode_rs_char(void *rs,unsigned char *data,
     unsigned char *parity);

int decode_rs_char(void *rs,unsigned char *data,int *eras_pos,
     int no_eras);

void free_rs_char(void *rs);

void encode_rs_8(unsigned char *data,unsigned char *parity,
     int pad);

int decode_rs_8(unsigned char *data,int *eras_pos,int no_eras,
     int pad);

void encode_rs_ccsds(unsigned char *data,unsigned char *parity,
     int pad);

int decode_rs_ccsds(unsigned char *data,int *eras_pos,int no_eras,
     int pad);

unsigned char Taltab[256];
unsigned char Tal1tab[256];

DESCRIPTION
These functions implement Reed-Solomon error control encoding and decoding. For optimal performance in a variety of applications, three sets of functions are supplied. To access these functions, add "-lfec" to your linker command line.

The functions with names ending in _int handle data in integer arrays, permitting arbitrarily large codewords limited only by machine resources.

The functions with names ending in _char take unsigned char arrays and can handle codes with symbols of 8 bits or less (i.e., with codewords of 255 symbols or less).

encode_rs_8 and decode_rs_8 implement a specific (255,223) code with 8-bit symbols specified by the CCSDS: a field generator of 1 + X + X^2 + X^7 + X^8 and a code generator with first consecutive root = 112 and a primitive element of 11. These functions use the conventional polynomial form, not the dual-basis specified in the CCSDS standard, to represent symbols. This code may be shortened by giving a non-zero pad value to produce a (255-pad,223-pad) code. The padding will consist of the specified number of zeroes at the front of the full codeword.

For full CCSDS compatibility, encode_rs_ccsds and decode_rs_ccsds are provided. These functions use two lookup tables, Taltab to convert from conventional to dual-basis, and Tal1tab to perform the inverse mapping from dual-basis to conventional form, before and after calls to encode_rs_8 and decode_rs_8.

The _8 and _ccsds functions do not require initialization.

To use the general purpose RS encoder or decoder (i.e., the _char or _int versions), the user must first call init_rs_int or init_rs_char as appropriate. The arguments are as follows:

symsize gives the symbol size in bits, up to 8 for init_rs_char or 32 for init_rs_int on a machine with 32-bit ints (though such a huge code would exhaust memory limits on a 32-bit machine). The resulting Reed-Solomon code word will have 2^symsize - 1 symbols, each containing symsize bits. The codeword may be shortened with the pad parameter described below.

gfpoly gives the extended Galois field generator polynomial coefficients, with the 0th coefficient in the low order bit. The polynomial must be primitive; if not, the call will fail and NULL will be returned.

fcr gives, in index form, the first consecutive root of the Reed Solomon code generator polynomial.

prim gives, in index form, the primitive element in the Galois field used to generate the Reed Solomon code generator polynomial.

nroots gives the number of roots in the Reed Solomon code generator polynomial. This equals the number of parity symbols per code block.

pad gives the number of leading symbols in the codeword that are implicitly padded to zero in a shortened code block.

The resulting Reed-Solomon code has parameters (N,K), where N = 2^symsize - pad - 1 and K = N-nroots.

The encode_rs_char and encode_rs_int functions accept the pointer returned by init_rs_char or init_rs_int, respectively, to encode a block of data using the specified code. The input data array is expected to contain K symbols (of symsize bits each, right justified in each char or int) and nroots parity symbols will be placed into the parity array, right justified.

The decode_ functions correct the errors in a Reed-Solomon codeword of N symbols up to the capability of the code. An optional list of "erased" symbol indices may be given in the eras_pos array to assist the decoder; this parameter may be NULL if no erasures are given. The number of erased symbols must be given in the no_eras parameter.

To maximize performance, the encode and decode functions perform no "sanity checking" of their inputs. Decoder failure may result if eras_pos contains duplicate entries, and both encoder and decoder will fail if an input symbol exceeds its allowable range. (Symbol range overflow cannot occur with the _8 or _ccsds functions, or with the _char functions when 8-bit symbols are specified.)

The decoder corrects the symbols "in place", returning the number of symbols in error. If the codeword is uncorrectable, -1 is returned and the data block is unchanged. If eras_pos is non-null, it is used to return a list of corrected symbol positions, in no particular order. This means that the array passed through this parameter must have at least nroots elements to prevent a possible buffer overflow.

The free_rs_int and free_rs_char functions free the internal space allocated by the init_rs_int and init_rs_char functions, respecitively.

The functions encode_rs_8 and decode_rs_8 do not have corresponding init and free, nor do they take the rs argument accepted by the other functions as their parameters are statically compiled. These functions implement a code equivalent to calling

init_rs_char(8,0x187,112,11,32,pad);

and using the resulting pointer with encode_rs_char and decode_rs_char.

RETURN VALUES
init_rs_int and init_rs_char return a pointer to an internal control structure that must be passed to the corresponding encode, decode and free functions. These functions return NULL on error.

The decode_ functions return a count of corrected symbols, or -1 if the block was uncorrectible.

AUTHOR
Phil Karn, KA9Q (karn@ka9q.net), based heavily on earlier work by Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy (harit@spectra.eng.hawaii.edu). Extra improvements suggested by Detmar Welz (dwelz@web.de).

COPYRIGHT
Copyright 2004, Phil Karn, KA9Q. May be used under the terms of the GNU Lesser General Public License (LGPL).

SEE ALSO
CCSDS 101.0-B-6: Telemetry Channel Coding. http://www.ccsds.org/documents/101x0b6.pdf

NOTE
CCSDS chose the "dual basis" symbol representation because it simplified the implementation of a Reed-Solomon encoder in dedicated hardware. However, this approach holds no advantages for a software implementation on a general purpose computer, so use of the dual basis is recommended only if compatibility with the CCSDS standard is needed, e.g., to decode data from an existing spacecraft using the CCSDS standard. If you just want a fast (255,223) RS codec without needing to interoperate with a CCSDS standard code, use encode_rs_8 and decode_rs_8.