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.TH REED-SOLOMON 3 .SH 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 .SH SYNOPSIS .nf .ft B #include "rs.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]; .fi .SH 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 "-lrs" to your linker command line. The functions with names ending in \fB_int\fR handle data in integer arrays, permitting arbitrarily large codewords limited only by machine resources. The functions with names ending in \fB_char\fR take unsigned char arrays and can handle codes with symbols of 8 bits or less (i.e., with codewords of 255 symbols or less). \fBencode_rs_8\fR and \fBdecode_rs_8\fR 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, \fInot\fR the dual-basis specified in the CCSDS standard, to represent symbols. This code may be shortened by giving a non-zero \fBpad\fR value to produce a (255-\fBpad\fR,223-\fBpad\fR) code. The padding will consist of the specified number of zeroes at the front of the full codeword. For full CCSDS compatibility, \fBencode_rs_ccsds\fR and \fBdecode_rs_ccsds\fR are provided. These functions use two lookup tables, \fBTaltab\fR to convert from conventional to dual-basis, and \fBTal1tab\fR to perform the inverse mapping from dual-basis to conventional form, before and after calls to \fBencode_rs_8\fR and \fBdecode_rs_8\fR. The \fB_8\fR and \fB_ccsds\fR functions do not require initialization. To use the general purpose RS encoder or decoder (i.e., the \fB_char\fR or \fB_int\fR versions), the user must first call \fBinit_rs_int\fR or \fBinit_rs_char\fR as appropriate. The arguments are as follows: \fBsymsize\fR gives the symbol size in bits, up to 8 for \fBinit_rs_char\fR or 32 for \fBinit_rs_int\fR 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^\fBsymsize\fR - 1 symbols, each containing \fBsymsize\fR bits. The codeword may be shortened with the \fBpad\fR parameter described below. \fBgfpoly\fR gives the extended Galois field generator polynomial coefficients, with the 0th coefficient in the low order bit. The polynomial \fImust\fR be primitive; if not, the call will fail and NULL will be returned. \fBfcr\fR gives, in index form, the first consecutive root of the Reed Solomon code generator polynomial. \fBprim\fR gives, in index form, the primitive element in the Galois field used to generate the Reed Solomon code generator polynomial. \fBnroots\fR gives the number of roots in the Reed Solomon code generator polynomial. This equals the number of parity symbols per code block. \fBpad\fR 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^\fBsymsize\fR - \fBpad\fR - 1 and K = N-\fBnroots\fR. The \fBencode_rs_char\fR and \fBencode_rs_int\fR functions accept the pointer returned by \fBinit_rs_char\fR or \fBinit_rs_int\fR, respectively, to encode a block of data using the specified code. The input data array is expected to contain K symbols (of \fBsymsize\fR bits each, right justified in each char or int) and \fBnroots\fR parity symbols will be placed into the \fBparity\fR array, right justified. The \fBdecode_\fR 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 \fBeras_pos\fR 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 \fBno_eras\fR parameter. To maximize performance, the encode and decode functions perform no "sanity checking" of their inputs. Decoder failure may result if \fBeras_pos\fR 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 \fB_8\fR or \fB_ccsds\fR functions, or with the \fB_char\fR 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 \fBeras_pos\fR 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 \fImust\fR have at least \fBnroots\fR elements to prevent a possible buffer overflow. The \fBfree_rs_int\fR and \fBfree_rs_char\fR functions free the internal space allocated by the \fBinit_rs_int\fR and \fBinit_rs_char\fR functions, respecitively. The functions \fBencode_rs_8\fR and \fBdecode_rs_8\fR do not have corresponding \fBinit\fR and \fBfree\fR, nor do they take the \fBrs\fR argument accepted by the other functions as their parameters are statically compiled. These functions implement a code equivalent to calling \fBinit_rs_char\fR(8,0x187,112,11,32,pad); and using the resulting pointer with \fBencode_rs_char\fR and \fBdecode_rs_char\fR. .SH RETURN VALUES \fBinit_rs_int\fR and \fBinit_rs_char\fR 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 \fBdecode_\fR functions return a count of corrected symbols, or -1 if the block was uncorrectible. .SH 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). .SH COPYRIGHT Copyright 2002, Phil Karn, KA9Q. May be used under the terms of the GNU General Public License (GPL). .SH SEE ALSO CCSDS 101.0-B-5: Telemetry Channel Coding. http://www.ccsds.org/documents/pdf/CCSDS-101.0-B-5.pdf .SH 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 \fBencode_rs_8\fR and \fBdecode_rs_8\fR.