Title :
A Systematic Reed-Solomon Encoder with Arbitrary Parity Positions
Author :
Brauchle, Joschi ; Koetter, Ralf
Author_Institution :
Inst. for Commun. Eng., Tech. Univ. Munchen, Munich, Germany
Abstract :
An efficient encoder circuit for a systematic Reed-Solomon code with arbitrary parity positions is presented. In contrast to the Reed-Solomon encoder circuits widely available today, the parity symbols produced by this encoder are not restricted to form a block of consecutive parity symbols at the beginning or end of the codeword, but may be spread arbitrarily within the codeword. A general structure of the parity-check matrix for such a code is derived by exploiting the special structure of Vandermonde matrices. From this general parity-check matrix, an expression for the calculation of the Reed-Solomon parity symbols at arbitrary positions within the codeword is found and an efficient hardware implementation of the proposed encoder is designed.
Keywords :
Reed-Solomon codes; matrix algebra; parity check codes; Vandermonde matrices; arbitrary parity positions; general structure; hardware implementation; parity check matrix; parity symbols; systematic Reed-Solomon encoder; Circuits; Code standards; Decoding; Encoding; Forward error correction; Galois fields; Hardware; Parity check codes; Reed-Solomon codes; Shift registers;
Conference_Titel :
Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE
Conference_Location :
Honolulu, HI
Print_ISBN :
978-1-4244-4148-8
DOI :
10.1109/GLOCOM.2009.5426304