The software implementation of decoding for RS code based on a new degree computationless modified Euclid (DCME) algorithm

Abstract

Purpose

The purpose of this paper is to design a decoding software for the Reed‐Solomon (RS) codes, which are using an efficient degree computationless algorithm based on the Euclidean algorithm. As a consequence, the complexity of this new decoding algorithm is dramatically reduced.

Design/methodology/approach

Applying the rules of polynomial in finite field, operation modules which can carry out multiplication, inverse calculation in GF(2⁸) are designed with “C++” language, and a RS codec software based on these is implemented. In this software, the new decoding algorithm computes the error locator polynomial and the error evaluator polynomial simultaneously without performing polynomial divisions, and there is no need for the degree computation cell and the degree comparison cell.

Findings

Owing to the help of this software, the paper can easily perform the RS code for different values of t and different primitive polynomials over GF(2^m) without re‐designing the programme.

Originality/value

It will be served as an efficient auxiliary technique for algorithm development and verification together with hardware design and debugging. Furthermore, an illustrative example of (255, 223) RS code using this program shows that the speed of the decoding process is approximately three times faster than that of the conventional decoding software.

Citation

Bao, T., Xu, J. and Wei, G. (2010), "The software implementation of decoding for RS code based on a new degree computationless modified Euclid (DCME) algorithm", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 2, pp. 338-346. https://doi.org/10.1108/03321641011014805