Architecture for Programmable Generator Polynomial Based Reed-Solomon Encoder and Decoder
Jaydeb Bhaumik, Anindya Sundar Das, Jagannath Samanta · 2013
Abstract — Reed-Solomon Codes are popularly used for error correction in many applications like storage devices (CD, DVD), wireless communications, high speed modems and satellite communications. In this paper, a modified scheme for programmable generator polynomial based Reed-Solomon encoder and decoder has been proposed. The works reported in this paper corrects errors in derived equations and decoder architecture proposed by Shayan et al. Moreover, modified architectures for programmable generator polynomial based Reed-Solomon encoder and decoder are reported. Index Terms — Reed-Solomon Code, Finite Field, Encoder and Decoder Architectures Programmable I. INTRODUCTION Reed-Solomon (RS) code was discovered by Irving Reed and Gus Solomon in 1960[1]. It is a linear block code and defined over finite field. RS code has a wide range of applications in wireless communications, high speed modems and storage devices (CD, DVD). Several important applications of RS codes have been discussed in [10]. A number of general encoding and decoding schemes of the RS codes may be found in the literature [11] [12]. The complexity of RS encoder and decoder increases with the error correcting capability of the codes. Hence, many researchers have directed their efforts to minimize the complexity of RS decoder. A high-speed architecture for Reed-Solomon decoders is proposed in [9]. VLSI design of a reconfigurable multi-mode Reed-Solomon codec for high speed communication systems with programmable codeword length and error correcting capability has been proposed in [5]. Most of the existing programmable RS codec have programmable codeword length and error correcting capability. Beside the application of RS code for error correction, it has applications in the design of diffusion layer for a substitution permutation networks type block cipher [10], secret sharing scheme, message authentication codes [7][8]. In [2], RS code has been used to design integrated code for both message authentication and error correction. In this scheme programmable generator polynomial based RS-code is employed but no architecture for the proposed scheme is mentioned in [2]. Decoding of Reed-Solomom code generated by any generator polynomial discussed in [3].