Design of Low-Complexity Decoder for Triple Error Correcting BCH Codes

Cho Yong Suk; Shin，Yong-Dal

doi:10.34163/jkits.2018.13.3.008

Journal of Knowledge Information Technology and Systems

Abbr : JKITS
2018, 13(3), pp.373-379
DOI : 10.34163/jkits.2018.13.3.008
Publisher : Korea Knowledge Information Technology Society
Research Area : Interdisciplinary Research

Cho Yong Suk ¹, Shin，Yong-Dal ²

¹유원(U1)대학교
²유원(U1)대학교

ABSTRACT

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a class of powerful multiple-error-correcting cyclic codes. Due to its powerful error-correction performance and reasonable hardware costs, the binary BCH codes have been widely used in data communications and storage systems for error control. In this paper, a design method of low-complexity decoder for triple error correcting binary BCH codes is presented, which is modified Peterson's direct solution method. In this method, all division operations over finite field GF(2^m)are eliminated from the computations of the error locator polynomial. BCH codes are defined over finite field GF(2^m) and all arithmetic operations are performed over this fields. Inversion in a finite field is time consuming and requires relatively complex circuitry. In conventional decoding algorithm of BCH codes are required finite field inversion. In this paper, inversionless decoder for triple error correcting BCH codes is proposed. The decoder comprises a syndrome computation circuit, a error locator polynomial computation circuit and a error location searching circuit, which can be implemented by linear feedback shift registers and logical gates. The attractive feature of this decoder is its remarkable simplicity from the point of view of hardware implementation. Futhermore, the proposed decoder has very simple control circuit and short decoding delay. Therefore this decoder can be implemented by simple hardware and also save buffer memory which stores received sequence.
KEYWORDS

Error correction codes, BCH codes, Peterson’s algorithm, Galois fields, Finite fields inversion
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