Title: A minimal search soft decision list decoding algorithm for Reed-Solomon codes

Authors: B. Yamuna; T.R. Padmanabhan

Addresses: Department of ECE, Amrita Vishwa Vidyapeetham, Amrita School of Engineering, Amrita Nagar, Coimbatore 641 112, Tamil Nadu, India ' Department of IT, Amrita Vishwa Vidyapeetham, Amrita School of Engineering, Amrita Nagar, Coimbatore 641 112, Tamil Nadu, India

Abstract: Given a received polynomial r(x) with coefficients in finite field soft decision decoding (SDD) is the process of identifying the most probable error polynomial e(x) with coefficients in finite field and hence the corresponding code polynomial c(x) ∈{C (x)}, where {C (x)} is the code set. The paper presents an algorithm for identifying this c(x) - called the target code word (TCW) here - and extends the same to identify the list of codewords as well. The uniqueness of the approach lies in identifying the TCW directly without the need for search over a much larger set as with many of the existing methods. The proposed method seeks codewords with the most likely error positions guessed in advance; this ushers in a further simplification with cyclic codes obviating the need for repeated algebraic decoding. The fact that restricting the error correcting range to d_min - 1 yields a unique decoded codeword, leads to a practical implementation of the said algorithm with attendant superiority in performance.

Keywords: Reed-Solomon codes; BCH codes; soft decision decoding; SDD; list decoding; error polynomial; maximum-likelihood-decoding; MLD.

DOI: 10.1504/IJICT.2014.057972

International Journal of Information and Communication Technology, 2014 Vol.6 No.1, pp.71 - 85

Received: 03 Sep 2012
Accepted: 21 Dec 2012
Published online: 26 Jul 2014 *

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