Title: A new burst error correcting method for Reed-Solomon codes based on composite parity-check matrices

Authors: Song Chol Pak; Nam Chol Yu

Addresses: Faculty of Applied Mathematics, Kim Chaek University of Technology, Pyongyang, North Korea ' School of Science and Engineering, Kim Chaek University of Technology, Pyongyang, North Korea

Abstract: This paper presents the construction method of composite parity-check (CPC) matrices and a new burst error correcting method for (n, k) Reed-Solomon (RS) codes based on CPC matrices. The proposed method is capable of finding burst error locations by only locations of symbol 0s of syndromes computed by CPC matrices and evaluating the corresponding error magnitudes using CPC matrices. The simulation results show that the proposed method can correct burst errors for the codes with the rate less than about 0.75 with lower complexity and correct burst errors of length up to n - k - 1 and burst erasures of length up to n - k.

Keywords: composite parity-check matrix; composite parity-check; CPC; burst error; longest zero span; Reed-Solomon codes; Reed-Solomon; RS.

DOI: 10.1504/IJICOT.2022.125806

International Journal of Information and Coding Theory, 2022 Vol.6 No.1, pp.22 - 34

Received: 12 Aug 2020
Accepted: 30 Sep 2020
Published online: 29 Sep 2022 *

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