Burst decoding of cyclic codes based on circulant parity-check matrices

Authors:
Shumei Song;Shu Lin;Khaled Abdel-Ghaffar;Zhi Ding;Wai H. Fong;Marc P. C. Fossorier
Affiliations:
Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;NASA Goddard Space Flight Center, Greenbelt, MD;ETIS Laboratory, ENSEA, UCP, CNRS, UMR, Cergy Pontoise, France
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

An error-burst correcting algorithm is developed based on a circulant parity-check matrix of a cyclic code. The proposed algorithm is more efficient than error trapping if the code rate is less than about 2/3. It is shown that for any (n, k) cyclic code, there is an n × n circulant parity-check matrix such that the algorithm, applied to this matrix, corrects error bursts of lengths up to the error-burst correction limit of the cyclic code. This same matrix can be used to efficiently correct erasure bursts of lengths up to n-k. The error-burst correction capabilities of a class of cyclic low-density parity-check (LDPC) codes constructed from finite geometries are also considered.