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On the Maximum burst-correcting Capability of Cyclic Hsu-Kasami-Chien codes

IEEE COMMUNICATIONS LETTERS 2017年第11期21卷 2352-2355页

作者： Zhou, Wei Lund Univ Dept Elect & Informat Technol S-22100 Lund Sweden

Hsu-Kasami-Chien (HKC) codes are a class of cyclic codes that can correct either burst or random errors. This letter studies the maximum burst-correcting capability of HKC codes. A necessary and sufficient condition for a b-burst-correcting cyclic HKC code is given and simplified as a generalized one for Fire codes. An upper bound on the burst-correcting capability of HKC codes is derived, which improves upon a previous bound. Explicit examples of HKC codes are presented. A design guideline for constructing HKC codes with given burst-error and random-error correcting capabilities is presented.

关键词： burst-correcting code cyclic code Hsu-kasami-chien code

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On the Maximum True burst-correcting Capability of Fire codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第10期62卷 5323-5342页

作者： Zhou, Wei Lin, Shu Abdel-Ghaffar, Khaled A. S. Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

Fire codes are cyclic codes generated by the product of two polynomials: a binomial that characterizes the code's guaranteed burst-correcting capability and an irreducible polynomial that characterizes the code length. However, the true burst-correcting capability of a Fire code may exceed its guaranteed burst-correcting capability, which can be thought of as the designed burst-correcting capability of the Fire code. The true burst-correcting capability of a Fire code depends on the irreducible polynomial used in code construction. In this paper, the maximum true burst-correcting capabilities of Fire codes are considered. Fire codes are classified based on three parameters: their designed burst-correcting capabilities, the least common multiple of the periods of the binomials, and the irreducible polynomials used in their constructions, and the ratios of the periods of primitive polynomials of the same degrees as the irreducible polynomials to the periods of the irreducible polynomials. It is shown that the maximum true burst-correcting capability of each class, which pertains to an infinite number of codes, can be determined by checking whether or not a finite number of incongruences have a solution. It is also shown that in each class, there is an infinite number of Fire codes, with increasing code lengths, that attain this maximum. The maximum true burst-correcting capabilities of several classes of Fire codes are determined. It is also shown that there are infinite sequences of irreducible polynomials that generate cyclic codes of rates approaching one and with burst-correcting capabilities that exceed any given number.

关键词： burst-correcting code cyclic code Fire code irreducible polynomial maximal cyclic code primitive polynomial

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