Fast Syndrome-Based Chase Decoding of Binary BCH Codes Through Wu List Decoding

We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed-Solomon (RS) codes by the authors (IEEE Trans. IT, 2022), by requiring only a single Kötter iteration per edge of the decodin...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 69; no. 8; p. 1
Main Authors: Shany, Yaron, Berman, Amit
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
BCH codes
Binary codes
Codes
Complexity
Decoding
Isomorphism
Modules
Polynomials
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed-Solomon (RS) codes by the authors (IEEE Trans. IT, 2022), by requiring only a single Kötter iteration per edge of the decoding tree. In comparison to the fast Chase algorithms presented by Kamiya (IEEE Trans. IT, 2001) and Wu (IEEE Trans. IT, 2012) for binary BCH codes, the polynomials updated throughout the algorithm of the current paper typically have a much lower degree. To achieve the complexity reduction, we build on a new isomorphism between two solution modules in the binary case, and on a degenerate case of the soft-decision (SD) version of the Wu list decoding algorithm. Roughly speaking, we prove that when the maximum list size is 1 in Wu list decoding of binary BCH codes, assigning a multiplicity of 1 to a coordinate has the same effect as flipping this coordinate in a Chase-decoding trial. The solution-module isomorphism also provides a systematic way to benefit from the binary alphabet for reducing the complexity in bounded-distance hard-decision (HD) decoding. Along the way, we briefly develop the Gröbner-bases formulation of the Wu list decoding algorithm for binary BCH codes, which is missing in the literature.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3263185