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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| Vydáno v: | IEEE transactions on information theory Ročník 69; číslo 8; s. 1 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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IEEE
01.08.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Shany, Yaron Berman, Amit |
| Author_xml | – sequence: 1 givenname: Yaron orcidid: 0000-0001-6149-9755 surname: Shany fullname: Shany, Yaron organization: Samsung Semiconductor Israel R&D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel – sequence: 2 givenname: Amit orcidid: 0000-0003-4502-8093 surname: Berman fullname: Berman, Amit organization: Samsung Semiconductor Israel R&D Center, 146 Derech Menachem Begin St, Tel Aviv, Israel |
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| SubjectTerms | Algorithms BCH codes Binary codes Codes Complexity Decoding Isomorphism Modules Polynomials |
| Title | Fast Syndrome-Based Chase Decoding of Binary BCH Codes Through Wu List Decoding |
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