Low-Complexity Chase Decoding of Hermitian Codes With Improved Interpolation and Root-Finding

This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable receive...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 73; no. 8; pp. 5509 - 5522
Main Authors: Liang, Jiwei, Zhao, Jianguo, Chen, Li
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Basis reduction
Codes
Complexity
Complexity theory
Decoding
early termination
Encoding
fast root-finding
Galois fields
Hermitian codes
Interpolation
Maximum likelihood decoding
Polynomials
re-encoding transform
Reliability
Symbols
Transforms
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by both the improved interpolation and root-finding. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable received symbols, <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> test-vectors are formulated, each of which is decoded by the interpolation based Guruswami-Sudan (GS) algorithm. To reduce both the interpolation complexity and latency, the re-encoding transform (ReT) is introduced through defining the Lagrange interpolation polynomials over the Hermitian function fields. The interpolation polynomial is further computed through module basis reduction (BR) that yields the Gröbner basis that contains the desired polynomial. The BR interpolation exhibits a greater parallelism than the conventional Kötter's interpolation. Moreover, the <inline-formula> <tex-math notation="LaTeX">2^{\eta } </tex-math></inline-formula> root-finding processes are facilitated by estimating the codewords directly from the interpolation outcomes. It eliminates the re-encoding computation for identifying the most likely candidate from the decoding output list. It is also shown that the average LCC decoding complexity can be further reduced by both assessing the re-encoding outcome and decoding the test-vectors progressively. They can achieve an early decoding termination once a codeword that satisfies the maximum likelihood (ML) criterion is found. Our simulation results demonstrate that the decoding complexity and latency can be significantly reduced over the existing decoding algorithms.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2024.3524035