Low-Complexity Chase Decoding of Reed-Solomon Codes Using Module

The interpolation based algebraic soft decoding yields a high decoding performance for Reed-Solomon (RS) codes with a polynomial-time complexity. Its computationally expensive interpolation can be facilitated using the module structure. The desired Gröbner basis can be achieved by reducing the basis...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 68; no. 10; pp. 6012 - 6022
Main Authors: Xing, Jiongyue, Chen, Li, Bossert, Martin
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Basis reduction
Codes
Complexity
Complexity theory
Cost analysis
Decoding
Encoding
Interpolation
low-complexity Chase decoding
Mathematical analysis
Maximum likelihood decoding
Modules
Polynomials
progressive decoding
Reed-Solomon codes
Transforms
Vectors (mathematics)
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:The interpolation based algebraic soft decoding yields a high decoding performance for Reed-Solomon (RS) codes with a polynomial-time complexity. Its computationally expensive interpolation can be facilitated using the module structure. The desired Gröbner basis can be achieved by reducing the basis of a module. This paper proposes the low-complexity Chase (LCC) decoding algorithm using this module basis reduction (BR) interpolation technique, namely the LCC-BR algorithm. By identifying <inline-formula> <tex-math notation="LaTeX">\eta </tex-math></inline-formula> unreliable symbols, <inline-formula> <tex-math notation="LaTeX">2^\eta </tex-math></inline-formula> decoding test-vectors will be formulated. The LCC-BR algorithm first constructs a common basis which will be shared by the decoding of all test-vectors. This eliminates the redundant computation in decoding each test-vector, resulting in a lower decoding complexity and latency. This paper further proposes the progressive LCC-BR algorithm that decodes the test-vectors sequentially and terminates once the maximum-likelihood decision decoding outcome is reached. Exploiting the difference between the adjacent test-vectors, this progressive decoding is realized without any additional memory cost. Complexity analysis shows that the LCC-BR algorithm yields a lower complexity and latency, especially for high rate codes, which will be validated by the numerical results.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2020.3011991