Iterative Hard-Decision Decoding Algorithms for Binary Reed-Muller Codes

In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping...

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Bibliographic Details
Published in:IEEE access Vol. 10; p. 1
Main Authors: Ni, Yong-Ting, Nguyen, Duc Nhat, Liao, Feng-Kai, Kao, Tzu-Chieh, Chen, Chao-Yu
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Binary codes
Binary system
bit-flipping
Codes
Decoding
Generators
Iterative decoding
Iterative methods
majority-logic decoding
Maximum likelihood decoding
Normalizing
Polar codes
Reed-Muller code
Reed-Muller codes
Reliability
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:In this paper, novel hard-decision iterative decoding algorithms for binary Reed-Muller (RM) codes are presented. First, two algorithms are devised based on the majority-logic decoding algorithm with reliability measures of the received sequence. The bit-flipping (BF) and the normalized bit-flipping (NBF) decoding algorithms are hard-decision decoding algorithms. According to the updated hard reliability measures, the BF and NBF algorithms flip one bit of the received hard-decision sequence at a time in each iteration. The NBF decoding algorithm performs better than the BF decoding algorithm by normalizing the reliability measures of the information bits. Moreover, the BF and NBF algorithms are modified to flip multiple bits in one iteration to reduce the average number of iterations. The modified decoding algorithms are called the multiple-bits-flipping (MBF) algorithm and the normalized multiple-bits-flipping (NMBF) algorithm, respectively. The proposed algorithms have low computational complexities and can converge rapidly after a small number of iterations. The simulation results show that the proposed hard-decision decoding algorithms outperform the conventional decoding algorithm.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2022.3180368