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International Symposium on Information Theory and its Applications

An Iterative Bit-Flipping Decoding Algorithm For Binary Reed-Muller Codes *

Yong-Ting Ni, Cheng-Yu Pai, Chao‐Yu Chen

Published Oct 24, 2020• 1 citation
OpenAlex

Abstract

This paper presents an iterative bit-flipping (BF) decoding algorithm for binary Reed-Muller (RM) codes. The BF decoding algorithm is a hard-decision decoding algorithm. According to the updated hard reliability measures, one bit of the received hard-decision sequence is flipped at a time in each iteration. The simulation results show that the proposed BF decoding algorithm outperforms the conventional hard-decision majority decoding.

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This paper presents an iterative bit-flipping (BF) decoding algorithm for binary Reed-Muller (RM) codes. The BF decoding algorithm is a hard-decision decoding algorithm. According to the updated hard reliability measures, one bit of the received hard-decision sequence is flipped at a time in each iteration. The simulation results show that the proposed BF decoding algorithm outperforms the conventional hard-decision majority decoding.
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.
We present a new soft decision majority decoding algorithm for Reed-Muller codes RM(r,m). First, the reliabilities of all received symbols are recalculated into the reliabilities of the parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to the more reliable parity checks. It is proven that for long low-rate codes RM(r,m), our soft decision algorithm outperforms its conventional hard decision counterpart by 10 log/sub 10/(/spl pi//2)/spl ap/2 dB at any given output bit error rate /spl epsi/<1/2.
We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM(r,m). First, the reliabilities of 2/sup m/ transmitted symbols are recalculated into the reliabilities of 2/sup m-r/ parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long low-rate codes RM(r,m), our soft-decision algorithm outperforms its conventional hard-decision counterpart by 10 log/sub 10/(/spl pi//2)/spl ap/2 dB at any given output error probability. For fixed code rate R and m/spl rarr//spl infin/, our algorithm increases almost 2/sup r/2/ times the correcting capability of soft-decision bounded distance decoding.
Bit-flipping (BF) algorithm has been widely employed in decoding linear block codes because of its simple implementation. We consider the most popular modified weighted bit-flipping (MWBF) algorithm and propose two novel LLR scaling based MWBF algorithms for RM (Reed-Muller) decoding. By introducing the log likelihood ratio as the scaling factor to tune the bit-based message and then approximately approaching the SNR adaption, the proposed two decoding algorithms outperform regular MWBF method with similar computational cost.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
This paper presents a novel iterative reliability-based bit flipping (BF) algorithm for decoding low-density parity-check codes. The new decoder is a single BF algorithm called two-round selection -based bit flipping. It introduces the idea of a two-round selection of the flipped bit, based successively on hard and soft received channel values. In the first stage, a set of unreliable bits is identified, and then a second selection is used, to pick out among them the bit to flip. In the second round of selection, the initial belief about received signals, contributes efficiently to selecting the best candidate bit. We demonstrate through simulations over the binary-input additive white Gaussian noise channel and the Rayleigh fading channel that the proposed algorithm exhibits better decoding performance when compared with some well-known soft decision BF algorithms. A complexity analysis of the proposal and a comparison to other BF decoders are also presented.