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IEEE International Conference on Communication Technology (ICCT)

An Improved Bit Flipping Min Sum Algorithm with Difference to Sum Ratio Factor Based on Unreliable Received Messages

Mingchun Qiu, Zhi Zhang, Yuzhen Huang

Published Oct 28, 2020• 0 citations
Publisher

Abstract

Low density parity-check (LDPC) codes is known for its outstanding performance near the Shannon limit. In this paper, an improved min sum algorithm with difference to sum ratio factor (DSR-MS) is proposed, which is called bit flipping min sum algorithm with DSR factor based on unreliable received messages (DSR-URMBFMS). It belongs to the hybrid decision decoding scheme. A novel assistant stage associated with the bit flipping (BF) algorithm is introduced after each failed iteration of DSR-MS, and the sequence with minimum sum of syndrome vector (SSV) is taken as the final decoding output. Simulation results show that the proposed algorithm achieves faster convergence rate and better performance than the DSR-MS algorithm.

DOI
10.1109/icct50939.2020.9295903

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Low density parity-check (LDPC) codes is known for its outstanding performance near the Shannon limit. In this paper, an improved min sum algorithm with difference to sum ratio factor (DSR-MS) is proposed, which is called bit flipping min sum algorithm with DSR factor based on unreliable received messages (DSR-URMBFMS). It belongs to the hybrid decision decoding scheme. A novel assistant stage associated with the bit flipping (BF) algorithm is introduced after each failed iteration of DSR-MS, and the sequence with minimum sum of syndrome vector (SSV) is taken as the final decoding output. Simulation results show that the proposed algorithm achieves faster convergence rate and better performance than the DSR-MS algorithm.
Low Density Parity Check Codes (LDPC) give groundbreaking performance which is known to approach Shannon's limits for sufficiently large block length. Historically and recently, LDPC have been known to give superior performance than concatenated coding. In the following paper, a proposal to modify the standard Min-Sum (MS) algorithm for decoding LDPC codes is presented. This is done by introduction of a difference to sum ratio factor, κ in the check to bit node updating process. The algorithm is further extended by implementing hard decision of the Bit-Flipping (BF) algorithm over the soft decision of MS algorithm. Simulation results demonstrate that the proposed algorithms are effective in imparting a better performance in terms of a lower bit error rate (BER) at medium to high signal to noise ratio (SNR) when compared to the traditional MS algorithm while adding fair amount of complexity.
In order to improve the bit-flipping (BF) decoding algorithms, a weighted hard-decision based BF decoding algorithm for low-density parity-check (LDPC) codes is presented, in which the weights of variable-nodes are employed. A new metric is defined for the weight of candidate bits not only in unsatisfied parity check equations but also in satisfied ones. The connection between min-sum decoding algorithm and the proposed algorithm is presented. Simulation results show that the new decoding algorithm can provide better FER performance and faster convergence speed than the original candidate bit based bit-flipping (CBBF) algorithm.
An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.
For LDPC decoding, bit-flipping (BF) algorithms are much simpler than the min-sum algorithms (MSA). However, BF algorithms have the disadvantages of poorer performances and higher iteration counts than MSA. This paper introduces the concepts of low correlation search and culprit vote to further improve the efficiency of the existing BF algorithms. High decoding performances and low iteration number are achieved by flipping those bits with low correlation as much as possible and introducing an additional syndrome vote procedure. As a result, the proposed algorithm can achieve significant decoding performance which is very close to the min-sum algorithm (MSA) but with much lower computation complexity.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.