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Journal of Circuits and Systems

A Modified belief propagation decoding algorithm for low-density parity-check codes based on oscillating iteration

Bao Jian-rong

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

According to no-convergence of falsely oscillating iteration in the low-density parity-check(LDPC) decoding at the range from medium to high SNRs(Signal to Noise Ratios),we propose a modified LDPC belief propagation(BP) decoding algorithm,i.e.soft value zero-forcing BP algorithm.By setting extrinsic information of the oscillating iteration bit nodes into zero,the impact on the iteratively decoding from false channel information is greatly reduced.And it also improves the performance of the decoding algorithm.Furthermore,a decision criterion of oscillating iteration nodes is presented to increase the accuracy of the decision.Simulation results show that the proposed algorithm has better decoding performance than that of the BP algorithm with the same iterations at medium and high SNRs.

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Aug 1, 2005•22 citations
According to no-convergence of falsely oscillating iteration in the low-density parity-check(LDPC) decoding at the range from medium to high SNRs(Signal to Noise Ratios),we propose a modified LDPC belief propagation(BP) decoding algorithm,i.e.soft value zero-forcing BP algorithm.By setting extrinsic information of the oscillating iteration bit nodes into zero,the impact on the iteratively decoding from false channel information is greatly reduced.And it also improves the performance of the decoding algorithm.Furthermore,a decision criterion of oscillating iteration nodes is presented to increase the accuracy of the decision.Simulation results show that the proposed algorithm has better decoding performance than that of the BP algorithm with the same iterations at medium and high SNRs.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
The paper presents a novel approach to reduce the bit error rate (BER) in iterative belief propagation (BP) decoding of low density parity check (LDPC) codes. The behavior of the BP algorithm is first investigated as a function of number of decoder iterations, and it is shown that typical uncorrected error patterns can be classified into 3 categories: oscillating, nearly-constant, or random-like, with a predominance of oscillating patterns at high Signal-to-Noise (SNR) values. A proposed decoder modification is then introduced based on tracking the number of failed parity check equations in the intermediate decoding iterations, rather than relying on the final decoder output (after reaching the maximum number of iterations). Simulation results with a rate ¿ (1024,512) progressive edge-growth (PEG) LDPC code show that the proposed modification can decrease the BER by as much as 10-to-40%, particularly for high SNR values.
To reduce the average number of decoding iterations in the region of low SNR(signal to noise ratio) and weaken the oscillation of the LLR(logarithm likelihood ratio),discovered the variation law of the check nodes'LLR and the checksum,in the error frame of the short and middle length LDPC codes.Based on the law,proposed an improved BP algorithm of LDPC decoding.In the algorithm,developed an early stopping criterion to reduce the average number of decoding iterations in the region of low SNR.And to improve the decoding performance by weakening the oscillation of the LLR,modified the update algorithm of check node.Simulation results show that,the algorithm reduces the number of iteration while the performance is not reduced in the region of low SNR,the decoding performance is improved while the number of iteration is not changed in the region of middle and high SNR.
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
In this paper we focus on the decoding error of the Log-Likelihood Ratio Belief Propagation (LLR-BP) decoding algorithm caused by oscillation. The decoding error caused by the oscillation is dominant in high b/N0 region. Oscillation of the LLR of the extrinsic value in the bit node process (ex-LLR) is propagated to the other bits and affects the whole decoding. The Ordered Statistic Decoding (OSD) algorithm is known to improve the error rate performance of the LLR-BP decoding algorithm. The OSD algorithm is performed by deciding the reliability of each bit based on a posteriori probability. In this paper we propose two decoding algorithms based on two types of oscillations of LLR for LDPC codes. One is the oscillation-based OSD algorithm with deciding the reliability of each bit based on oscillation. The other is the oscillation-based LLR-BP decoding algorithm that modifies ex-LLR based on oscillation. In the oscillation-based LLR-BP decoding algorithm, when ex-LLR oscillates, then we reduce the magnitude of this ex-LLR to reduce the effects on the other bits. Both algorithms improve the decoding errors caused by oscillation. From the computer simulations, we show that paying attention to the oscillation, we can improve the error rate performance of the LLR-BP decoding algorithm.