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Radio and communications technology

Comparison of several decoding algorithms for LDPC

Pei Bao-chen

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The performance and application future of the channel coding is determined by the decoding algorithms.The advantage of the LDPC is the decoding algorithm. This paper introduces several decoding algorithms for LDPC including Log-BP algorithm,Min-Sum algorithm and modified Min-Sum algorithm. Simulations are done for the decoding algorithms which is sent through additive white Gaussian noise (AWGN) channel. The analysis of the Bit Error Performance and the complexity for decoding algorithms is shown that Modified Min-Sum algorithm is the best algorithm which fits for the application of the hardware.

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The performance and application future of the channel coding is determined by the decoding algorithms.The advantage of the LDPC is the decoding algorithm. This paper introduces several decoding algorithms for LDPC including Log-BP algorithm,Min-Sum algorithm and modified Min-Sum algorithm. Simulations are done for the decoding algorithms which is sent through additive white Gaussian noise (AWGN) channel. The analysis of the Bit Error Performance and the complexity for decoding algorithms is shown that Modified Min-Sum algorithm is the best algorithm which fits for the application of the hardware.
Under the condition of the Additive White Gaussian Noise(AWGN) channel,both the hard and soft decision decoding algorithms suitable for LDPC codes are simulated and comparatively analyzed based on analyzing the decoding algorithm for LDPC codes.The variable message correlation for Log-Likelihood-Ratio Belief-Propagation(LLR-BP) algorithm in soft decision algorithm is decreased by introducing a multiplicative correction factor.The simulation results show that the decoding error-correction performance of the modified LLR-BP algorithm is greatly improved with little increase of computing complexity.
In this paper,several conventional decoding algorithms of LDPC(Low-Density Parity-Check) codes over Additive White Gaussian Noise(AWGN) channels are investigated,and an improved decoding algorithm based on integer operation is proposed. Compared to normalized min-sum algorithm,a modified factor to improve the decoding performance is designed according to the states of hard decision in each iteration. It is convenient for hardware implementation with integer operation.The simulation results show that the algorithm performs better than LLR BP decoding algorithm in 2.1 dB and decodes fast with low complexity.
The LDPC codes decoding algorithm over additive white gaussian noise(AWGN) channels was studied,and a min-sum algorithm based on integer operation was proposed for decoding LDPC codes.All the variables were fixed length integers in this algorithm,which was very convenient for hardware implementation.At the signal-to-noise ratios(SNR) above 3dB,its performance was equal to that of sum-product algorithm whose variables were high precision floating point numbers.Also,a coefficient was designed to modify the min-sum algorithm,whose decoding performance was improved greatly especially at low SNR.And another achievement had been found that this algorithm had a lower error floor at high SNR.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.
In this paper, we propose the modified minsum decoding algorithm of LDPC(Low-Density Parity-Check) code in the simplified difference-domain on the basis of detailed analysis of LDPC decoding algorithm in difference-domain. The simulation indicates that the proposed decoding algorithm offers almost no performance degradation compared with the BP(Belief Propagation) decoding algorithm in log-domain and the decoding algorithm in difference-domain and offers better performance than minsum decoding algorithm in log-domain and greatly reduces the computation complexity in AWGN(Additive White Gaussian Noise) channel and under BPSK(Binary Phase Shift Keying) modulation.
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.