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ACTA PHOTONICA SINICA

Optimization of Two BP-based Decoding Algorithms for LDPC Codes Based on MMSE Criterion under Weak Turbulence Channel

冷蛟锋 Leng Jiaofeng, 郝士琦 Hao Shiqi, 吕旭光 Lü Xuguang, 周建国 Zhou Jianguo, 赵楠翔 Zhao Nanxiang

Published Jan 1, 2012• 0 citations
Publisher

Abstract

Due to high complexity of Belief Propagation(BP) algorithm,several kind of BP-based simplified decoding algorithms are analyzed.Based on the Minimum Mean Square Erro(MMSE) criterion,optimal design of the scaled BP-based and offset BP-based algorithms is discussed.The theoretical formulas and numerical calculations on the optimal factors for these two BP-based algorithms are provdied.The simualtion resutls for the(6,3)regualr LDPC codes of lengths 1008 on the weak atmospheric turbulence channel demonstrate that the scaeld BP-based and offset BP-based aglorithms with the proposed factors are better than Min-Sum Algorithm,and even can achieve the performance better than that of the BP algorithm,and have lower complexity compared with BP algortihm.

DOI
10.3788/gzxb20124103.0277

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Due to high complexity of Belief Propagation(BP) algorithm,several kind of BP-based simplified decoding algorithms are analyzed.Based on the Minimum Mean Square Erro(MMSE) criterion,optimal design of the scaled BP-based and offset BP-based algorithms is discussed.The theoretical formulas and numerical calculations on the optimal factors for these two BP-based algorithms are provdied.The simualtion resutls for the(6,3)regualr LDPC codes of lengths 1008 on the weak atmospheric turbulence channel demonstrate that the scaeld BP-based and offset BP-based aglorithms with the proposed factors are better than Min-Sum Algorithm,and even can achieve the performance better than that of the BP algorithm,and have lower complexity compared with BP algortihm.
In this paper, we use the minimum mean square error (MMSE) criterion to design the scaled and offset belief propagation (BP)-based decoding algorithms for short low-density parity-check (LDPC) codes on the fast Rayleigh fading channel. Based on the MMSE criterion, the theoretical formulas and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (Chen et al., 2005 and Gallager, 1962) regular LDPC codes on the fast Rayleigh fading channel demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance better than that of the BP algorithm.
An improved decoding algorithm based on minimum mean square error(MMSE) for low-density parity-check(LDPC) codes is proposed.The new algorithm combines processing methods of two modified uniformly most powerful(UMP) BP-based algorithms(normalized UMP BP-based algorithm and offset UMP BP-based algorithm) and attains the corresponding normalization factor and offset factor according to MMSE criterion.Simulations indicate that,compared with the two above-mentioned algorithms,a gain of 0.03 dB can be achieved at bit error rate(BER) of 10-6 with the proposed algorithm when a(3,6) regular LDPC code of code length 1 008 and code rate 1/2 is used.
In this paper, a modified Belief Propagation (BP) decoding algorithm for low-density parity check (LDPC) codes based on minimum mean square error (MMSE) criterion is proposed. This modified algorithm uses linear equation to replace the hyperbolic function in the original BP algorithm and optimizes the linear approximation error based on MMSE criterion. As a result, compared with the standard BP algorithm the computational complexity is reduced significantly as the modified algorithm requires only addition operations to implement. Besides that simulation results show our modified algorithm can achieve an error performance very close to the BP algorithm on the additive white Gaussian noise channel.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
In this letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.
A uniformly most powerful (UMP) belief propagation (BP) based algorithm is referred to as a simplified version of a BP algorithm with reduced complexity but performance loss for low density parity check (LDPC) codes. To compensate the performance loss, the normalized BP based algorithm was proposed, where the normalization factor was derived by mean ratio or by minimizing the mean square error. In this paper, an improved novel normalized BP based algorithm is proposed. The normalization uses multiplicative factor instead of divisional factor. The novel scheme shows better performance than the existing normalized BP based algorithms while keeping the same implementation complexity. The simulation is done for two kinds of LDPC codes: random constructed codes and finite geometry codes. At high signal-to-noise ratio (SNR) region, the proposed scheme can achieve even better performance than BP algorithm for short length random constructed LDPC codes.