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Beijing Youdian Xueyuan xuebao

An Improved Decoding Algorithm for LDPC Codes

XU Yong-tai

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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 order to make up for the performance defects of UMP BP-Based decoding algorithm relative to LLR BP decoding algorithm,this paper proposed a modified decoding algorithm.Parameters of the proposed algorithm which combined the advantage of Normalized BP-Based decoding algorithm and Offset BP-Based decoding algorithm were calculated according to minimum mean square error rule.The simulation results show that the LDPC decoding performance of modified UMP BP-Based decoding algorithm is more effective than that of UMP BP-Based decoding algorithm,Normalized BP-Based decoding algorithm and Offset BP-Based decoding algorithm under the same condition of bit error rate.
In order to make up for the performance defects of UMP BP-Based decoding algorithm relative to LLR BP decoding algorithm, a modified UMP BP-Based decoding algorithm is proposed. Parameters of the proposed algorithm are confirmed according to minimum mean square error rule and it has the generality for decoding of all LDPC codes. The simulation results show that the LDPC decoding performance of modified UMP BP-Based decoding algorithm is more effective than that of UMP BP-Based decoding algorithm, Normalized BP-Based decoding algorithm and Offset BP-Based decoding algorithm under the same condition of bit error rate.
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.
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.
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.
In order to reduce the performance loss of UMP BP-based decoding algorithm relative to LLR-BP decoding algorithm,an improved UMP BP-based decoding algorithm is proposed.When the check nodes process the message,the normalized BP-based decoding algorithm and offset BP-based decoding algorithm are integrated effectively by setting a correction factor and an offset factor reasonably.When the variable nodes process the message,an oscillation compensation algorithm based on LLR-BP decoding algorithm is introduced.Simulation results show that based on the irregular LDPC codes and under the condition of the same bit error rate within a certain range,the improved UMP BP-based decoding algorithm improves the decoding performance greatly compared with the three decoding algorithms which are based on UMP BP,normalized BP and offset BP decoding algorithms,respectively,and therefore quite efficiently approaches to the LLR-BP decoding algorithm which has excellent performance.