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Journal of Southwest University

Research of LDPC Decoding Based on Modified LLR BP Algorithm

Hua Qu

Published Jan 1, 2009• 3 citations
OpenAlex

Abstract

The Tanner graph of long LDPC codes usually has no loops and LLR BP algorithm is the best soft-decision decoding algorithm.But the Tanner graph of short LDPC codes usually has loops,so information within variable nodes doesn't satisfy the condition of independent identical distribution and the decoding performance of LLR BP algorithm will decrease.In this paper,a modified LLR BP algorithm is proposed,which can reduce the relativity of information within variable nodes by adjusting the iterative process of variable nodes information.Simulation results show that the LDPC decoding performance of the modified LLR BP algorithm is more effective than that of LLR BP algorithm,Normalized BP algorithm and offset BP algorithm.

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The Tanner graph of long LDPC codes usually has no loops and LLR BP algorithm is the best soft-decision decoding algorithm.But the Tanner graph of short LDPC codes usually has loops,so information within variable nodes doesn't satisfy the condition of independent identical distribution and the decoding performance of LLR BP algorithm will decrease.In this paper,a modified LLR BP algorithm is proposed,which can reduce the relativity of information within variable nodes by adjusting the iterative process of variable nodes information.Simulation results show that the LDPC decoding performance of the modified LLR BP algorithm is more effective than that of LLR BP algorithm,Normalized BP algorithm and offset BP algorithm.
In iterations processing of LLR BP algorithm for LDPC decoding,the computational of check nodes renewal is high;The decoding performance will be reduced,while there are lots of loops in short LDPC codes.According to these problems,a new LLR BP decoding algorithm based on Hybrid Check-Variable offset processing is proposed in this paper.Decrease complexity by adjusting amplitudes of check nodes processing and relativity of variable nodes by adjusting their information.Simulation results show that this improved decoding algorithm,compared with LLR BP algorithm,is consideration to decoding performance of LDPC and computational complexity.
In iterations processing of LLR BP algorithm for LDPC decoding, the computational complexity of check nodes renewal is high; The decoding performance will be reduced, while there are lots of loops in short LDPC codes. According to these problems, a new LLR BP decoding algorithm based on Hybrid Check-Variable offset processing is proposed in this paper. Decrease complexity by adjusting amplitudes of check nodes processing and relativity of variable nodes by adjusting their information. Simulation results show that this improved decoding algorithm, compared with LLR BP algorithm, is consideration to decoding performance of LDPC and computational complexity.
In order to make up for the performance defects of Min-sum decoding algorithm relative to LLR BP decoding algorithm and reduce implementation complexity of LLR-BP algorithm,a modified Min-sum decoding algorithm is proposed.When the check nodes process the message,parameters of the proposed algorithm are confirmed according to minimum mean square error rule,and the normalized BP-based decoding algorithm and the offset BP-based decoding algorithm are integrated effectively.At the same time,we introduce the correction factor and the offset factor into this algorithm reasonably.The simulation results show that decoding performance of modified Min-sum decoding algorithm is more effective than that of Min-sum decoding algorithm,normalized BP-based decoding algorithm and offset BP-based decoding algorithm under the same condition of bit error rate,and it approaches to the performance of LLR-BP decoding algorithm.
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.
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 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.