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Study on Decoding Algorithm for LDPC Codes under AWGN Channel

Yong Wang

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
Recently one decoding algorithm called as beyond belief propagation (BP) algorithm for LDPC Codes is derived using the knowledge of trapping set and different from standard BP algorithm, whose performance outperforms that of the latter over binary symmetric channel (BSC). However, the former is not suitable for additive white Gaussian noise (AWGN) channel. In this paper how to improve bit error rate (BER) performance of Beyond BP Algorithm is investigated over AWGN channel. It is found that this algorithm can be modified through setting appropriate penalty factor and obtains better performance than BP one over AWGN channel. The simulation results show dependently on choosing penalty factor modified Beyond BP Algorithm outperforms BP one over AWGN channel in high signal noise rate (SNR) region or almost whole SNR one and there are some differences for different code rates. Concretely, for medium or low code rate proposed algorithm can obtain more performance gain relative to high one when short frame is used.
This article compares the Bit Error Rate (BER) performance of soft and hard decision decoding algorithms of LDPC codes on AWGN channel at different code rates and Signal to Noise Ratio (SNR) levels. Even though, hard decision decoding algorithm is computationally simple, its BER performance is not appreciable. Devising soft decision decoding algorithms which are simple and good in BER performance requires comparison of probabilistic and log domain methods. Towards this, a code word is generated through modulo(2) addition between message bits and generator matrix. After Binary Phase Shift Keying (BPSK) modulation the AWGN noise is introduced to the modulated code word. BER performance is computed by comparing the message decoded by soft and hard decision algorithms with the transmitted message. The experiment is conducted in MATLAB. Soft decision decoding algorithm in log domain provides better BER performance than hard decision decoding algorithm regardless of the SNR level.
At present, Low-Density Parity-Check (LDPC) codes widely used in many fields of communications have the best performance of all the Error Correcting Codes (ECC). This paper mainly studies the decoding algorithms of LDPC. It proposes an improved algorithm which is named Check-Variable nodes Hybrid(CVH) algorithm on the basis of the existing algorithms. The CVH algorithm can reduce the computational complexity during the check-node update while overcome with the correlation between the variable-node news in a code with circles. As well as, comparing with the original algorithms the performance of the new one saves 0.1 and 0.3 dB than Log-likelihood Ratios (LLR) Belief Propagation (BP) and BP - based algorithms under Additive White Gaussian Noise (AWGN) channel when the Bit Error Rate (BER) falls to through the simulation. This point shows that this algorithm can increase the decoding performance and reduce the error rate effectively.
The decoding of the LDPC codes by the belief propagation(BP) algorithm for the additive white Gaussian noise(AWGN) channel requires an accurate estimation of the signal-to-noise ratio(SNR) for the computation of the a posteriori probabilities(APPs) of the received bits that serve as the decoder inputs.An erroneous estimation of SNR at the decoder is referred to as SNR mismatch.In this paper,we study the effects of the SNR mismatch on the bit error rate(BER) performance of the LDPC codes for the AWGN channel.The correct-factor function is achieved by approximating the check node update equation of the BP algorithm.It is concluded that the effect of SNR under-estimation on decoding is more sensitive than SNR over-estimation based on the correct-factor function.The simulation results also indicate the conclsion.
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.