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Journal of Optoelectronics·laser

Decoding technology and performance analysis of LDPC code over APD receiver for space optical communication

Yang Song

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Quasi-cyclic low-density parity-check(QC-LDPC) codes have excellent performance,but in order to obtain the optimal performance on a specific channel,the decoding method needs to be modified to adapt to the corresponding channel model.In this paper,we apply QC-LDPC codes into the channel based on avalanche photodiode(APD) receiver in the space optical communication system.The main work is to analyze the error performance and modify the belief propagation(BP) iterative decoding algorithm that uses probability density function(PDF) of the output sequences in the multiplicative noise channel model.We introduce a new method to compute the log-likelihood ratio(LLR) initialization for the LLR-BP decoding in the APD receiver channel.The simulation results show that the adaptation of QC-LDPC decoding on the accurate Webb-Gaussian model has better performance than that on approximate asymmetric Gaussian model,and almost no additional hardware complexity is increased.Moreover,the former can bring more than 1 dB net coding gain compared with the latter at the bit error rate(BER) of 10-6 under ideal channel conditions.

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Quasi-cyclic low-density parity-check(QC-LDPC) codes have excellent performance,but in order to obtain the optimal performance on a specific channel,the decoding method needs to be modified to adapt to the corresponding channel model.In this paper,we apply QC-LDPC codes into the channel based on avalanche photodiode(APD) receiver in the space optical communication system.The main work is to analyze the error performance and modify the belief propagation(BP) iterative decoding algorithm that uses probability density function(PDF) of the output sequences in the multiplicative noise channel model.We introduce a new method to compute the log-likelihood ratio(LLR) initialization for the LLR-BP decoding in the APD receiver channel.The simulation results show that the adaptation of QC-LDPC decoding on the accurate Webb-Gaussian model has better performance than that on approximate asymmetric Gaussian model,and almost no additional hardware complexity is increased.Moreover,the former can bring more than 1 dB net coding gain compared with the latter at the bit error rate(BER) of 10-6 under ideal channel conditions.
We study the decoding performance of low-density parity-check (LDPC) code based on Watermark scheme under different percentages of water-mark bits over 100 Gb/s differential quadrature phase shift keying (DQPSK) high-speed optical communication system. We also find the optimum percentage of water-mark bits according to the performance comparison. Simulation result shows an improvement of 0.5 dB net code gain by using the optimum Watermark scheme at a post-forward error correction bit error rate (BER) of 10-9, comparing with the traditional log-likelihood ratios belief propagation decoding algorithm. Also, for the same BER, there is a decrease in the number of iterations used in LDPC decoding.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
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.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
In the paper, we construct the non-binary quasi-cyclic low-density parity check (NB-QC-LDPC) code from the quasi-cyclic low-density parity check (QC-LDPC) code. The NB-QC-LDPC code over the Galois field GF(4) is suitable for 100Gb/s optical communication systems with QPSK or DQPSK modulation formats. We also study the bit error ratio (BER) performance of the NB-QC-LDPC code by using the Log-Fourier Sum and Product decoding algorithm (LFSPA). The numerical results show that the NB-QC-LDPC code with code length 500 can provide approximately 5.5dB coding gain at the BER of 910- and outperform QC-LDPC code by 0.7dB.
Several decoding algorithms based on oscillation Log-likelihood ratio (LLR) for Lowdensity parity-check (LDPC) codes are investigated in this paper, based on which, an improved decoding algorithm which uses the accumulated LLR as the final bit decision merit is proposed. This approach improves the decoding performance with only a very small increase in storage and computation. Combined with normalized belief-propagation (BP), two algorithms are given, which are named as accumulate normalized BP (ACC-Nor-BP) and compare-add normalized BP (CA-Nor-BP). The storage requirements and computational complexity of ACC-Nor-BP is lower than that of CA-Nor-BP and CA-BP, but performance is close to the CA-Nor-BP and better than CA-BP; therefore ACC-Nor-BP algorithm is an effectively improved BP algorithm which has a good balance between performance and complexity.