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International Conference on Wireless Communications, Networking and Mobile Computing

Modified APP-Based Decoding Algorithm for Low-Density Parity Check Codes

Xinran Wang, Yan Zhang, Jinlei Chen

Published Sep 1, 2011• 3 citations
Publisher

Abstract

In this paper, a modified a posteriori probability (APP) based algorithm for the decoding of low- density parity-check (LDPC) codes is proposed. The modified APP-based algorithm utilizes an additional processing in the bit nodes to improve the accuracy instead of the check nodes normalization performed in normalized APP-based algorithm. The modified APP- based algorithm yields desirable trade-off between performance and decoding complexity.

DOI
10.1109/wicom.2011.6039977

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•Oct 24, 2018•1 citation
In this paper, a modified a posteriori probability (APP) based algorithm for the decoding of low- density parity-check (LDPC) codes is proposed. The modified APP-based algorithm utilizes an additional processing in the bit nodes to improve the accuracy instead of the check nodes normalization performed in normalized APP-based algorithm. The modified APP- based algorithm yields desirable trade-off between performance and decoding complexity.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.
In this paper we explore the impact of self-correction (SC) modification on performance of a posteriori probability (APP) based decoding algorithm for LDPC codes. Influence of self-correction technique was investigated for decoders with 3, 2 and 1 bit input quantization. It was shown that performance of decoders with quantized input can be significantly improved in comparison with regular APP-based decoding algorithm, and in some cases with Min-Sum algorithm. Convergence of algorithm is almost the same as for Min-Sum decoding. Performance and convergence results are presented for two CCSDS (8176, 7156) and IEEE 802.3an (2048, 1723) LDPC codes for APP-based, SC APP-based and Min-Sum decoding algorithms.
A modified Min-Sum algorithm for low-density parity check codes is proposed in this paper. The inaccurate check node messages of the Min-Sum algorithm compared to the belief propagation (BP) algorithm are compensated by modified variable node messages, which is different from the normalized Min-Sum algorithm. The modified factor is obtained before decoding program and only one extra multiplication is needed in one cycle. So the increased complexity is fairly low. The simulation results show that the bit error rate (BER) and average number of iteration of the modified Min-Sum algorithm are very close to the BP algorithm, the modified algorithm can improve the BER performance compared to the Min-Sum algorithm while added complexity slightly.
The LDPC (Low-Density Parity-Check) decoder must operate soft decisions calculated using: LLR (Log-Likelihood Ratio) or APP (A Posteriori Probability) according to the decoding algorithm used. The exact calculation of these decisions for high order constellations involves complicated operations. In this work, a method to simplify the APP calculation is introduced. It is programmed to adapt as perfectly as possible the transmission system to the channel type in question. This method leads to simplify the implementation of the transmission system. Simulation results show that, under the Gaussian channel, the simplified APP algorithm for 16-QAM achieves the same performance that obtained with the exact APP, while for 64-QAM we have a small performance degradation. The same simplified APP algorithm that used for the Gaussian channel can be applied, with minor operations added, for Rayleigh channel, and it shows a small performance loss with respect to the exact APP.