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Asia-Pacific Conference on Communications (APCC)

Improved augmented belief propagation decoding based on oscillation

Mu Zhou, Xiqi Gao

Published Oct 1, 2008• 3 citations
OpenAlex

Abstract

The augmented belief propagation (ABP) decoding using previous node selection methods for low-density parity check (LDPC) codes with a large number of short cycles is investigated on the additive white Gaussian noise (AWGN) channel in this paper. Based on the observations obtained from the investigation, a new node selection method is proposed. It is shown that oscillation plays an important role in the ABP decoding and needs to be controlled. It is also shown that the most possible variable nodes needed to stop oscillation in cycles should be selected and kept stable in correct values in the ABP decoding. A parallel decoding scheme is also proposed, which proves that a better method exists. Simulation results confirm that the new method outperforms the previous ones for short LDPC codes on the AWGN channel.

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The augmented belief propagation (ABP) decoding using previous node selection methods for low-density parity check (LDPC) codes with a large number of short cycles is investigated on the additive white Gaussian noise (AWGN) channel in this paper. Based on the observations obtained from the investigation, a new node selection method is proposed. It is shown that oscillation plays an important role in the ABP decoding and needs to be controlled. It is also shown that the most possible variable nodes needed to stop oscillation in cycles should be selected and kept stable in correct values in the ABP decoding. A parallel decoding scheme is also proposed, which proves that a better method exists. Simulation results confirm that the new method outperforms the previous ones for short LDPC codes on the AWGN channel.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
We propose an augmented belief-propagation (BP) decoder for low-density parity-check (LDPC) codes which can be used on memoryless or intersymbol-interference (ISI) channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol-selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared with the standard locally operating BP decoder) for short LDPC codes decoded on both memoryless and ISI Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.
We propose an augmented belief propagation (BP) decoder for low-density parity check (LDPC) codes which can be utilized on memoryless or intersymbol interference channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where, at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared to the standard locally-operating BP decoder) for short LDPC codes decoded on both memoryless and intersymbol interference Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.
In this paper, we propose an efficient implementation of the augmented belief propagation (ABP) algorithm for low-density parity-check codes over general memoryless channels. ABP is a multistage BP based decoder that uses a backtracking processing when decoding fails. The algorithm proceeds in two main steps, namely a symbol selection step and an augmented decoding step. The former is based on a criterion related both to the stopping subgraph connectivity and to the input reliability, while the latter can be either implemented using a list based or a greedy approach. Compared to the original implementation, we consider a different approach for both steps. First, the proposed node selection is only based on the dynamic of sign changes of the extrinsic messages at the variable nodes output. This enables us to consider indifferently general memoryless channels, while still taking into account the graph irregularity. Then, we propose a simple yet efficient implementation of the augmented decoding procedure based on pruning of the branching tree The proposed algorithm shows near maximum likelihood decoding performance while decreasing the overall complexity (computation and memory) of the original algorithm. Moreover, complexity-performance trade-off is an built-in feature for this kind of algorithm.
In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.