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IEEE Communications Letters

Reliability-Based Iterative Decoding Algorithm for LDPC Codes With Low Variable-Node Degree

Joan Marc Català Pérez, Francisco García-Herrero, Javier Valls, Kai Liu, Shu Lin

Published Oct 15, 2014• 1 citation
Publisher

Abstract

In this letter, a new reliability-based iterative majority-logic decoding (RBI-MLGD) algorithm that computes the extrinsic information of previous iterations of the variable node is proposed. This decoding algorithm is called historical-extrinsic reliability-based iterative decoder (HE-RBID) and improves the bit-error-rate performance of the previous RBI-MLGD. HE-RBID is particularly interesting for codes with a low degree of variable node, where traditional RBI-MLGD algorithms do not provide a good behavior. HE-RBID ensures a good performance without searching for the minimum at the check node and only by exchanging 1-bit messages between variable and check nodes.

DOI
10.1109/lcomm.2014.2363112

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In this letter, a new reliability-based iterative majority-logic decoding (RBI-MLGD) algorithm that computes the extrinsic information of previous iterations of the variable node is proposed. This decoding algorithm is called historical-extrinsic reliability-based iterative decoder (HE-RBID) and improves the bit-error-rate performance of the previous RBI-MLGD. HE-RBID is particularly interesting for codes with a low degree of variable node, where traditional RBI-MLGD algorithms do not provide a good behavior. HE-RBID ensures a good performance without searching for the minimum at the check node and only by exchanging 1-bit messages between variable and check nodes.
A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M)RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M)RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.
In this paper, an adaptive decoding algorithm for majority-logic decodable LDPC codes is present based on a recent work by Chen et al. Different from the RBI-MSD algorithm, the presented adaptive reliability-based iteration min-sum decoding algorithm does not need to predesignate the scaling factor, which is optimized by discretized density evolution. In the adaptive RBIMSD algorithm, an adaptive scaling factor is induced for each check node to modify the extrinsic message. The adaptive scaling factor is computed by the ratio of the second minimum and the maximum value among the message, which is received by the check nodes. Simulation results show that, the performance of the adaptive RBI-MSD algorithm is almost as well as that of the original RBI-MSD algorithm but with a little (or negligible) computation increase.
Majority-logic algorithms are devised for decoding non-binary LDPC codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-LDPC codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical LDPC codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.
Non-binary low-density parity-check (NB-LDPC) codes tend to exhibit much better performance than their binary counterparts while suffering from very high computational complexity. As a type of hard-decision NB-LDPC decoding algorithm, the iterative reliability-based majority-logic decoding (IRB-MLGD) algorithms are attractive for their low computation complexity, coming with obvious performance degradation. Aiming at improving the error-correction performance, in this paper, we introduce few redundant bits to the original NB-LDPC encoding and the corresponding checksum operations to the improved iterative soft reliability-based (IISRB)-MLGD. Based on the joint coding and decoding method, the obtained redundancy-aided (RA)-IISRB decoding algorithm shows significant performance improvement while maintaining the low-complexity property. Simulation results demonstrate that the proposed algorithm can achieve a more than 1.0dB extra coding gain over the original IISRB with a slight decrease of code rate.
In this paper, we present a reliability-based iterative proportionality-logic decoding algorithm for two classes of structured low-density parity-check (LDPC) codes. The main contributions of this paper include: 1) Syndrome messages instead of extrinsic messages are processed and exchanged between variable nodes and check nodes, which can reduce the decoding complexity; 2) a more flexible decision mechanism is developed in which the decision threshold can be self-adjusted during the iterative process. Such decision mechanism is particularly effective for decoding the majority-logic decodable codes; 3) only part of the variable nodes satisfying the pre-designed criterion are involved for the presented algorithm, which is in the proportionality-logic sense and can further reduce the computational complexity. Simulation results show that, when combined with factor correction techniques and appropriate proportionality parameter, the presented algorithm performs well and can achieve fast decoding convergence rate while maintaining relative low decoding complexity, especially for small quantized levels (3-4 bits). The presented algorithm provides a candidate for those application scenarios where the memory load and the energy consumption are extremely constrained.
A reliability-based iterative majority-logic decoding algorithm for regular low-density parity-check (LDPC) codes was recently proposed by Huang et al. In this paper we present an improved version of that algorithm by introducing a different reliability measure for each check-sum of the parity-check matrix, and taking it into account in the computation of the extrinsic information that is used to update the reliability measure of each received bit in each iteration. Some simulations results are given, which show that the new algorithm, while requiring very little additional computational complexity, not only achieves a considerable error performance gain over the standard one, but also, importantly, outperforms the iterative decoding based on belief propagation (IDBP), especially for short and medium block length finite-geometry (FG) LDPC codes.