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IEEE Transactions on Communications

Comparisons Between Reliability-Based Iterative Min-Sum and Majority-Logic Decoding Algorithms for LDPC Codes

Haiqiang Chen, Kai Zhang, Xiao Ma, Baoming Bai

Published Jun 28, 2011• 23 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2011.060911.100065

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2014•0 citations
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, we present a modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for structured LDPC codes. The MRBI-MLGD algorithm uses the initial rather than the last updated message value in the iteration procedure, which works resembling a turbo decoder. Furthermore, the MRBI-MLGD algorithm is an integer message passing algorithm and mainly requires logical and integer operations. Simulation results show that, compared to the original one, the MIRB-MLGD algorithm can achieve better performance with slightly increased computational complexity.
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.
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.
Recently, an iterative soft information reliability-based majority-logic (ISRB-MLG) decoding algorithm was proposed for Euclidean geometry LDPC (EG-LDPC) and Projective geometry LDPC (PG-LDPC) codes. This paper first presents an iterative soft information reliability-based min-sum (ISRB-MS) decoding algorithm based on ISRB-MLG and traditional min-sum decoding algorithm. The performance of ISRB-MS algorithm is greatly improved with a little more complexity than ISRB-MLG algorithm, it mainly needs integer additions and logical operations. Different from traditional min-sum decoding algorithm, the extrinsic information transfer of ISRB-MS algorithm is simplified, we use the full information that all check nodes pass rather than the extrinsic information to update the bit nodes information. Then a modified iterative soft information reliability-based min-sum (MISRB-MS) decoding algorithm is proposed. Compared to (ISRB-MS) algorithm, MISRB-MS algorithm multiplies a scaling factor, so it needs some extra multiplication, but it achieves better performance. Simulation results show that the two algorithms achieve excellent performance and fast convergence rate, they only needs about 10 iterations, if an appropriate scaling factor is chosen, the performance of MISRB-MS algorithm very closes to that of sum-product algorithm (SPA).
In this paper, we present an iterative reliability-based modified majority-logic decoding algorithm for two classes of structured low-density parity-check codes. Different from the conventional modified one-step majority-logic decoding algorithms, we design a turbo-like iterative strategy to recover the performance degradation caused by the simply flipping operation. The main computational loads of the presented algorithm include only binary logic and integer operations, resulting in low decoding complexity. Furthermore, by introducing the iterative set, a very small proportion (less than 6%) of variable nodes are involved in the reliability updating process, which can further reduce the computational complexity. Simulation results show that, combined with the factor correction technique and a well-designed non-uniform quantization scheme, the presented algorithm can achieve a significant performance improvement and a fast decoding speed, even with very small quantization levels (3-4 bits resolution). The presented algorithm provides a candidate for trade-offs between performance and complexity.
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.