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Electronic and Mechanical Engineering and Information Technology

The modified reliability-based iterative majority-logic decoding algorithm for structured LDPC codes

Haiqiang Chen, Jinfeng Li, Tuanfa Qin

Published Aug 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1109/emeit.2011.6023701

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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.
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.
This paper presents a majority-logic based message-passing algorithm for decoding non-binary LDPC codes. Recently, many majority-logic decoding (MLGD) algorithms make huge efforts on reducing the computational complexity for decoding non-binary LDPC codes. Inspired by one step majority-logic decoding and q-ary sum-product algorithm, we devise a novel iterative double-reliability-based (IDRB) MLGD algorithm which carries out an efficient trade-off between decoding computational complexity and error performance. The proposed algorithm achieves a remarkable enhancement on error correct ability and yet requires only integer operations and finite field operations. Simulation results on two NB-LDPC codes show that we succeed in achieving significant coding gain compared with IHRB- and ISRB-MLGD with limited complexity increase.
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.
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.
Non-binary low-density parity-check (NB-LDPC) codes usually exhibit much better performance than their binary counterparts. Among NB-LDPC decoding algorithms, the iterative reliability-based majority-logic decoding (MLGD) algorithms are attractive for their low computation complexity, at the cost of performance degradation. In this brief, based on the improved iterative soft reliability-based (IISRB)-MLGD algorithm, we propose a clipped-modified (CM)-IISRB algorithm, which achieves better decoding performance with lower computational complexity. First, two modifications are introduced to the IISRB algorithm, which considerably reduces the decoding complexity with negligible performance loss. Second, an unsaturated-clipping method that facilitates significant performance improvement is presented. Simulation results show that the new algorithm outperforms the IISRB by about 0.2dB for the 256-ary (255, 175) example code. Moreover, based on a new storage reduction method, an optimized architecture is developed for the CM-IISRB algorithm. Synthesis results demonstrate that the proposed decoder can achieve very low hardware complexity, comparable to that of the iterative hard reliability-based (IHRB) decoder.
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.