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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Hybrid Message-Passing Algorithm and Architecture for Decoding Cyclic Non-binary LDPC Codes

Yichao Lu, Gang He, Guifen Tian, Satoshi Goto

Published Jan 1, 2013• 0 citations
Publisher

Abstract

Recently, non-binary low-density parity-check (NB-LDPC) codes starts to show their superiority in achieving significant coding gains when moderate codeword lengths are adopted. However, the overwhelming decoding complexity keeps NB-LDPC codes from being widely employed in modern communication devices. This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity. It achieves competitive error performance compared with conventional Min-max algorithm. Simulation result on a (255,174) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity NB-LDPC decoding algorithms. A partial-parallel NB-LDPC decoder architecture for cyclic NB-LDPC codes is also developed based on this algorithm. Optimization schemes are employed to cut off hard decision symbols in RAMs and also to store only part of the reliability messages. In addition, the variable node units are redesigned especially for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.

DOI
10.1587/transfun.e96.a.2652

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Recently, non-binary low-density parity-check (NB-LDPC) codes starts to show their superiority in achieving significant coding gains when moderate codeword lengths are adopted. However, the overwhelming decoding complexity keeps NB-LDPC codes from being widely employed in modern communication devices. This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity. It achieves competitive error performance compared with conventional Min-max algorithm. Simulation result on a (255,174) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity NB-LDPC decoding algorithms. A partial-parallel NB-LDPC decoder architecture for cyclic NB-LDPC codes is also developed based on this algorithm. Optimization schemes are employed to cut off hard decision symbols in RAMs and also to store only part of the reliability messages. In addition, the variable node units are redesigned especially for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.
This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity, while achieving competitive error performance compared with conventional min-max algorithm. Simulation result on a (255,175) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity non-binary LDPC (NB-LDPC) decoding algorithms. Based on this algorithm, a partial-parallel decoder architecture is implemented for cyclic NB-LDPC codes, where the variable node units are redesigned and the routing network is optimized for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts at the cost of higher decoding complexity when the codeword length is moderate. The recently developed iterative reliability-based majority-logic NB-LDPC decoding has better performance-complexity tradeoffs than previous algorithms. This paper first proposes enhancement schemes to the iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Compared to the IHRB algorithm, our enhanced (E-)IHRB algorithm can achieve significant coding gain with small hardware overhead. Then low-complexity partial-parallel NB-LDPC decoder architectures are developed based on these two algorithms. Many existing NB-LDPC code construction methods lead to quasi-cyclic or cyclic codes. Both types of codes are considered in our design. Moreover, novel schemes are developed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. In addition, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous designs based on the Min-max decoding algorithm, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts at the cost of higher decoding complexity when the codeword length is moderate. The recently developed iterative reliability-based majority-logic NB-LDPC decoding has better performance complexity tradeoffs than previous algorithms. This paper first proposes enhancement schemes to the iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Compared to the IHRB algorithm, our enhanced (E)-IHRB algorithm can achieve significant coding gain with small hardware overhead. Then low-complexity partial-parallel NB-LDPC decoder architectures are developed based on these two algorithms. Moreover, novel schemes are developed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. In addition, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. our proposed decoders have at least tens of times lower complexity with moderate coding gain loss.
When the code is not long, non-binary low-density parity- check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes at the cost of higher decoding complexity. The recently developed iterative reliability-based majority-logic NB- LDPC decoding can achieve better performance-complexity tradeoffs than previous algorithms. Many existing NB-LDPC code construction schemes lead to quasi-cyclic or cyclic codes. In this paper, efficient low- complexity NB-LDPC decoder architectures are developed for these two types of codes based on the newly proposed iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Particularly, novel schemes are designed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. Moreover, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous decoders based on the Min-max algorithm, the proposed IHRB-MLGD decoder architectures can achieve tens of times higher efficiency for codes with similar length and rate with moderate coding gain loss.
Non-binary low-density parity-check (NB-LDPC) codes have better error-correcting performance than their binary counterparts at the cost of higher decoding complexity when the code length is moderate. Compared to other NB-LDPC decoding algorithms, the iterative reliability-based majority-logic decoding can achieve better performance-complexity tradeoff. In this paper, an efficient partial-parallel shift-message decoder architecture is proposed for cyclic NB-LDPC codes based on the iterative soft reliability-based majority-logic decoding (ISRB-MLGD) algorithm. The message shifting is implemented by memories concatenated with variable node units to reduce the area. Although the accumulated soft reliabilities in the ISRB algorithm require longer word length, and accordingly longer critical path and larger memory, the decoder architecture and control logic can be simplified. Particularly, the check node units are modified so that the message switching network can be eliminated. Compared to the iterative hard reliability-based decoder for a (255, 175) NB-LDPC code over GF(28), the proposed ISRB decoder can achieve around 0.8dB coding gain with less than three times hardware complexity.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate. For the first time, this paper proposes a partial-parallel decoder architecture based on the Min-max algorithm for quasi-cyclic NB-LDPC codes. A novel boundary tracking based scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In addition, layered decoding is applied, and the hardware units are optimized to reduce the latency and area. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity analysis, the proposed decoder with 5 iterations for a (837,726) code over GF(25) can easily achieve 60 Mbps throughput on ASIC devices. It is 40% more efficient than prior designs.