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IEEE International Conference on Electronics, Circuits and Systems (ICECS)

A 5G-code based iterative Non-Binary LDPC decoder

Dimitris Chytas, Vassilis Paliouras

Published Nov 28, 2021• 1 citation
Publisher

Abstract

This paper proposes an iterative Non-Binary LDPC (NB-LDPC) decoder for non-binary codes constructed using the 5G base matrices. Motivated by the binary to non-binary replacement method, we construct NB-LDPC matrices devised directly from the 5G base matrices. Subsequently, we develop an iterative decoding scheme able to facilitate parallelism due to its low complexity and to offer high performance due to its fast convergence. BER plots comparing Min-sum binary decoder (over 5G base matrices) to our proposed NB decoder reveal a performance gain of 0.5 dB in certain cases. Furthermore, hardware synthesis results obtained for a 45-nm ASIC technology are provided in order to quantify the throughput rate and area requirements of the proposed architecture. It is shown that the proposed decoding architecture, because of its independence on the lifting size factor, can offer higher throughput rate than the binary ones for small codeword lengths and code rates. In addition, as Galois Field (GF) order increases, the throughput rate increases too. Finally, the throughput-to-area show that the proposed NB architecture is generally suitable for small lifting size factors.

DOI
10.1109/icecs53924.2021.9665548

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This paper proposes an iterative Non-Binary LDPC (NB-LDPC) decoder for non-binary codes constructed using the 5G base matrices. Motivated by the binary to non-binary replacement method, we construct NB-LDPC matrices devised directly from the 5G base matrices. Subsequently, we develop an iterative decoding scheme able to facilitate parallelism due to its low complexity and to offer high performance due to its fast convergence. BER plots comparing Min-sum binary decoder (over 5G base matrices) to our proposed NB decoder reveal a performance gain of 0.5 dB in certain cases. Furthermore, hardware synthesis results obtained for a 45-nm ASIC technology are provided in order to quantify the throughput rate and area requirements of the proposed architecture. It is shown that the proposed decoding architecture, because of its independence on the lifting size factor, can offer higher throughput rate than the binary ones for small codeword lengths and code rates. In addition, as Galois Field (GF) order increases, the throughput rate increases too. Finally, the throughput-to-area show that the proposed NB architecture is generally suitable for small lifting size factors.
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Compared to binary Low-Density Parity-Check (LDPC) codes, nonbinary LDPC (NB-LDPC) codes have better error correction performance under short-to-moderate block lengths or high-order modulations. Traditional min-sum-based soft decoding algorithms for NB-LDPC codes suffer from large computational complexity, which leads to inefficient hardware implementations. The Multiple-symbol-reliability weighted Bit-Reliability-Based (MwBRB) hard decoding algorithm achieves a good tradeoff between error correction performance and decoding complexity. However, efficient hardware implementations based on the MwBRB algorithm have not been investigated. In this brief, an improved layered MwBRB algorithm is first proposed, which results in faster convergence rate than the MwBRB algorithm. Then, an ultra-high-throughput low-complexity decoder architecture with an efficient partially parallel processing schedule is also presented. Finally, the proposed architecture is coded with RTL and synthesized under the TSMC 90-nm CMOS technology. The synthesis results demonstrate that the proposed decoder for a (837, 726) quasi-cyclic NB-LDPC code over GF(25) achieves a throughput of 21.66 Gbps and an area efficiency of 4.77 Gbps/M-gates under the TSMC 90-nm CMOS technology. The proposed decoder reaches a throughput more than 20 Gbps for the first time among the prior NB-LDPC decoders, and the area efficiency is far beyond the state-of-the-art designs.
Non-Binary Low-Density-Parity-Check codes (NB-LDPC) have shown superior performance but its huge complexity and low throughput prevent it from practical applications. This paper presents a novel architecture to implement a kind of high-throughput low-complexity irregular quasi-cyclic NB-LDPC decoder over GF (16) based on Extended Min-Sum (EMS) Algorithm. Double clocks are adopted in this paper. The low frequency clock at 60 MHz serves as the system clock and the high frequency clock at 480 MHz works for check nodes and variable nodes thus they can be reused 8 times during one system clock period as a result the complexity can be largely reduced. Synthesis result shows that the throughput can achieve 68.57 Mbps at 5 iterations. FPGA testing result shows that the decoder has little performance degradation compared with its floating model and it can provide about 0.5 dB coding gain compared with its binary LDPC code of the same block length. The proposed architecture can be conveniently extended to higher Galois Filed such as GF (64) or GF (256) and it can be applied for different code length and rate by modifying a slight part of the decoder. Compared with previous works, the decoder proposed in this paper is more efficient for practical applications.
Non-binary low-density parity-check (NB-LDPC) codes show higher error-correcting performance than binary low-density parity-check (LDPC) codes when the codeword length is moderate and/or the channel has bursts of errors. The need for high-speed decoders for future digital communications led to the investigation of optimized NB-LDPC decoding algorithms and efficient implementations that target high throughput and low energy consumption levels. We carried out a comprehensive survey of existing NB-LDPC decoding hardware that targets the optimization of these parameters. Even though existing NB-LDPC decoders are optimized with respect to computational complexity and memory requirements, they still lag behind their binary counterparts in terms of throughput, power and area optimization. This study contributes to an overall understanding of the state-of-the-art on application-specific integrated-circuit (ASIC), field-programmable gate array (FPGA) and graphics processing units (GPU) based systems, and highlights the current challenges that still have to be overcome on the path to more efficient NB-LDPC decoder architectures.
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Low Density Parity Check (LDPC) codes, is a linear block code having the decoding performance closer to Shannon's limit.Nonbinary LDPC is the class of binary LDPC, which works on the higher order Galois field.The decoding performance of non-binary (NB) LDPC is better than binary LDPC for moderate code lengths.The increased computation with the increased order of field is the major challenge in hardware realization of NB-LDPC.The extension of conventional sum-product algorithm, known as extended Min-Sum (EMS) algorithm, with reduced computational complexity is used in this paper.However, a tradeoff exists between computational complexity and decoding performance. This paper aims at reducing the computational complexity by focusing on the Parity Check Matrix (PCM) modifications. The bottleneck of the design is large memory requirement and more computation intensive. The modification in the EMS algorithm can be incorporated to design low complexity hardware architecture of NB-LDPC decoder.