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arXiv:2011.13147 · IEEE Transactions on Vehicular Technology

Generalized Mutual Information-Maximizing Quantized Decoding of LDPC Codes With Layered Scheduling

Peng Kang, Kui Cai, Xuan He, Shuangyang Li, Jinhong Yuan

Published Mar 28, 2022• 19 citations
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Abstract

In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm. In particular, we propose the MIM density evolution (MIM-DE) to construct the lookup tables (LUTs) for the node updates. The computational complexity and memory requirements are discussed and compared to the LUT decoder variants. For applications with low-latency requirement, we consider the layered schedule to accelerate the convergence speed of decoding quasi-cyclic LDPC codes. In particular, we develop the layered MIM-DE to design the LUTs based on the MS algorithm, leading to the MIM layered quantized MS (MIM-LQMS) decoder. An optimization method is further introduced to reduce the memory requirement for storing the LUTs. Simulation results show that the MIM quantized decoders outperform the state-of-the-art LUT decoders in the waterfall region with both 3-bit and 4-bit precision over the additive white Gaussian noise channels. For small decoding iterations, the MIM quantized decoders also achieve a faster convergence speed compared to the benchmarks. Moreover, the 4-bit MIM-LQMS decoder can approach the error performance of the floating-point layered BP decoder within 0.3 dB in the moderate-to-high SNR regions, over both the AWGN channels and the fast fading channels.

DOI
10.1109/tvt.2022.3162579

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arXiv:1904.06666•Apr 14, 2019•6 citations
In this paper, we propose a framework of the mutual information-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes by using simple mappings and fixed-point additions. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm. In particular, we propose the MIM density evolution (MIM-DE) to construct the lookup tables (LUTs) for the node updates. The computational complexity and memory requirements are discussed and compared to the LUT decoder variants. For applications with low-latency requirement, we consider the layered schedule to accelerate the convergence speed of decoding quasi-cyclic LDPC codes. In particular, we develop the layered MIM-DE to design the LUTs based on the MS algorithm, leading to the MIM layered quantized MS (MIM-LQMS) decoder. An optimization method is further introduced to reduce the memory requirement for storing the LUTs. Simulation results show that the MIM quantized decoders outperform the state-of-the-art LUT decoders in the waterfall region with both 3-bit and 4-bit precision over the additive white Gaussian noise channels. For small decoding iterations, the MIM quantized decoders also achieve a faster convergence speed compared to the benchmarks. Moreover, the 4-bit MIM-LQMS decoder can approach the error performance of the floating-point layered BP decoder within 0.3 dB in the moderate-to-high SNR regions, over both the AWGN channels and the fast fading channels.
In this paper, we propose a general framework of the mutual infomration-maximizing (MIM) quantized decoding for low-density parity-check (LDPC) codes, which can outperform the state-of-the-art lookup table (LUT) decoder by using simple mappings and fixed-point additions for the node updates. Our decoding method is generic in the sense that it can be applied to LDPC codes with arbitrary degree distributions, and it can be implemented based on either the belief propagation (BP) algorithm or the min-sum (MS) algorithm, leading to the MIM quantized BP (MIM-QBP) decoder and the MIM quantized MS (MIM-QMS) decoder, respectively. In particular, we approximate the check node (CN) update of the MIM-QBP decoder by a max-product operation and obtain the MIM-QMS decoder, which simplifies the decoder design and requires less resource consumption. To avoid the precision degradation, we introduce a dynamic reconstruction method to optimize the variable node update for different iterations. Some practical aspects of the proposed decoders such as the design and decoding complexity are also discussed. Simulation results show that the MIM-QBP decoder outperforms the LUT decoders in the waterfall region with both 3-bit and 4-bit precision. Moreover, the 4-bit MIM-QMS decoder can even surpass the floating-point BP decoder in the error-floor region.
In this paper, we propose a mutual information-maximizing quantized layered min-sum (MIM-QLMS) decoder for quasi-cyclic low-density parity-check (QC-LDPC) codes. Our proposed decoder operates similarly to a layered min-sum decoder with additional reconstruction and quantization operations by using single-input lookup tables (LUTs). In particular, we first develop the protograph-based MIM density evolution to design the LUTs, which may differ for each iteration and each edge in the protograph of the QC-LDPC codes. Furthermore, to minimize the memory requirement for storing the LUTs, we propose an optimization method to unify all LUTs into only four distinct LUTs, which can be used for all decoding iterations. To the best of our knowledge, the proposed MIM-QLMS decoders are the first class of layered finite alphabet iterative decoders (FAIDs) that are designed based on accurately tracking the probability distributions of the exchanged messages. Simulation results show that for 3-bit (resp. 4-bit) exchanged message precision, the proposed MIM-QLMS decoders can reasonably (resp. generally) outperform the state-of-the-art layered FAIDs and the layered normalized min-sum decoder, in terms of both the error rate performance and the average number of iterations.
In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified density evolution to design a unique set of lookup tables (LUTs) that can be used for rate-compatible LDPC codes. The constructed LUTs are optimized based on their discrepancy values and a merge function to reduce the memory requirement. Numerical results show that the proposed rate-compatible MIM-QMS decoder can reduce the memory requirement for decoding by up to 94.92 % compared to the benchmark rate-compatible LUT-based decoder with generally faster convergence speed. In addition, the proposed decoder can approach the performance of the floating-pointing belief propagation decoder within 0.15 dB.
A severe problem for mutual information-maximizing lookup table (MIM-LUT) decoding of low-density parity-check (LDPC) code is the high memory cost for using large tables, while decomposing large tables to small tables deteriorates decoding error performance. In this paper, we propose a systematic method, called mutual information- maximizing quantized belief propagation (MIM-QBP) decoding, to remove the lookup tables used for MIM-LUT decoding. Our method leads to a very practical decoder, namely the MIM-QBP decoder, which can be implemented based only on simple mappings and additions. Simulation results show that the proposed MIM-QBP decoder can outperform the state-of-the-art MIM-LUT decoder. Moreover, the MIM-QBP decoder with only 3 bits per message can outperform the floating-point belief propagation (BP) decoder at high signal-to-noise ratio (SNR) regions with a maximum of 10 iterations.
In this paper, we propose a finite alphabet iterative decoder (FAID) named rate-compatible mutual-information-maximizing quantized shuffled min-sum (RC-MIM-QSMS) decoder, for decoding quasi-cyclic low-density parity-check (QC-LDPC) codes with various code rates. Our proposed decoder exchanges the coarsely quantized messages represented by symbols from finite alphabets and adopts single-input lookup tables (LUTs) to implement the node updates. To construct the LUTs used for decoding, we first propose a modified density evolution by considering the shuffled schedule to generate the LUTs which vary with different layers and iterations. Furthermore, to reduce the memory requirement for storing the LUTs, we optimize the constructed LUTs into a unique set of LUTs that only change with different decoding iterations. To the best of our knowledge, the RC-MIM-QSMS decoder is the first one to integrate the rate compatibility of LDPC codes with the shuffled decoding schedule. Simulation results show that the proposed RC-MIM-QSMS decoder outperforms the floating-point shuffled belief propagation decoder in the high signal-to-noise region and achieves comparable convergence speed to other state-of-the-art FAIDs. Moreover, the RC-MIM-QSMS decoder is able to save up to 93.22% memory requirement compared to the benchmark MIM-FAIDs.
In this paper, we propose a class of finite alphabet iterative decoder (FAID), called mutual information-maximizing quantized belief propagation (MIM-QBP) decoder, for decoding regular low-density parity-check (LDPC) codes. Our decoder follows the reconstruction-calculation-quantization (RCQ) decoding architecture that is widely used in FAIDs. We present the first complete and systematic design framework for the RCQ parameters, and prove that our design with sufficient precision at node update is able to maximize the mutual information between coded bits and exchanged messages. Simulation results show that the MIM-QBP decoder can always considerably outperform the state-of-the-art mutual information-maximizing FAIDs that adopt two-input single-output lookup tables for decoding. Furthermore, with only 3 bits being used for each exchanged message, the MIM-QBP decoder can outperform the floating-point belief propagation decoder at the high signal-to-noise ratio regions when testing on high-rate LDPC codes with a maximum of 10 and 30 iterations.