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IEEE Transactions on Circuits & Systems II Express Briefs

Efficient Implementation of a Threshold Modified Min-Sum Algorithm for LDPC Decoders

Yanfang Liu, Wei Tang, David G. M. Mitchell

Published Jun 11, 2020• 18 citations
Publisher

Abstract

In this brief, we present a hardware efficient implementation of a threshold modified min-sum algorithm (MSA) to improve the performance of a low density parity-check (LDPC) decoder. The proposed architecture introduces a novel lookup table based threshold attenuation technique, called threshold attenuated MSA (TAMSA). The proposed TAMSA implementation is shown to improve bit error rate (BER) performance compared to the conventional AMSA and MSA. Furthermore, a layered version of the TAMSA implementation is investigated to reduce hardware cost. Utilizing circuit optimization techniques, including a parallel computing structure, the proposed layered TAMSA field-programmable gate array (FPGA) implementation results show that the modified architecture requires no extra circuit power or circuit area compared to conventional AMSA, and only 0.07% extra leaf cells compared to conventional MSA.

DOI
10.1109/tcsii.2020.3001601

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IEICE Electronics Express•Jan 1, 2015•3 citations
In this brief, we present a hardware efficient implementation of a threshold modified min-sum algorithm (MSA) to improve the performance of a low density parity-check (LDPC) decoder. The proposed architecture introduces a novel lookup table based threshold attenuation technique, called threshold attenuated MSA (TAMSA). The proposed TAMSA implementation is shown to improve bit error rate (BER) performance compared to the conventional AMSA and MSA. Furthermore, a layered version of the TAMSA implementation is investigated to reduce hardware cost. Utilizing circuit optimization techniques, including a parallel computing structure, the proposed layered TAMSA field-programmable gate array (FPGA) implementation results show that the modified architecture requires no extra circuit power or circuit area compared to conventional AMSA, and only 0.07% extra leaf cells compared to conventional MSA.
For decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs), i.e., in the “waterfall region” of the bit error rate curve. This paper demonstrates that, for quantized decoders, MSA actually outperforms AMSA and OMSA in the “error floor” region, and that all three algorithms suffer from a relatively high error floor. This motivates the introduction of a modified MSA that is designed to outperform MSA, AMSA, and OMSA across all SNRs. The new algorithm is based on the assumption that trapping sets are the major cause of the error floor for quantized LDPC decoders. A performance estimation tool based on trapping sets is used to verify the effectiveness of the new algorithm and also to guide parameter selection. We also show that the implementation complexity of the new algorithm is only slightly higher than that of AMSA or OMSA. Finally, the simulated performance of the new algorithm, using several classes of LDPC codes (including spatially coupled LDPC codes), is shown to outperform MSA, AMSA, and OMSA across all SNRs.
It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signal-to-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.
Min sum algorithm (MSA) is widely used for decoding Low Density Parity Check (LDPC) codes in many modern Digital Video Broadcasting (DVB) as a simplification for Sum Product Algorithm (SPA) which greatly reduce the implementation complexity. This paper presents a design of modified variable scaling min sum LDPC decoding algorithm for DVB-S2/S2X/T2. The proposed design is a combination between the variable Normalized Min Sum Algorithm (NMSA) and the Offset Min Sum Algorithm (OMSA) which provides a trade-off between decoding complexity and error correcting performance. It improves the use of the Min Sum Algorithm (MSA) by 39%. A proposal for how to implement the proposed algorithm using FPGA is also introduced. The structure used is partially parallel layered decoder architecture.
The objective of this work is to propose a modified Min-Sum decoding Low Density Parity Check (LDPC) algorithm and perform the hardware implementation analysis of Min-Sum, optimized Min-Sum and modified Min-Sum decoders. The Min-Sum algorithm mainly uses the process of finding the minimum and addition. Hence the number of multiplications is drastically reduced which helps in reducing the complexity of implementation. Adding an optimisation factor to the decoder increases the accuracy and reduces the number of iterations required to compute the decoded message. Hence the process of optimisation reduces the overall decoding time required. Modified Min-Sum algorithm is proposed to further improve the performance by decreasing the number of stages in the decoding process which reduces the complexity in Field Programmable Gate Array (FPGA) implementation.
This paper proposes a low-complexity min-sum algorithm for decoding low-density parity-check codes. It is an improved version of the single-minimum algorithm where the two-minimum calculation is replaced by one minimum calculation and a second minimum emulation. In the proposed one, variable correction factors that depend on the iteration number are introduced and the second minimum emulation is simplified, reducing by this way the decoder complexity. This proposal improves the performance of the single-minimum algorithm, approaching to the normalized min-sum performance in the water-fall region. Also, the error-floor region is analyzed for the code of the IEEE 802.3an standard showing that the trapping sets are decoded due to a slow down of the convergence of the algorithm. An error-floor free operation below BER=10-15is shown for this code by means of a field-programmable gate array (FPGA)-based hardware emulator. A layered decoder is implemented in a 90-nm CMOS technology achieving 12.8 Gbps with an area of 3.84 mm2.
Conditional termination check min-sum algorithm (MSA) using the difference of the first two minima is proposed for faster decoding speed and lower power consumption of low-density parity-check (LDPC) code decoders. Judging from the size of the difference in LDPC decoding scheduling, the proposed method dynamically decides whether the termination checking steps will be skipped or not. The simulation results show that the decoding speed is improved up to 7%, and the power consumption is reduced by up to 16.43% without any loss of error correcting performance. Also, the additional hardware cost of the proposed method is negligible compared to conventional LDPC decoders.