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Improved controlled start-up stochastic LDPC decoder for efficient FPGA-based implementation

Ghania Zerari, Abderrezak Guessoum

Published Dec 1, 2015• 1 citation
Publisher

Abstract

This paper introduces a new and an improved controlled start-up stochastic (CSS) architecture of Low-Density Parity-Check (LDPC) decoding, to implement fully parallel FPGA-based decoders. The developed architecture uses a new variable nodes structure with larger internal memory lengths, to improve the convergence, without significant additional field programmable gate array (FPGA) resource. To validate the advantage of the proposed approach, a medium (1024, 512) and short (200, 100) codes are implemented. The results of Xilinx Virtex-6 VLX240T FPGA shoes that the variable node internal memories lengths can be increased from 2-bit, used in CSS and Delayed Stochastic (DS) decoders, to 64-bit without addition resource.

DOI
10.1109/intee.2015.7416861

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This paper introduces a new and an improved controlled start-up stochastic (CSS) architecture of Low-Density Parity-Check (LDPC) decoding, to implement fully parallel FPGA-based decoders. The developed architecture uses a new variable nodes structure with larger internal memory lengths, to improve the convergence, without significant additional field programmable gate array (FPGA) resource. To validate the advantage of the proposed approach, a medium (1024, 512) and short (200, 100) codes are implemented. The results of Xilinx Virtex-6 VLX240T FPGA shoes that the variable node internal memories lengths can be increased from 2-bit, used in CSS and Delayed Stochastic (DS) decoders, to 64-bit without addition resource.
This paper concerns a new and powerful Low-Density Parity-Check (LDPC) stochastic decoding algorithm, called Controlled Start-up Stochastic (CSS) decoding, to implement fully parallel LDPC decoders. The proposed algorithm uses a clever starting point computing method to improve the convergence as well as to reduce the latency of the decoding process, without a significant hardware complexity cost. Using this stochastic method, in low signal-to-noise ratio (SNR) region, a short LDPC code can outperforms the fixed point state-of-the-art (2048, 1723) LDPC code. To validate the performance of the proposed algorithm, a (48, 24) LDPC code are implemented on Xilinx Virtex-6 VLX240T field programmable gate array device, with and without the CSS method. The new algorithm provides a decoding speed seven times faster and a Bit Error Rate (BER) hundred times better at E3/N0=4.5 dB. In addition, the results provide a BER better than the 6 bits offset min-sum algorithm (OMSA) and better than the 6 bits sum-product algorithm (SPA) for the (2048, 1723) LDPC code, below E3/N0=3.9 dB and Eb/N0=4.3 dB respectively. The obtained results show that, the proposed algorithm is the first stochastic algorithm which can outperform the OMSA and SPA algorithms, with less hardware complexity.
Stochastic decoding is a new approach to iterative decoding on graphs. This paper presents a hardware architecture for fully parallel stochastic low-density parity-check (LDPC) decoders. To obtain the characteristics of the proposed architecture, we apply this architecture to decode an irregular state-of-the-art (1056,528) LDPC code on a Xilinx Virtex-4 LX200 field-programmable gate-array (FPGA) device. The implemented decoder achieves a clock frequency of 222 MHz and a throughput of about 1.66 Gb/s atEb/N0=4.25 dBE_{b}/N_{0}={\hbox {4.25~dB}}Eb​/N0​=4.25 dB(a bit error rate of10−810^{-8}10−8). It provides decoding performance within 0.5 and 0.25 dB of the floating-point sum-product algorithm with 32 and 16 iterations, respectively, and similar error-floor behavior. The decoder uses less than 40% of the lookup tables, flip-flops, and IO ports available on the FPGA device. The results provided in this paper validate the potential of stochastic LDPC decoding as a practical and competitive fully parallel decoding approach.
This paper proposes a hardware-and memoryefficient architecture for Low-Density Parity-Check (LDPC) decoding, targeting enhanced-performance applications with constrained resources.The design integrates two novel techniques: (i) the Variable Single minimum Min-Sum (VSMS) algorithm, which reduces hardware complexity by identifying the first minimum value and its position during check node processing, while improving error correction through a correction factor applied in variable node updates; and (ii) a memory splitting strategy that exploits the structural properties of LDPC codes to optimize memory usage.Implementation on a Xilinx Kintex UltraScale+ (xcku5p) FPGA demonstrates a reduction in storage requirements by over 46.2% compared to conventional decoders.Furthermore, the proposed decoder achieves a performance gain of up to 0.38 dB at a Bit Error Rate (BER) of 10⁻⁸, outperforming traditional Min-Sum-based approaches.
This paper studies low-complexity high-speed decoder architectures for quasi-cyclic low density parity check (QC-LDPC) codes. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. Enhanced partially parallel decoding architectures are proposed to linearly increase the throughput of conventional partially parallel decoders through introducing a small percentage of extra hardware. Based on the proposed architectures, a (8176, 7154) Euclidian geometry-based QC-LDPC code decoder is implemented on Xilinx field programmable gate array (FPGA) Virtex-II 6000, where an efficient nonuniform quantization scheme is employed to reduce the size of memories storing soft messages. FPGA implementation results show that the proposed decoder can achieve a maximum (source data) decoding throughput of 172 Mb/s at 15 iterations
Nonbinary low-density parity-check (NB-LDPC) codes constructed over GF(q) (q >; 2) can achieve higher coding gain than binary LDPC codes when the code length is moderate. A complete partial-parallel decoder architecture based on the Min-max algorithm is proposed for quasi-cyclic NB-LDPC codes in this paper. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm5) has also been synthesized on a Xilinx Virtex-2 Pro FPGA device. It can achieve a throughput of 9.30 Mbps when 15 decoding iterations are carried out.