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International SoC Design Conference

Efficient Min-Max nonbinary LDPC decoding on GPU

Huyen Pham Thi, Sabooh Ajaz, Hanho Lee

Published Nov 1, 2014• 7 citations
Publisher

Abstract

This paper presents an novel modified Min-Max algorithm (MMMA) and an efficient implementation of an nonbinary LDPC (NB-LDPC) decoder on a graphics processing unit (GPU) to achieve both great flexibility and scalability. The MMMA for check node processing removes the multiplications over Galois-field in merger step and significantly reduces the decoding latency. The proposed MMMA provides a better BER performance than previous algorithm. The experimental results show that the GPU-based implementation of the proposed NB-LDPC decoder provides higher throughput and the coding gain under low 10−8BER comparted to CPU-based implementation.

DOI
10.1109/isocc.2014.7087640

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This paper presents an novel modified Min-Max algorithm (MMMA) and an efficient implementation of an nonbinary LDPC (NB-LDPC) decoder on a graphics processing unit (GPU) to achieve both great flexibility and scalability. The MMMA for check node processing removes the multiplications over Galois-field in merger step and significantly reduces the decoding latency. The proposed MMMA provides a better BER performance than previous algorithm. The experimental results show that the GPU-based implementation of the proposed NB-LDPC decoder provides higher throughput and the coding gain under low 10−8BER comparted to CPU-based implementation.
This paper presents an efficient implementation of a parallel block-layered nonbinary quasi-cyclic low-density parity-check (NB-QC-LDPC) decoder on a graphics processing unit (GPU) to achieve significant improvements in both flexibility and scalability. An efficient block-layered scheme and a data structure suitable for parallel computing are proposed to perform decoding on the GPU. The scheme is applied to a min-max decoding algorithm that exploits the inherent massive parallelization capabilities of NB-QC-LDPC decoder. The results of the proposed approach demonstrate that the layered scheme can be efficiently implemented in a GPU device. Moreover, experimental results show that the proposed GPU-based block-layered NB-QC-LDPC decoder provides a faster decoding runtime compare to CPU-based implementation and obtains a coding gain under a low 10-10 BER and low 10-7 FER.
Compared to binary low-density parity-check (LDPC) codes, nonbinary (NB) LDPC codes can achieve higher coding gain when the codeword length is moderate, but at the cost of higher decoding complexity. One major bottleneck of NB-LDPC decoding is the complicated check node processing. In this paper, a novel relaxed check node processing scheme is proposed for the min-max NB-LDPC decoding algorithm. Each finite field element of GF(2p) can be uniquely represented by a linear combination of p independent field elements. Making use of this property, an innovative method is developed in this paper to first find a set of the p most reliable variable-to-check messages with independent field elements, called the minimum basis. Then, the check-to-variable messages are efficiently computed from the minimum basis. With very small performance loss, the complexity of the check node processing can be substantially reduced using the proposed scheme. In addition, efficient VLSI architectures are developed to implement the proposed check node processing and the overall NB-LDPC decoder. Compared to the most efficient prior design, the proposed decoder for a (837, 726) NB-LDPC code over GF(25) can achieve 52% higher efficiency in terms of throughput-over-area ratio.
Nonbinary low-density parity-check (NB-LDPC) codes offer a superior error correction capability compared to the existing binary counterparts. However, there exist two major disadvantages in NB-LDPC decoders that they require substantial hardware resources, particularly at the check node unit (CNU), and high latency in the decoding process. In this brief, a novel minimal-set trellis min-max (MS-TMM) algorithm for NB-LDPC decoders is proposed to reduce the complexity of the CNU and enhance the decoding throughput. The decoder architecture based on the proposed MS-TMM algorithm is implemented for the (837, 726) NB-LDPC code over Galois field GF(32) using 90-nm CMOS technology. The implementation results show that the proposed architecture offers a great reduction in hardware complexity and highest efficiency compared to the state-of-the-art works. Additionally, the proposed decoder architecture is able to achieve a throughput of 1.704 Gbps and 2.254 Gbps at eight and six iterations respectively, which is a considerable improvement compared to the previous works.
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.
A flexible and scalable approach for LDPC decoding on CUDA based Graphics Processing Unit (GPU) is presented in this paper. Layered decoding is a popular method for LDPC decoding and is known for its fast convergence. However, efficient implementation of the layered decoding algorithm on GPU is challenging due to the limited amount of data-parallelism available in this algorithm. To overcome this problem, a kernel execution configuration that can decode multiple codewords simultaneously on GPU is developed. This paper proposes a compact data packing scheme to reduce the number of global memory accesses and parity-check matrix representation to reduce constant memory latency. Global memory bandwidth efficiency is improved by coalescing simultaneous memory accesses of threads in a half-warp into a single memory transaction. Asynchronous data transfers are used to hide host memory latency by overlapping kernel execution with data transfers between CPU and GPU. The proposed implementation of LDPC decoder on GPU performs two orders of magnitude faster than the LDPC decoder on a CPU and four times faster than the previously reported LDPC decoder on GPU. This implementation achieves a throughput of 160Mbps, which is comparable to dedicated hardware solutions.
Non-binary low-density parity check (NB-LDPC) codes are an extension of binary LDPC codes with significantly better performance.Although various kinds of low-complexity iterative decoding algorithms have been proposed, there is a big challenge for VLSI implementation of NBLDPC decoders due to its high complexity and long latency.In this brief, highly efficient check node processing scheme, which the processing delay greatly reduced, including Min-Max decoding algorithm and check node unit are proposed.Compare with previous works, less than 52% could be reduced for the latency of check node unit.In addition, the efficiency of the presented techniques is design to demonstrate for the (620, 310) NB-QC-LDPC decoder.