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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

Efficient decoder design for high-throughput LDPC decoding

Zhiqiang Cui, Zhongfeng Wang, Xinmiao Zhang, Qingwei Jia

Published Nov 1, 2008• 24 citations
Publisher

Abstract

In this paper, a matrix permutation scheme is proposed to convert a generic QC-LDPC code to a shift-structured LDPC code. Thus, efficient VLSI architectures can be developed to achieve very high decoding throughput with low hardware complexity. Furthermore, novel implementation schemes for min-sum algorithm based column-layered decoding are presented. The proposed approaches provide very efficient ways for high-speed decoder design of generic QC-LDPC codes.

DOI
10.1109/apccas.2008.4746351

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In this paper, a matrix permutation scheme is proposed to convert a generic QC-LDPC code to a shift-structured LDPC code. Thus, efficient VLSI architectures can be developed to achieve very high decoding throughput with low hardware complexity. Furthermore, novel implementation schemes for min-sum algorithm based column-layered decoding are presented. The proposed approaches provide very efficient ways for high-speed decoder design of generic QC-LDPC codes.
Layered decoding is well appreciated in low-density parity-check (LDPC) decoder implementation since it can achieve effectively high decoding throughput with low computation complexity. This work, for the first time, addresses low-complexity column-layered decoding schemes and very-large-scale integration (VLSI) architectures for multi-Gb/s applications. At first, the min-sum algorithm is incorporated into the column-layered decoding. Then algorithmic transformations and judicious approximations are explored to minimise the overall computation complexity. Compared to the original column-layered decoding, the new approach can reduce the computation complexity in check node processing for high-rate LDPC codes by up to 90% while maintaining the fast convergence speed of layered decoding. Furthermore, a relaxed pipelining scheme is presented to enable very high clock speed for VLSI implementation. Equipped with these new techniques, an efficient decoder architecture for quasi-cyclic LDPC codes is developed and implemented with 0.13 µm VLSI implementation technology. It is shown that a decoding throughput of nearly 4 Gb/s at a maximum of 10 iterations can be achieved for a (4096, 3584) LDPC code. Hence, this work has facilitated practical applications of column-layered decoding and particularly made it very attractive in high-speed, high-rate LDPC decoder implementation.
Low-density parity-check (LDPC) codes are one of the most promising error-correcting codes approaching Shannon capacity and have been adopted in many applications. However, the efficient implementation of high-throughput LDPC decoders adaptable for various channel conditions still remains challenging. In this paper, a low-complexity reconfigurable VLSI architecture for high-speed LDPC decoders is presented. Shift-LDPC codes are incorporated within the design and have shown not only comparable decoding performance to computer-generated random codes but also high hardware efficiency in high-speed applications. The single-minimum Min-Sum decoding scheme and the nonuniform quantization scheme are explored to reduce the complexity of computing core and the memory requirement. The well-known Benes network is employed to construct the configurable permutation network to support multiple shift-LDPC codes with various code parameters. The ASIC implementation results of an (8192, 7168) (4, 32)-regular shift-LDPC decoder demonstrate a maximum decoding throughput of 3.6 Gbits/s at 16 iterations, which outperforms the state-of-the-art design for high-speed flexible LDPC decoders by many times with even less hardware.
In this paper, we propose an extended layered decoding approach for low density parity check (LDPC) codes. Compared to conventional layered decoding algorithms, the proposed approach has no constraint in the column weight of each layer. Hence, it enables more flexibility in high-throughput LDPC decoder design with layered decoding. Simulations on structured and random LDPC codes show that the proposed decoding method achieves significantly faster convergence and slightly better error correction performance than the conventional two phase massage passing sum-product algorithm. We also propose an efficient highly parallel decoder architecture for generic quasi-cyclic LDPC codes to facilitate the practical application of the proposed decoding scheme.
VLSI-based decoding of geometric low-density parity-check (LDPC) codes using the sum-product or min-sum algorithms is known to be very difficult due to large memory requirement and high interconnection complexity caused by high variable and column degrees. In this paper, a low-complexity high-performance algorithm is introduced for decoding of such high-weight LDPC codes. The developed soft-bit-flipping (SBF) algorithm operates in a similar way to the bit-flipping (BF) algorithm but further utilizes reliability of estimates to improve error performance. A hybrid decoding scheme comprised of the BF and SBF algorithms is also proposed to shorten the decoding time. Parallel and pipelined VLSI architecture is developed to increase the throughput without consuming much chip area. The (1057, 813) and (273, 191) projective-geometry LDPC codes are used for performance evaluation, and the former is designed in VLSI.
In this paper, we propose an efficient message passing architecture for permutation matrices based LDPC code decoders. Min-sum algorithm is reformulated to facilitate significant reduction of routing complexity and memory usage. For a (2048, 1723) (6, 32) LDPC code with 4-bit quantization, 54% outgoing wires per variable node unit and 90% outgoing wires per check node unit can be saved. To further reduce hardware complexity, an optimized nonuniform quantization scheme using only 3 bits to represent each message has been investigated. The simulation result shows that it has only 0.25dB performance loss from the floating-point SPA
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