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IEEE Transactions on Signal Processing

Joint $(3, k)$ -Regular LDPC Code and Decoder/Encoder Design

Tong Zhang, Keshab K. Parhi

Published Mar 23, 2004• 72 citations
Publisher

Abstract

Recently, low-density parity-check (LDPC) codes have attracted a lot of attention in the coding theory community. However, their real-world applications are still problematic mainly due to the lack of effective decoder/encoder hardware design approaches. In this paper, we present a joint (3,k)-regular LDPC code and decoder/encoder design technique to construct a class of (3,k)-regular LDPC codes that not only have very good error-correcting capability but also exactly fit to high-speed partly parallel decoder and low-complexity encoder implementations. We also develop two techniques to further modify this joint design scheme to achieve more flexible tradeoffs between decoder hardware complexity and decoding speed.

DOI
10.1109/tsp.2004.823508

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Joint (3,k)(3, k)(3,k) -Regular LDPC Code and Decoder/Encoder Design
Recently, low-density parity-check (LDPC) codes have attracted a lot of attention in the coding theory community. However, their real-world applications are still problematic mainly due to the lack of effective decoder/encoder hardware design approaches. In this paper, we present a joint (3,k)-regular LDPC code and decoder/encoder design technique to construct a class of (3,k)-regular LDPC codes that not only have very good error-correcting capability but also exactly fit to high-speed partly parallel decoder and low-complexity encoder implementations. We also develop two techniques to further modify this joint design scheme to achieve more flexible tradeoffs between decoder hardware complexity and decoding speed.
Gallager's low-density parity-check (LDPC) codes have recently received a lot of attention because of their excellent performance. The decoder hardware implementation is obviously one of the most crucial issues determining the extent of LDPC applications in the real world. The straightforward fully parallel decoder architecture usually incurs too high complexity for many practical purposes and should be transformed to a partly parallel realization. We propose a joint code and decoder design approach to construct a class of (3, k)-regular LDPC codes which exactly fit to a partly parallel decoder implementation. The partly parallel decoder architecture is suitable for efficient VLSI implementation and it has been shown that the jointly developed (3, k)-regular LDPC codes have very good performance.
In the past few years, Gallager's low-density parity-check (LDPC) codes received a lot of attention and many efforts have been devoted to analyzing and improving their error-correcting performance. However, little consideration has been given to the LDPC decoder VLSI implementation. The straightforward fully parallel decoder architecture usually incurs too high complexity for many practical purposes and should be transformed to a partly parallel realization. Unfortunately, due to the randomness of LDPC codes, it is nearly impossible to develop an effective transformation for an arbitrarily given LDPC code. We propose a joint code and decoder design approach to construct a class of (3, k)-regular LDPC codes which exactly fit a partly parallel decoder implementation and have a very good performance. Moreover, for such LDPC codes, we propose a systematic, efficient encoding scheme by effectively exploiting the sparseness of its parity check matrix.
Recently, low-density parity-check (LDPC) codes have attracted much attention because of their excellent error-correcting performance and highly parallelizable decoding scheme. However, the effective VLSI implementation of an LDPC decoder remains a big challenge and is a crucial issue in determining how well we can exploit the benefits of the LDPC codes in real applications. In this paper, following the joint code and decoder design philosophy, we propose a semi-random design scheme to construct the LDPC codes that not only exhibit very good error-correcting performance but also effectively fit to partially parallel VLSI decoder implementations. The corresponding partially parallel decoder has a very regular structure and simple control mechanism. Our computer simulations show that such LDPC codes achieve very good performance comparable to their counterparts constructed in a fully random scheme, which however have little chance of fitting to partially parallel decoder implementations.
Because of their excellent error-correcting performance, low-density parity-check (LDPC) codes have recently attracted a lot of attention. In this paper, we are interested in the practical LDPC code decoder hardware implementations. The direct fully parallel decoder implementation usually incurs too high hardware complexity for many real applications, thus partly parallel decoder design approaches that can achieve appropriate trade-offs between hardware complexity and decoding throughput are highly desirable. Applying a joint code and decoder design methodology, we develop a high-speed -regular LDPC code partly parallel decoder architecture based on which we implement a -bit, rate- -regular LDPC code decoder on Xilinx FPGA device. This partly parallel decoder supports a maximum symbol throughput of Mbps and achieves BER at 2 dB over AWGN channel while performing maximum decoding iterations.
This paper presents a design approach for low-density parity-check (LDPC) coding system hardware implementation by jointly conceiving irregular LDPC code construction and VLSI implementations of encoder and decoder. The key idea is to construct good irregular LDPC codes subject to two constraints that ensure the effective LDPC encoder and decoder hardware implementations. We propose a heuristic algorithm to construct such implementation-aware irregular LDPC codes that can achieve very good error correction performance. The encoder and decoder hardware architectures are correspondingly presented.