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SiPS ... design and implementation - IEEE Workshop on Signal Processing Systems

Studies on Practical Low Complexity Decoding of Low-Density Parity-Check Codes

Zhiqiang Cui, Zhongfeng Wang

Published Oct 1, 2007• 0 citations
Publisher

Abstract

This paper studies practical low complexity decoding of Low Density Parity-Check (LDPC) codes. We first investigate VLSI implementation issues of two state-of-the-art Weighted Bit Flipping (WBF) based decoding algorithms that were recently proposed in the literature. Then we present an optimized 2-bit soft decoding approach. It is shown that the proposed approach has comparable hardware complexity with either of the two WBF-based algorithms while it has significantly better decoding performance.

DOI
10.1109/sips.2007.4387547

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This paper studies practical low complexity decoding of Low Density Parity-Check (LDPC) codes. We first investigate VLSI implementation issues of two state-of-the-art Weighted Bit Flipping (WBF) based decoding algorithms that were recently proposed in the literature. Then we present an optimized 2-bit soft decoding approach. It is shown that the proposed approach has comparable hardware complexity with either of the two WBF-based algorithms while it has significantly better decoding performance.
Recently, various decoding algorithms with Low Density Parity Check (LDPC) codes have been proposed. Most algorithms can be divided into a hard decision algorithm and a soft decision algorithm. The Weighted Bit Flipping (WBF) algorithm that is between a hard decision and a soft decision algorithms has been proposed. The Bootstrapped WBF and Modified WBF algorithms have been proposed to improve the error rate performance and decoding complexity of the WBF algorithm. In this letter, we apply the Bootstrap step to the Modified WBF algorithm. We show that the Bootstrapped modified WBF algorithm outperforms the WBF, Bootstrapped WBF, and Modified WBF algorithms. Moreover, we show that the Bootstrapped modified WBF algorithm has the lowest decoding complexity.
Abstract We propose a method to substantially reduce the computational complexity of iterative decoders of low-density parity-check (LDPC) codes which are based on the weighted bit-flipping (WBF) algorithm. In this method, the WBF-based decoders are modified so that the flipping function is calculated only over a reduced set of variable nodes. An explicit expression for the achieved complexity gain is provided and it is shown that for a code of block length N, the decoding complexity is reduced from O(N2) to O(N). Moreover, we derive an upper bound for the difference in the frame error rate of the reduced-set decoders and the original WBF-based decoders, and it is shown that the error performances of the two decoders are essentially the same.
Abstract- Low Density Parity Check (LDPC) codes can be decoded in various ways, namely the Bit-Flipping (BF) algorithm, the Weighted BF algorithm (WBF) ， the Belief Propagation (BP) algorithm and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. In this paper, a novel self-reliability-based weighted bit-flipping decoding scheme for low-density parity-check codes is proposed. Improvement in performance is observed in comparison with the modified weighted bit-flipping decoding scheme, and the decoding complexity can be significantly reduced as well. Key-Words:- Low-density parity-check (LDPC) codes, decoding algorithm, bit flipping, self reliability
Based on decoding performance, complexity and latency of finite-geometry low-density parity-check (LDPC) codes, an efficient decoding algorithm is proposed. The algorithm is a hybrid bit-flipping (BF)/majority-logic (MLG) algorithm. In the algorithm, there are two stages. At the first stage, a code is decoded with bit-flipping (BF) with a small fixed number of iterations. Then the output from bit-flipping (BF) decoder is decoded by majority-logic (MLG) decoding. And in bit-flipping (BF) decoding, a new method is used to find the least reliable position. In the hybrid algorithm, there aren't real operations. Simulation results show that the algorithm provides 0.3dB coding gain over weight bit-flipping (WBF) decoding, and within 1 dB away from sum-product algorithm (SPA) decoding.