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IEEE Communications Letters

Bootstrap decoding of low-density parity-check codes

A. Nouh, Amir H. Banihashemi

Published Sep 1, 2002• 34 citations
Publisher

Abstract

An initial bootstrap step for the decoding of low-density parity-check (LDPC) codes is proposed. Decoding is initiated by first erasing a number of less reliable bits. New values and reliabilities are then assigned to erasure bits by passing messages from nonerasure bits through the reliable check equations. The bootstrap step is applied to the weighted bit-flipping algorithm to decode a number of LDPC codes. Large improvements in both performance and complexity are observed.

DOI
10.1109/lcomm.2002.803481

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An initial bootstrap step for the decoding of low-density parity-check (LDPC) codes is proposed. Decoding is initiated by first erasing a number of less reliable bits. New values and reliabilities are then assigned to erasure bits by passing messages from nonerasure bits through the reliable check equations. The bootstrap step is applied to the weighted bit-flipping algorithm to decode a number of LDPC codes. Large improvements in both performance and complexity are observed.
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.
Reliability ratio based weighted bit-flipping algorithm is one of the best hard decision decoding algorithms in performance. Recently several modifications are done to this technique either to improve performance or to lower the complexity. The implementation efficient reliability ratio based weighted bit-flipping is developed targeting decreasing processing time of the decoding process. In this paper we are targeting improving performance of recent developed algorithm named low complex implementation efficient reliability ratio based weighted bit-flipping by adding a bootstrap step to the decoding technique which leads to increase in reliability of received bits then number of decoded bits will be increased leading to improve in performance. Also a modification done to bootstrap step for further increase the performance.
Low density parity check (LDPC) codes can be decoded in various ways, namely the bit-flipping (BF) algorithm, the weighted BF (WBF) algorithm and the log-likelihood ratio belief propagation (LLR-BP) algorithm, and so on. These algorithms provide a wide range of tradeoffs among decoding complexity, decoding speed, and error rate performance. Recently, the bootstrapped WBF (BWBF) algorithm has been proposed to improve the error rate performance and the decoding complexity of the WBF algorithm. In this paper, we study the effects of the predetermined threshold /spl alpha/ of the bootstrap step on BER for various LDPC codes. Furthermore, we apply the bootstrap step to the LLR-BP algorithm. We evaluate the BWBF and the bootstrapped LLR-BP (B-LLR-BP) algorithms on a fast fading channel. We show that the optimal threshold depends on the row and column weights of the LDPC codes. We also show that the BWBF algorithm provides a large improvements in both the error rate performance and the decoding complexity on a fast fading channel. Moreover, we show that the LLR-BP algorithm hardly receives the effect of the bootstrap step.
An improved bit-flipping decoding algorithm is proposed for low-density parity-check(LDPC) codes in this paper.Two influences on error probabilities of code bits are considered: the influence of the number of code bits included in an unsatisfied check,and the influence of the number of unsatisfied checks of each code bit.No soft information is required for decoding.Simulation results show that improvement on performance is observed for the proposed algorithm,and it provides better performance over several soft-decision bit-flipping decoding algorithms for LDPC codes with large girth.