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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Bootstrapped Modified Weighted Bit Flipping Decoding of Low Density Parity Check Codes

Yoichi Inaba

Published Apr 1, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.1093/ietfec/e89-a.4.1145

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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.
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.
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.
It is proved that hard decision algorithms are more appropriate than a soft decision for low-density parity-check (LDPC) decoding since they are less complex at the decoding level. On the other hand, it is notable that the soft decision algorithm outperforms the hard decision one in terms of the bit error rate (BER) gap. In order to minimize the BER and the gap between these two families of LDPC codes, a new LDPC decoding algorithm is suggested in this paper, which is based on both the normalized min-sum (NMS) and modified-weighted bit-flipping (MWBF). The proposed algorithm is named normalized min sum- modified weighted bit flipping (NMSMWBF). The MWBF is executed after the NMS algorithm. The simulations show that our algorithm outperforms the NMS in terms of BER at 10-8 over the additive white gaussian noise (AWGN) channel by 0.25 dB. Furthermore, the proposed NMSMWBF and the NMS are both at the same level of decoding difficulty.
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.