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International Symposium on Wireless Pervasive Computing

Theoretic approach to BP-based WBF decoding algorithm of LDPC codes

Erl‐Huei Lu, Tso-Cho Chen, Pen‐Yao Lu

Published Nov 1, 2013• 8 citations
Publisher

Abstract

A theoretic approach to the belief-propagation - based weighted bit-flipping (BP-based WBF) algorithm is proposed for decoding low-density parity-check codes. The decoding algorithm can be easily simplified to IMWBF, MWBF, WBF or BF decoding algorithms by setting different parameters; hence it could offer a high flexible performance/complexity trade-off for hybrid decoding.

DOI
10.1109/iswpc.2013.6707424

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A theoretic approach to the belief-propagation - based weighted bit-flipping (BP-based WBF) algorithm is proposed for decoding low-density parity-check codes. The decoding algorithm can be easily simplified to IMWBF, MWBF, WBF or BF decoding algorithms by setting different parameters; hence it could offer a high flexible performance/complexity trade-off for hybrid decoding.
LDPC (Low Density Parity Check Codes) is a low -density puppet test code applied to channel codes. Among the existing LDPC decoding algorithms, the LLR-BP decoding arithmetic is too complicated to calculate the calculation due to the containing a large number of bilateral positive cut functions. Therefore, this article proposes a LDPC decoding algorithm that combines the Modified Weighted Bit Flipping Decoding Algorithm (MWBF) with the Logarithmic Likelihood Ratio Based Confidence Propagation Algorithm (LLR-BP). In the process of the LLR-BP decoding iteration, the introduction of the MWBF algorithm not only does it reduce the complexity of iteration and decoding, but also avoids the traditional weighted bit-flipping decoding algorithm (WBF). Excessive effects of code performance.
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.
Two simple and efficient weighted bit flipping(WBF)decoding algorithms for low density paritycheck(LDPC)codes are proposed,in which the sum of the variable nodes' magnitude is introduced to compute the reliability of the parity checks.Simulation results shows that the performance of one of the improved scheme is better than that of traditional WBF and modified WBF(MWBF)algorithms about 1.65dB and 1.31dB at BER of 10-5 over an additive white Gaussian noise channel,respectively,while the average number of decoding iterations is significantly reduced.
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.
A natural relationship between weighted bit-flipping (WBF) decoding and message-passing decoding is explored. This understanding can help us develop a dual WBF decoding algorithm from one type of message-passing decoding algorithm and vice versa. For min-sum decoding, one can find that its dual WBF algorithm is the algorithm proposed by Jiang et al. For belief-propagation (BP) decoding, we propose a new WBF algorithm and show its performance advantage. For some high-rate low-density parity-check (LDPC) codes of large row weight, it is shown that the WBF algorithm proposed by Liu and Pados performs extraordinarily well. However, its dual message- passing decoding does not work well. Furthermore, we propose a parallel implementation framework for various WBF algorithms. Compared to serial implementations, various WBF algorithms in their parallel form converge significantly faster and often perform better.