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International Conference on Computational Intelligence and Security (CIS)

Improved BP Decoding Algorithm for Nonbinary LDPC Codes Based on Bit-flipping Method

Man Teng, Xingcheng Liu, Zerong Deng

Published Dec 1, 2008• 0 citations
Publisher

Abstract

Nonbinary LDPC codes demonstrated excellent performance. However, how to reduce the decoding complexity for such codes without performance degradation is still a problem to be solved. In this paper, the bit-flipping method is introduced into the standard Fourier transform decoding algorithm for decoding nonbinary LDPC codes. Simulation results show that the proposed method gains better BER performance with efficiently reduce of the decoding computation complexity in high Eb/N0 regions.

DOI
10.1109/cis.2008.152

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Nonbinary LDPC codes demonstrated excellent performance. However, how to reduce the decoding complexity for such codes without performance degradation is still a problem to be solved. In this paper, the bit-flipping method is introduced into the standard Fourier transform decoding algorithm for decoding nonbinary LDPC codes. Simulation results show that the proposed method gains better BER performance with efficiently reduce of the decoding computation complexity in high Eb/N0 regions.
An improved decoding algorithm is presented in order to solve the problem of inconvenient for hardware implementation in decoding algorithm for non-binary LDPC codes based on the FFT-BP algorithm. The innovation of the new algorithm is the importing of the logarithmic operations, which will transform multiplication operations to addition operations in the logarithmic domains. Thus the presented algorithm has the advantages of the reduced complexity and the more convenient hardware implementation. A simulation is made using regular non binary LDPC codes under White Gaussian Noise channel based on GF(4). The result shows that the decoding complexity is much more reduced with the performance decrease by about 0.07 dB when BER( Bit Error Rate )is 10-4.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
To solve the problem of high computational complexity and inconvenient for hardware implementation in original decoding algorithm for non-binary LDPC codes,two simplified decoding algorithms are introduced for nonbinary LDPC codes: the fast Fourier transform belief propagation(FFT-BP) decoding algorithm and the Log-domain belief propagation(Log-BP) decoding algorithm. The performance comparison between two different decoding algorithms for LDPC Codes over GF(q) is investigated at high code rates(1/2~1) over AWGN channel.The performance curves show that by the decreasing of code rate,both coding gains and the distances from Shannon limit increase with the two algorithms,which means that non-binary LDPC Codes are suit for applications at high rates.Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable improvement in computational complexity at the cost of sacrificing some performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.
A Hybrid Bit Flip(HBF) decoding algorithm for Low-Density Parity-Check (LDPC) codes is proposed in this paper. The algorithm makes full use of the soft output of belief-propagation (BP) (decoding) algorithm for LDPC codes, and greatly improves the bit error rate (BER) of the classical bit-flip (BF) algorithm. The simulation results in AWGN channel show that the HBF algorithm outperforms the BP algorithm under almost the same computational complexity. Furthermore, the former can achieve much lower error floor than the latter can do.
A new low complexity and implement efficient bit-flipping decoding algorithm for Low-Density Parity-Check(LDPC) codes is presented in this paper.The proposed algorithm computes the flipping function by the intrinsic value of the message node,and it reduces the requirement of the information from other message nodes.So,it has a lower complexity and still guarantees the reliability of the flipping function.The simulation results for RS-based LDPC codes using the proposed algorithm show that it has the performance approaching the IMWBF algorithm or even better.
The problem of low-complexity linear programming (LP) decoding of nonbinary low-density parity-check (LDPC) codes is considered, and an iterative LP decoding algorithm is presented. Results that were previously derived for binary LDPC codes are extended to the nonbinary case. Both simple and generalized nonbinary LDPC codes are considered. It is shown how the algorithm can be implemented efficiently using a finite-field fast Fourier transform. Then, the convergence rate of the algorithm is analyzed. The complexity of the algorithm scales linearly in the block length, and it can approximate, up to an arbitrarily small relative error, the objective function of the exact LP solution. When applied to a typical code from an appropriate nonbinary LDPC code ensemble, the algorithm can correct a constant fraction of errors in linear (in the block length) computational complexity. Computer experiments with the new iterative LP decoding algorithm show that, in the error floor region, it can have better performance compared to belief propagation decoding, with similar computational requirements.