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International Journal of Communications Network and System Sciences

Simulation Analysis of Multiple BP Decoding Algorithm and FFT-BP Decoding Algorithm

Wei Xin, Zhigang Li, Zheng Dou

Published Jan 1, 2017• 0 citations
Publisher

Abstract

In order to solve the problem that the original decoding algorithm of multi-band LDPC codes is high and is not conducive to hardware implementation, two simplified decoding algorithms for multi-band LDPC codes are studied: the reliability propagation based on fast Fourier transform Code algorithm (FFT-BP) and log-BP decoding algorithm based on logarithmic operations. The simulation results show that the FFT-BP decoding algorithm is more convenient and efficient.

DOI
10.4236/ijcns.2017.108b027

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In order to solve the problem that the original decoding algorithm of multi-band LDPC codes is high and is not conducive to hardware implementation, two simplified decoding algorithms for multi-band LDPC codes are studied: the reliability propagation based on fast Fourier transform Code algorithm (FFT-BP) and log-BP decoding algorithm based on logarithmic operations. The simulation results show that the FFT-BP decoding algorithm is more convenient and efficient.
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.
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.
Two different decoding algorithms for non-binary LDPC codes: the fast Fourier transform belief propagation (FFT-BP) decoding algorithm and the Log-domain belief propagation (Log-BP) decoding algorithm are introduced in this paper. Their performance advantage of 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 with the decreasing of code rate, both coding gains and the distances from Shannon limit increase under the two algorithms, which means for non- binary LDPC Codes to be suitable for applications at high rates. Meanwhile it is shown that Log-BP decoding algorithm may contribute a considerable saving in computational complexity at the cost of sacrifice small performance, which is important for Log-BP decoding algorithm to be applied in hardware implementation.
In this paper, an improved decoding algorithm for Non-binary low density parity check (NB-LDPC) codes with low decoding complexity and suitable for field-programmable gate array (FPGA) implementation is proposed, which is a mixed logarithmic domain FFT-BP decoding algorithm (Mixed Log-FFT-BP) for the problem of high complexity of the existing decoding algorithms for Non-binary LDPC codes. The algorithm combines the traditional Log-BP algorithm with the FFT-BP algorithm, and simplifies the update of the check nodes in the iterative decoding process. A large number of convolution operations are converted into multiplication operations in frequency domain by using FFT transform and IFFT transform. The multiplication of the original FFT-BP algorithm is converted into the addition and look-up table operations in the logarithmic domain. Then, the logarithm of the probability information is directly solved, so that it can be decoded in the logarithmic domain, which saves the computation of the log likelihood ratio, and then reduces the complexity. Simulation results show that under the additive Gauss white noise channel, when the bit error rate is 10-5, compared with BP algorithm, Log-Bp algorithm and FFT-BP algorithm, the performance of Mixed Log-FFT-BP algorithm is not decreased, and all of them remain within the range of 0.1-0.2dB.
In this paper, we present a simplification of log-BP algorithm which is able to reduce iterative times of decoding algorithm and save the hardware resource of decoder for LDPC codes. This simplification designs an improved layered-iterative decoding method without reducing the decoding performance, of which speed the updating of check nodes and variable nodes. Simulation results show that the improved layered-iterative log-BP algorithm with six-time iteration exhibits similar decoding performance to the traditional log-BP algorithm with ten-time iteration. When the improved log-BP and traditional log-BP both are simulated in ten-time iteration, the SNR of improved layer-iterative method decreases about 0.25 dB than that of traditional log-BP in the BER of 1e-2.