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Journal of Chongqing University. English Edition

Performance Analysis of High-rate Non-binary LDPC Codes Under AWGN Channels

Jie Bao

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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, 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.
Low Density Parity Check Codes (LDPC) are a group of channel codes which can be decoded using a graph. LDPC codes are known to give near Shannon limit performance in Additive White Gaussian Channel (AWGN), but for large block-lengths and irregular construction. To overcome this limitation, it has been proposed to define codes over a higher order Galois Field. In this paper,we construct a regular cycle non binary LDPC code over GF(q), where q=2p.We use a Fast Fourier Transform (FFT) based low complexity algorithm to decode the LDPC code defined over a large Galois Field. We evaluate the performance of these codes in AWGN channel using computer simulations and show that they are giving excellent BER performance.
Low Density Parity Check (LDPC) codes have excellent error correcting performance. LDPC codes are one of the block coding techniques and it performs near Shannon limit and recommended for many practical applications. Non-binary LDPC codes extension of binary LDPC in error correcting property especially for short and moderate block length. In many digital communication systems these codes have strong competitors of turbo codes for error control. Low Density Parity Check as it name is suggests that in a parity check matrix (H) consists of very small number of non-zero elements comparing with zero elements. The strength of the LDPC code defines Parity Check Matrix (PCM). LDPC code contains two types of decoding algorithms hard and soft decision algorithm. By comparing with other traditional decoding algorithm FFT based sum product algorithm reduced computation complexity with better decoding performance. In this paper, LDPC codes for FFT based sum product decoding algorithm performances are analysed for various order of Galois Field GF(q) using AWGN channel. Decoding performance measured in terms of symbol error rate which improve with increasing order of Galois field.