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IEEE Vehicular Technology Conference

Performance of low-density parity-check (LDPC) code with UMP BP-based algorithm and quantizer on Rayleigh fading channels

A. Ohhashi, Tomoaki Otsuki Ohtsuki

Published Apr 23, 2004• 4 citations
Publisher

Abstract

In this paper, we evaluate the error rate performance of LDPC codes with the BP algorithm and the UMP BP-based algorithm on Rayleigh fading channels. We also evaluate the effects of quantization with two algorithms on Rayleigh fading channels. We show that the UMP BP-based algorithm can achieve a good trade-off between error rate performance and decoding complexity. We also show that the error rate performance for 5-bit or 7-bit quantization is identical to that for no quantization.

DOI
10.1109/vetecs.2003.1207150

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In this paper, we evaluate the error rate performance of LDPC codes with the BP algorithm and the UMP BP-based algorithm on Rayleigh fading channels. We also evaluate the effects of quantization with two algorithms on Rayleigh fading channels. We show that the UMP BP-based algorithm can achieve a good trade-off between error rate performance and decoding complexity. We also show that the error rate performance for 5-bit or 7-bit quantization is identical to that for no quantization.
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.
In this paper, we use the minimum mean square error (MMSE) criterion to design the scaled and offset belief propagation (BP)-based decoding algorithms for short low-density parity-check (LDPC) codes on the fast Rayleigh fading channel. Based on the MMSE criterion, the theoretical formulas and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (Chen et al., 2005 and Gallager, 1962) regular LDPC codes on the fast Rayleigh fading channel demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance better than that of the BP algorithm.
An improved decoding algorithm based on minimum mean square error(MMSE) for low-density parity-check(LDPC) codes is proposed.The new algorithm combines processing methods of two modified uniformly most powerful(UMP) BP-based algorithms(normalized UMP BP-based algorithm and offset UMP BP-based algorithm) and attains the corresponding normalization factor and offset factor according to MMSE criterion.Simulations indicate that,compared with the two above-mentioned algorithms,a gain of 0.03 dB can be achieved at bit error rate(BER) of 10-6 with the proposed algorithm when a(3,6) regular LDPC code of code length 1 008 and code rate 1/2 is used.
This paper studies the finite precision effects on the LDPC decoding performance with high order modulation over Rayleigh fading channels. We compare the performance of different quantization schemes and decoding algorithms using discretized density evolution over code ensembles of various code rates. We find that the min-sum algorithm with a simple correction term using 5 bits for quantization offers a very good performance in all code rate and modulation combinations. The loss is only 0.1 dB compared to floating point implementation. Direct implementation of the sum product algorithm with 6-bit quantization suffers a much larger performance loss when high rate LDPC codes are used. Both software simulations and test results of a hardware decoder implemented on FPGA verify these conclusions.
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In order to make up for the performance defects of UMP BP-Based decoding algorithm relative to LLR BP decoding algorithm,this paper proposed a modified decoding algorithm.Parameters of the proposed algorithm which combined the advantage of Normalized BP-Based decoding algorithm and Offset BP-Based decoding algorithm were calculated according to minimum mean square error rule.The simulation results show that the LDPC decoding performance of modified UMP BP-Based decoding algorithm is more effective than that of UMP BP-Based decoding algorithm,Normalized BP-Based decoding algorithm and Offset BP-Based decoding algorithm under the same condition of bit error rate.