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Journal of Nanjing University of Posts and Telecommunications

Research of Fixed Point of LDPC Decoding over Rice Channel

Chengqi Xu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Research of the fixed point which appears in decoding process of LDPC codes is important to further analyze the decoding mechanism and speed up decoding convergence.Firstly,a new optimization scheme which combines DDE(Discrete Density Evolution)for offset BP-based decoding algorithm with differential evolution is presented for optimizing irregular LDPC codes.Then the optimized degree distribution pair and threshold of LDPC codes over Rice channel are given,with the maximum bit node degree 10 and code rate R=1/2,1/3.Furthermore,we analyze a series of simulated curves related to LDPC decoding fixed point and threshold phenomenon.Simulation results show that the node with higher degree contributes more to the decoding for LDPC codes.Therefore,we tentatively put forward two kinds of thinking to improve LDPC decoding algorithm.

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Research of Density Evolution of LDPC Codes over Rice Channels

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arXiv:1409.4760•International Symposium on Telecommunications•Sep 1, 2014•4 citations
Research of the fixed point which appears in decoding process of LDPC codes is important to further analyze the decoding mechanism and speed up decoding convergence.Firstly,a new optimization scheme which combines DDE(Discrete Density Evolution)for offset BP-based decoding algorithm with differential evolution is presented for optimizing irregular LDPC codes.Then the optimized degree distribution pair and threshold of LDPC codes over Rice channel are given,with the maximum bit node degree 10 and code rate R=1/2,1/3.Furthermore,we analyze a series of simulated curves related to LDPC decoding fixed point and threshold phenomenon.Simulation results show that the node with higher degree contributes more to the decoding for LDPC codes.Therefore,we tentatively put forward two kinds of thinking to improve LDPC decoding algorithm.
Noise threshold of Low Density Parity Check (LDPC) codes ensemble could be calculated by density evolution of the decoding messages. According to the threshold, performance of the decoding algorithm could be evaluated and degree distribution pairs of irregular LDPC codes also might be optimized. In this paper, for regular LDPC codes on Rice channel, Discrete Density Evolution(DDE) for BP,BP-based and offset BP-based decoding algorithm were compared on different quantization level and step. Furthermore, degree distribution pairs of the irregular LDPC codes were optimized on Rice channel, which was based on DDE for offset BP-based decoding algorithm, the corresponding threshold is also calculated. Finally, the Probability Mass Function (PMF) evolution curve of optimized irregular LDPC codes with code rate 1/2 on Rice channel is given.
For irregular LDPC codes,the density evolution method can track the messages to find out the noise threshold, enabling optimization of the degree distribution. A new optimized scheme for irregular LDPC codes is proposed in this paper, which is combining Zhengya He's modified particle swarm optimization (PSO) algorithm with discrete density evolution (DDE) for the offset BP-based decoding algorithm. Several optimized degree distribution pairs and corresponding threshold of LDPC codes over Rician channel were given using the proposed scheme. The performance of the optimized LDPC codes was also analyzed. Simulation results shows that the proposed scheme is effective.
To design low-density parity-check (LDPC) codes with asymmetric channels and analyze their performance, an achievable asymmetric discrete density evolution method is proposed, which is based on offset min-sum decoding. First, the iterative formula of low-complexity asymmetric channel discrete density evolution is derived by means of combinatorics, difference method and the binomial theorem. The iterative formula is applied to further optimize the design of the LDPC codes using the offset min-sum decoding, and the optimal degree distributions and performance of the LDPC codes under different quantization ranges and step sizes are obtained under the asymmetric channel. Finally, the optimal offset values under high-precision quantization are obtained. The results show that under the asymmetric channel, the complexity of the proposed asymmetric density evolution method based on the offset min-sum decoding is reduced by an order of magnitude than that using the original method. For a fixed code rate, the smaller the variable node degree of the regular codes, the better the performance and the smaller the optimal offset value. For irregular LDPC codes, the optimal degree distributions and offset values are determined according to the differential evolution algorithm. For a fixed code rate, the larger the maximum variable node degree, the better the performance of irregular codes.
Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.
Density evolution is a new method for analyzing the asymptotic performance of network capability approaching error-correcting codes. For irregular LDPC codes with message-passing decoding, the density evolution method can track the messages to find out the threshold, enabling optimization of the degree distribution. In this paper, the principle of density evolution combined with the decoding process is firstly explored. Then, two algorithms for programming the evolution proceeding are discussed: the discretized density evolution and the Gaussian approximation, as well as their application conditions. Finally, simulation results are presented.
We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution (DE), a numerical method for analyzing the behavior of iterative decoding convergence of a LDPC code. We have used the method of [16] for designing of a LDPC code with optimal rate. This has been done for a given parity check node degree distribution, erasure probability and specified DE constraint. The fast behavior of DE and found optimal rate with this method compare with the previous DE constraint.