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IEEE Mediterranean Electrotechnical Conference (MELECON)

Magnetization performance of BP-Based algorithm

Manel Abdelhedi, Omessaad Hamdi, Ammar Bouallègue

Published Jan 1, 2010• 0 citations
Publisher

Abstract

In this paper, we present the performance of the Belief Propagation-Based (BP-Based) algorithm as a function of the magnetization. Previous works, have shown that the BP algorithm, is equivalent to the Thouless- Anderson-Palmer(TAP) approach, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) algorithm and its simplification, the BP-Based algorithm using this method.

DOI
10.1109/melcon.2010.5476248

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In this paper, we present the performance of the Belief Propagation-Based (BP-Based) algorithm as a function of the magnetization. Previous works, have shown that the BP algorithm, is equivalent to the Thouless- Anderson-Palmer(TAP) approach, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) algorithm and its simplification, the BP-Based algorithm using this method.
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Low-density parity-check (LDPC) codes are very efficient for communicating reliably through a noisy channel. N.Sourlas [1] showed that LDPC codes, which revolutionize the codes domain and used in many communications standards, can be mapped onto an Ising spin systems. Besides, it has been shown that the Belief-Propagation (BP) algorithm, the LDPC codes decoding algorithm, is equivalent to the Thouless- Anderson-Palmer (TAP) approach [2]. Unfortunately, no study has been made for the other decoding algorithms. In this paper, we develop the Log-Likelihood Ratios-Belief Propagation (LLR-BP) algorithm and its simplifications the BP-Based algorithm and the λ-min algorithm with the TAP approach. We present the performance of these decoding algorithms using statistical physics argument i.e., we present the performance as function of the magnetization.
Low-density parity-check (LDPC) codes are based on random construction. Because of this randomness, it is not easy to analyze them with the traditional methods of information theory. N. Sourlas was the first to point out that LDPC codes have a similarity with Ising spin systems of statistical physics. Besides, it has been shown that the Belief-Propagation algorithm, the LDPC codes decoding algorithm, is equivalent to the Thouless-Anderson-Palmer(TAP) approach. In this paper, we develop the log likelihood ratios-Belief Propagation (LLR-BP) algorithm and its simplifications the BP-Based algorithm and the λ-min algorithm with the TAP approach.
Low-density parity-check (LDPC) codes are based on random construction. Because of this randomness, it is not easy to analyze them with the traditional methods of communication theory. N.Sourlas [6] was the first to point out that LDPC codes have a similarity to Ising spin systems in statistical physics. Besides, it has been shown that the Belief-Propagation algorithm, the decoding algorithm of LDPC codes, is equivalent to the Thouless-Anderson-Palmer(TAP) [9] approach. In this paper, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) and the BP-Based decoding algorithms with the TAP approach.
The belief propagation (BP) algorithm for polar codes has attracted significant attention due to its soft-output property and high parallelism. However, the BP algorithm is not comparable with the successive cancellation list (SCL) algorithm in terms of the error-correction performance. In this paper, we propose a high-stage BP flip (HSBPF) algorithm to further improve the error-correction performance of the BP algorithm by analyzing the distribution of log-likelihood ratio (LLR) values. Simulation results show that the decoding latency can be reduced by 30% with the proposed algorithm. Moreover, benefiting from the simplified message passing of the factor graph, the computational complexity of the proposed algorithm is also significantly reduced compared with the existing algorithms.
This paper proposes a modified belief propagation( MBP) decoder for polar codes,in which the log-likelihood ratios( LLRs) associated with the frozen nodes would be revised by a selective correction parameter when the LLRs of frozen nodes are wrongly calculated. By using the Gaussian approximation,an appropriate parameter is obtained creatively. The principles of log-domain BP decoder and corresponding modified decoding algorithm are described in this paper. Finally,computational complexity analysis and performance simulation are given. Data results indicate that compared with the existing BP decoder,the modified BP decoder can obtain a better bit error performance of about 0. 2 dB at the cost of a little computational complexity.