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Global Information Infrastructure and Networking Symposium

Iterative decoding algorithms of LDPC codes using TAP approach

Manel Abdelhedi, Omessaad Hamdi, Ammar Bouallègue

Published Jun 1, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1109/giis.2009.5307067

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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.
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 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.
In this paper, we present the decoding algorithms of Low-density parity-check (LDPC) codes using statistical physics arguments. Previous works, have shown that the Belief-Propagation (BP) algorithm, is equivalent to the Thouless-Anderson-Palmer (TAP) [1] approach. In this paper, we develop the log-likelihood ratios-Belief Propagation (LLR-BP) algorithm and its simplification, the λ-min algorithm using this method developed in the study of disordered systems. The obtained results by simulation confirm that the λ-min algorithm gets closer to the LLR-BP algorithm as λ increases.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
To improve the decoding speed and reduce the complexity of low-density parity-check (LDPC) codes, this paper proposes a hybrid LDPC decoding algorithm that combined with the distribution characteristics of log-likelihood ratio (LLR) of all variable node information before each iteration. During the process of decoding, there is a judgment based on an interval value and a threshold value to select the Belief Propagation (BP) algorithm or the Minimal Sum (MS) algorithm to decode, so the proposed hybrid algorithm effectively combines the excellent performance of BP algorithm and the simple operation of MS algorithm. The simulation results show that the algorithm can greatly reduce the computational complexity and achieve similar decoding performance compared with the BP algorithm.