Abstract
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.
Highlights
Low-density parity-check (LDPC) codes were first discovered by Gallager [3], in his thesis, in 1962 and have recently been rediscovered by Mackay and Neal [3,4]
We have been interested in the decoding of LDPC codes from a statistical physics approach
We have examined the correspondence between LDPC codes and Ising spin systems
Summary
Low-density parity-check (LDPC) codes were first discovered by Gallager [3], in his thesis, in 1962 and have recently been rediscovered by Mackay and Neal [3,4]. The methods of statistical physics developed in the study of disordered systems proved to be efficient for studying the properties of these codes One of these methods is the Thouless-AndersonPalmer (TAP) [2] approach which is shown equivalent to the BP algorithm by kabashima, et al [8]. We develop the Log-Likelihood RatiosBelief Propagation (LLR-BP), the BP-Based and the λ-min decoding algorithms with the TAP approach. Their performance is evaluated as a function of a statistical physics parameter which is the magnetization.
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