Analytical Solution of Covariance Evolution for Irregular LDPC Codes

The scaling law developed by Amraoui et al. is a powerful technique to estimate the block erasure probabilities of finite- length low-density parity-check (LDPC) codes. Solving a system of differential equations called covariance evolution, one can obtain the scaling parameter. However, the covarian...

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Veröffentlicht in:	IEEE transactions on information theory 2012-07, Vol.58 (7), p.4770-4780
Hauptverfasser:	Nozaki, Takayuki, Kasai, Kenta, Sakaniwa, Kohichi
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Binary erasure channel (BEC) Codes Coding, codes covariance evolution Decoding Differential equations Equations Exact sciences and technology Information theory Information, signal and communications theory Iterative decoding Joining processes low-density parity-check (LDPC) codes peeling algorithm (PA) Probability distribution Random variables scaling law Signal and communications theory Telecommunications and information theory
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Zusammenfassung:	The scaling law developed by Amraoui et al. is a powerful technique to estimate the block erasure probabilities of finite- length low-density parity-check (LDPC) codes. Solving a system of differential equations called covariance evolution, one can obtain the scaling parameter. However, the covariance evolution has not been analytically solved. In this paper, we present the analytical solution of the covariance evolution for irregular LDPC code ensembles.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2012.2191668