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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Bibliographic Details
Published in:IEEE transactions on information theory 2012-07, Vol.58 (7), p.4770-4780
Main Authors: Nozaki, Takayuki, Kasai, Kenta, Sakaniwa, Kohichi
Format: Article
Language:English
Subjects:
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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Summary: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