Analytical Solution of Covariance Evolution for Irregular LDPC Codes

• Published in: IEEE transactions on information theory Vol. 58; no. 7; pp. 4770 - 4780
• Main Authors: Nozaki, Takayuki, Kasai, Kenta, Sakaniwa, Kohichi
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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; Binary channel; Differential equation; Irregular code; Algorithm; Scaling law; Covariance; Binary erasure channel (BEC); low-density parity-check (LDPC) codes; Analytical method; Error correcting code; Parity check codes; Delamination; peeling algorithm (PA); covariance evolution
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2191668

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.