Generalized and Doubly Generalized LDPC Codes With Random Component Codes for the Binary Erasure Channel

• Published in: IEEE transactions on information theory Vol. 56; no. 4; pp. 1651 - 1672
• Main Authors: Paolini, E., Fossorier, M.P.C., Chiani, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Asymptotic properties; Binary erasure channel; Block codes; Channel capacity; Channel coding; Channels; Code standards; Codes; Coding, codes; Communication channels; Communication system control; Computer Science; Engineering Sciences; Evolution; Exact sciences and technology; EXIT chart; Genetic algorithms; Information analysis; information functions; Information processing; Information theory; Information, signal and communications theory; Iterative decoding; low-density parity-check (LDPC) codes; Mathematical analysis; Mathematical models; Parity check codes; Power generation; Signal and communications theory; Signal and Image Processing; split information functions; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Waterfalls; Performance evaluation; Binary channel; information functions; Evolutionary algorithm; Code distance; Channel coding; Random codes; Information transmission; EXIT chart; Iterative decoding; Binary erasure channel; low-density parity-check (LDPC) codes; split information functions; Numerical simulation; Error correcting code; Parity check codes; Minimal distance; Parity check
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2040938

In this paper, a method for the asymptotic analysis of generalized low-density parity-check (GLDPC) codes and doubly generalized low-density parity-check (D-GLDPC) codes over the binary erasure channel (BEC), based on extrinsic information transfer (EXIT) chart, is described. This method overcomes the problem consisting of the impossibility to evaluate the EXIT function for the check or variable component codes, in situations where the information functions or split information functions for component codes are unknown. According to the proposed technique, GLDPC codes and D-GLDPC codes where the generalized check and variable component codes are random codes with minimum distance at least 2, are considered. A technique is then developed which finds the EXIT chart for the overall GLDPC or D-GLDPC code, by evaluating the expected EXIT function for each check and variable component code. This technique is finally combined with the differential evolution algorithm in order to generate some good GLDPC and D-GLDPC edge distributions. Numerical results of long, random codes, are presented which confirm the effectiveness of the proposed approach. They also reveal that D-GLDPC codes can outperform standard LDPC codes and GLDPC codes in terms of both waterfall performance and error floor.