Regular and irregular progressive edge-growth tanner graphs

• Published in: IEEE transactions on information theory Vol. 51; no. 1; pp. 386 - 398
• Main Authors: Xiao-Yu Hu, Eleftheriou, E., Arnold, D.M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Bandwidth; Codes; Coding, codes; Computer simulation; Construction; Entropy; Exact sciences and technology; Girth; Graph representations; Graphs; Image coding; Information systems; Information theory; Information, signal and communications theory; Joints; LDPC codes over; low-density parity-check (LDPC) codes; Lower bounds; PEG Tanner graphs; progressive edge growth (PEG); Random processes; Rate distortion theory; Signal and communications theory; Signal processing; Signal processing algorithms; Speech processing; Symbols; Telecommunications and information theory; Video compression; LDPC codes over GF(q); PEG Tanner graphs; low-density parity-check (LDPC) codes; Iterative method; Parity check codes; Graph theory; Decoding; Algorithm; Girth; Optimization; progressive edge growth (PEG)
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2004.839541

We propose a general method for constructing Tanner graphs having a large girth by establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) algorithm. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. Simple variations of the PEG algorithm can also be applied to generate linear-time encodeable LDPC codes. Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF(q) (q>2) are investigated. Simulation results show that the PEG algorithm is a powerful algorithm to generate good short-block-length LDPC codes.