Abstract: An overview of graphical representations for low-density parity-check (LDPC) codes is given. A parallel between graph (hypergraph)-based codes and LDPC codes is drawn based on these representations. Constructions of generalized LDPC codes called woven graph codes with constituent block and convolutional codes are considered. Asymptotical bounds on the minimum (free) distance of woven graph codes are presented. Examples of woven graph codes with convolutional constituent codes having large and extremely large free distances are given. Simulation results of maximum-likelihood decoding of woven graph codes are presented and discussed. Relation to nonbinary LDPC codes is explained. Examples are given.
Biography: Irina E. Bocharova was born in Leningrad, U.S.S.R., 1955. She received the Diploma in Electrical Engineering in 1978 from the Leningrad Electro-technical Institute and the Ph.D. degree in technical sciences in 1986 from Leningrad Institute of Aircraft Instrumentation.
Since 2007, she has been Associate Professor at the State University of Information Technologies, Mechanics and Optics. Her research interests include convolutional codes, communication systems, source coding and its applications to speech, audio and image coding. She has more than 60 papers published in journals and proceedings of international conferences, and seven U.S. patents in speech, audio and video coding. She has authored the textbook «Compression for Multimedia», Cambridge University Press, 2010.
Professor Bocharova was awarded the Lise Meitner Visiting Chair in engineering at Lund University, Lund, Sweden twice (January--June 2005 and 2011). In 2014 she received Scopus Russia Award.
Abstract: A unified approach to construct and optimize codes determined by their sparse parity-check matrices is presented. Replacing the nonzero elements of a binary parity-check matrix (the base or parent matrix) either by circulants or by companion matrices of elements from a finite field GF(2^m), we obtain quasi-cyclic (QC) LDPC block codes and binary images of nonbinary LDPC block codes, respectively. By substituting monomials of a formal variable $D$ we obtain the polynomial description of an LDPC convolutional code. A set of performance measures applicable to different classes of LDPC codes are considered and a greedy algorithm for code performance optimization is presented. For a few classes of LDPC codes examples of codes combining good error-correcting performance with compact representation are obtained. The low encoding and decoding complexity is an additional advantage of these codes. Moreover, a specific channel model can easily be embedded into the optimization loop. Thereby, the code can be optimized for a specific channel. The efficiency of such an optimization is demonstrated via an example of Faster Than Nyquist (FTN) signaling using LDPC codes.
Biography: Boris D. Kudryashov was born in Leningrad, U.S.S.R., 1952. He received the Diploma in Electrical Engineering in 1974 and the Ph.D. in technical sciences degree in 1978 both from the Leningrad Institute of Aerospace Instrumentation, and the Doctor of Science degree in 2005 from Institute of Problems of Information Transmission, Moscow.
Since November 2007, he has been Professor at the State University on Information Technologies, Mechanics and Optics, St.-Petersburg, Russia. His research interests include coding theory, information theory and applications to speech, audio and image coding. He has authored a textbook on information theory (in Russian), and has more than 80 papers published in journals and proceedings of international conferences, 20 U.S. patents in image, speech and audio coding.