Generalized Random Gilbert-Varshamov Codes

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• Albert Guillen i Fabregas, ICREA, Universitat Pompeu Fabra and University of Cambridge
• Friday 29 November 2019, 11:00-12:00
• Room 909B, EEE Building.

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We introduce a random coding technique for transmission over discrete memoryless channels reminiscent of the basic construction attaining the Gilbert-Varshamov bound for codes in Hamming spaces. The code construction is based on drawing codewords recursively from a fixed type class, in such a way that a newly generated codeword must be at a certain minimum distance from all previously chosen codewords, according to some generic distance function. We show that the random coding scheme attains an error exponent that is at least as high as both the random-coding exponent and the expurgated exponent, recovering the Csiszar and Korner exponent as a special case. We show that cost-constrained version of the proposed random coding scheme yields the dual expression of the above error exponent and extends its validity for general alphabets, possibly non-finite.

Albert Guillen i Fabregas is an ICREA Research Professor at the Department of Information and Communication Technologies, Universitat Pompeu Fabra and a Director of Research (part time) at the Department of Engineering, University of Cambridge. He received the Telecommunication Engineering Degree and the Electronics Engineering Degree from Universitat Politecnica de Catalunya and Politecnico di Torino, respectively in 1999, and the PhD in Communication Systems from Ecole Polytechnique Federale de Lausanne in 2004. He has held appointments at the New Jersey Institute of Technology, Telecom Italia, European Space Agency, Institut Eurecom, University of South Australia and the University of Cambridge. He is a recipient of both Starting and Consolidator Grants from the European Research Council. He is a member of the Young Academy of Europe, Senior Member of the IEEE , Editor of the IEEE Transactions on Information Theory, Foundations and Trends in Communications and Information Theory and previously of the IEEE Transactions on Wireless Communications. He was a General co-Chair of the 2016 IEEE International Symposium on Information Theory, Barcelona, July 2016.

This talk is part of the COMMSP Seminar series.

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