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On hypercontractivity and the mutual information between Boolean functions
, Article 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013, Monticello, IL ; Oct , 2013 , Pages 13-19 ; 9781479934096 (ISBN) ; Gohari, A. A ; Kamath, S ; Nair, C ; Sharif University of Technology
IEEE Computer Society
2013
Abstract
Hypercontractivity has had many successful applications in mathematics, physics, and theoretical computer science. In this work we use recently established properties of the hypercontractivity ribbon of a pair of random variables to study a recent conjecture regarding the mutual information between binary functions of the individual marginal sequences of a sequence of pairs of random variables drawn from a doubly symmetric binary source
Empirical coordination in a triangular multiterminal network
, Article IEEE International Symposium on Information Theory - Proceedings ; 2013 , Pages 2149-2153 ; ISSN: 21578095 ; ISBN: 9781479904464 ; Bahrami, M ; Mirmohseni, M ; Aref, M. R ; Sharif University of Technology
2013
Abstract
In this paper, we investigate the problem of the empirical coordination in a triangular multiterminal network. A triangular multiterminal network consists of three terminals where two terminals observe two external i.i.d correlated sequences. The third terminal wishes to generate a sequence with desired empirical joint distribution. For this problem, we derive inner and outer bounds on the empirical coordination capacity region. It is shown that the capacity region of the degraded source network and the inner and outer bounds on the capacity region of the cascade multiterminal network can be directly obtained from our inner and outer bounds. For a cipher system, we establish key distribution...
On Körner-Marton's sum modulo two problem
, Article IWCIT 2015 - Iran Workshop on Communication and Information Theory, 6 May 2015 through 7 May 2015 ; May , 2015 ; 9781479982356 (ISBN) ; Gohari, A ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
In this paper we study the sum modulo two problem proposed by Körner and Marton. In this source coding problem, two transmitters who observe binary sources X and Y, send messages of limited rate to a receiver whose goal is to compute the sum modulo of X and Y. This problem has been solved for the two special cases of independent and symmetric sources. In both of these cases, the rate pair (H(X|Y), H(Y|X)) is achievable. The best known outer bound for this problem is a conventional cut-set bound, and the best known inner bound is derived by Ahlswede and Han using a combination of Slepian-Wolf and Körner-Marton's coding schemes. In this paper, we propose a new outer bound which is strictly...