Information Theoretic Limits for Secure Multimedia and Magnetic Recording
Kiyavash, Negar
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https://hdl.handle.net/2142/80996
Description
Title
Information Theoretic Limits for Secure Multimedia and Magnetic Recording
Author(s)
Kiyavash, Negar
Issue Date
2006
Doctoral Committee Chair(s)
Blahut, Richard E.
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
The second part of this thesis addresses the problem of finding the capacity of two-dimensional (1, infinity) constrained channels for a binary alphabet. The Shannon capacity of a constrained channel is generalized to a notion of soft capacity which allows violations of the constraint. By drawing an analogy with an Ising array of the same geometry, it is proven that finding the soft capacity is equivalent to finding the partition function of the Ising model. Therefore, the problem of finding the capacity of a two-dimensional (1, infinity) constrained channel is reduced to the problem of finding an eigenvalue of a matrix.
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