Combinatorial Aspects of Shannon Theory

Dear Colleagues,

Combinatorial tools have played a key role in information theory since as early as Shannon's 1948 paper, which used counting techniques to study constrained coding and random coding—an early instance of the probabilistic method—to prove the channel coding theorem. Information theory, in turn, has inspired work in combinatorics, inter alia, through Shannon's work on the zero-error capacity and subsequent work on error-free source-coding and communications. This cross fertilization continued unabatedly over the years and has led to numerous results in both fields.

It is the purpose of this Special Issue to explore recent developments at the interface between the two fields. While appreciating the impact that combinatorics has had on code construction, our focus is more on Shannon theory than on coding theory. On the combinatorics side, we seek results where information theory plays a key role either in the formulation or in the solution. Topics of interest include, but are not limited to:

• Zero-error capacity (constrained or unconstrained);
• Zero-error list capacity;
• Erasures-only/zero undetected errors capacity;
• The capacity of deletion/insertion/substitution channels;
• Graph-theoretic aspects of information theory;
• Information theoretic proofs in extremal combinatorics;
• Noisy Boolean functions in information theory.

Prof. Dr. Amos Lapidoth
Dr. Or Ordentlich
Prof. Dr. Ofer Shayevitz
Guest Editors

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• zero-error and erasures-only capacity
• noisy Boolean functions
• extremal combinatorics
• the capacity of the delete/substitute/insert channel