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Combinatorial Reasoning in Information Theory Combinatorial techniques play a crucial role in the investigation of problems in Informa-
 

Summary: Combinatorial Reasoning in Information Theory
Noga Alon
Abstract
Combinatorial techniques play a crucial role in the investigation of problems in Informa-
tion Theory. We describe a few representative examples, focusing on the tools applied, and
mentioning several open problems.
1 Introduction
Combinatorial ideas play a prominent role in the study of problems in Information theory. Indeed,
the whole theory can be developed using a combinatorial approach, as done, for example, in [12].
In this brief survey we discuss several examples in which tools from Combinatorics and Graph
Theory are applied in the investigation of problems in Information Theory. The combinatorial
approach seems especially powerful for tackling problems in zero-error information theory which
deals with scenarios in which no positive probability of error is tolerated. Problems of this type are
discussed in a significant number of papers starting with [23], and are also the focus of the present
short paper. This is not meant to be a comprehensive treatment of the subject, but hopefully
provides an interesting description of several intriguing information theoretic results obtained by
combinatorial reasoning.
2 The Shannon Capacity of graphs
For an undirected graph G = (V, E), let Gn denote the graph whose vertex set is V n in which
two distinct vertices (u1, u2, . . . , un) and (v1, v2, . . . , vn) are adjacent iff for all i between 1 and n

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics