Communicating without errors

Abstract

Let us see what Shannon meant by “channel” and “rate of transmission.” We are given a set V of symbols, and a message is just a string of symbols from V. We model the channel as a graph G = (V,E), where V is the set of symbols, and E the set of edges between unreliable pairs of symbols, that is, symbols which may be confused during transmission. For example, communicating over a phone in everyday language, we connnect the symbols B and P by an edge since the receiver may not be able to distinguish them. Let us call G the confusion graph.