Typicality graphs and their properties

Let X and Y be finite alphabets and P<inf>XY</inf> a joint distribution over them, with P<inf>X</inf> and P<inf>Y</inf> representing the marginals. For any ∈ > 0, the set of n-length sequences x<sup>n</sup> and y<sup>n</sup> that are jointly typical [1] according to P<inf>XY</inf> can be represented on a bipartite graph. We present a formal definition of such a graph, known as a typicality graph, and study some of its properties. These properties arise in the study of several multiuser communication problems.