An inequality on guessing and its application to sequential decoding

Abstract

Let (X,Y) be a pair of discrete random variables with X taking values from a finite set. Suppose the value of X is to be determined, given the value of Y, by asking questions of the form 'is X equal to x?' until the answer is 'yes'. Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. The main result is a tight lower bound on nonnegative moments of G(X|Y). As an application, lower bounds are given on the moments of computation in sequential decoding. In particular, a simple derivation of the cutoff rate bound for a single-user channels is obtained, and the previously unknown cutoff rate region of multi-access channels is determined.