On the optimal asymptotic performance of universal ordering and of discrimination of individual sequences

The authors consider the problem of ordering strings of a fixed length over a discrete alphabet according to decreasing probabilities of having been emitted by an unknown finite-state source. Data compression is applied to derive a universal algorithm that solves this problem with an optimal asymptotic performance. This result is employed in the solution of the following problem: discriminate an individual sequence as emitted by an independently identically distributed random source of equally likely symbols or as a signal corrupted by noise. Tight lower and upper bounds on the asymptotic performance of finite-state discriminators are given.<>