Finite-precision intrinsic randomness and source resolvability

Abstract

Random number generators are important devices in randomized algorithms, Monte-Carlo methods, and in simulation studies of random systems. A random number generator is usually modeled as a random source emitting independent, equally likely random bits. In practice, the random source one has at hand can deviate from this idealized model, and the random number generator operates by applying a deterministic mapping on the output of the (nonideal) random source. The deterministic mapping is chosen so that the resulting process approximates, in some sense, a sequence of independent, equally likely random bits. A prime measure of the intrinsic randomness of a given source X is the maximal rate at which random bits can be extracted from X by suitably mapping its output. This maximal rate depends on the statistics of the source X and on the sense of approximation. We study the problem of finite-precision random bit generation, where the accuracy measure is the variational distance. The relevant information theory is addressed.