An Efficient Generation Method for Uniformly Distributed Random Numbers
Problems of Information Transmission
Intrinsic Randomness Problem in the Framework of Slepian-Wolf Separate Coding System
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Smooth entropy and Rényi entropy
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Source and channel simulation using arbitrary randomness
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
| Hi-index | 754.84 |
Suppose we are given a random source and want to use it as a random number generator; at what rate can we generate fair bits from it? We address this question in an information-theoretic setting by allowing for some arbitrarily small but nonzero deviation from “ideal” random bits. We prove our results with three different measures of approximation between the ideal and the obtained probability distributions: the variational distance, the d-bar distance, and the normalized divergence. Two different contexts are studied: fixed-length and variable-length random number generation. The fixed-length results of this paper provide an operational characterization of the inf-entropy rate of a source, defined in Han and Verdu (see ibid., vol.39, no.3, p.752-772, 1993) and the variable-length results characterize the liminf of the entropy rate, thereby establishing a pleasing duality with the fundamental limits of source coding. A feature of our results is that we do not restrict ourselves to ergodic or to stationary sources