The single-user separation theorem of joint source-channel coding has been proved previously for wide classes of sources and channels. We find an information-stable source/channel pair which does not satisfy the separation theorem. New necessary and sufficient conditions for the transmissibility of a source through a channel are found, and we characterize the class of channels for which the separation theorem holds regardless of the source statistics.>

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.>