Source and Channel Simulation Using Arbitrary Randomness

Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger necessary condition. As the approximation criteria, vanishing variational distance between the original and the approximated quantity is used for both of the problems. Both necessary and sufficient conditions for the two problems are based on some individual properties of the sources and the channel and are relatively easy to evaluate. In particular, unlike prior results for this problem, our results do not require solving an optimization problem to test simulatability. The results are illustrated with several non-ergodic examples.