Channel intrinsic randomness

We study channel intrinsic randomness, defined as the maximum random bit rate that can be extracted from a channel output independently of an input with known statistics. Independence and uniformity of the extracted process are measured by means of the variational distance between distributions. We obtain an expression for channel intrinsic randomness in terms of the statistics of the channel and its input process, which holds for arbitrary discrete channels and arbitrary discrete inputs. We discuss the connection between channel intrinsic randomness and secret-key distillation, and show that channel intrinsic randomness appears as the natural operation behind key distillation. As a supporting result, we obtain achievable secret-key rates for compound sources.