Spectrum Invariancy Under Output Approximation for Full-Rank Discrete Memoryless Channels

Given a channel, the resolvability of an input process is the minimum randomness of those input processes whose output statistics approximate the original output statistics with arbitrary accuracy. We give a formula for the resolvability of any input process when the channel is full-rank discrete memoryless. When the input process is stationary and ergodic, its resolvability is equal to its mutual information rate. This result is obtained as a corollary of a theorem that shows that if two input processes result in approximately the same output statistics, then their corresponding information spectra (distributions of normalized information density) are almost identical.