Comparison of two optimum rates for noiseless encoding of a nonstationary information source

A nonstationary finite-alphabet information source μ is noiselessly encoded, first by adaptive block to variable-length codes and then by finite-state codes of this kind. It is shown that if μ belongs to a certain class of sources that includes those with finite-order Markov memory, then a stationary input-restricted channel exists such that in the first case the optimum encoding rate is equal to the largest conditional entropy for channel input given channel output, whereas in the second case it is the largest channel output entropy. A sufficient condition for the two rates to be equal is also given