A prefix-free coding for finite-state noiseless channels with small coding delay

We consider a problem to build good prefix-free code for the transmission of a stationary memoryless source across a finite-state noiseless channel with unequal symbol costs. Our scheme is an improvement of Golin and Rote´s algorithm for constructing good prefix-free codes to the state dependent noiseless channel case by removing an assumption that channel has only one state. As an application of our scheme, we suggest better codes to minimize the expected cost for given discrete memoryless sources and the run-length coding with (d, k)-constrained noiseless channel.