Time-invariant trellis encoding of ergodic discrete-time sources with a fidelity criterion

The theory of sliding-block codes (nonlinear, time-invariant, discrete-time filters) is employed to obtain general source coding theorems for ergodic sources using time-invariant trellis coding (time-invariant decoding filter and replicating trellis). The results are coupled with the theory of universal block source codes to obtain universal trellis source coding theorems for classes of sources. It is shown for a certain class of sources that the problem of designing good trellis codes is equivalent to that of simulating general random processes by filtering digital memoryless sources.