Sliding-block source coding

Both noiseless source coding and source coding with a fidelity criterion are traditionally accomplished via the mapping of consecutive nonoverlapping source blocks into code blocks of fixed or variable length. Here we use an easy application and interpretation of the Kolmogorov-Ornstein isomorphism theorem of ergodic theory to prove the existence of a new class of noiseless source coding techniques consisting of nonlinear time-invariant discrete-time filters. The output codes are physically stationary, are not of variable length, require no buffers except for the filter memory, are not catastrophically affected by occasional channel errors, and provide a new interpretation of noiseless source coding. An information-theoretic interpretation of an early special case of the isomorphism theorem provides an example. The noiseless sliding-block theorem is then coupled with the sliding-block source coding subject to a fidelity criterion theorem to obtain a general sliding-block source coding theorem for noiseless and almost noiseless Channels. The approach, assumptions, and results are compared and contrasted with the special cases of quantization, delta modulation, and block stationary convolutional, trellis, tree, Viterbi, and sequential source coding techniques.