Sliding-block source coding. (English) Zbl 0308.94015

Gray, Robert M.

IEEE Trans. Inf. Theory 21, 357-368 (1975).

The traditional Shannon theory focuses almost exclusively on block coding techniques, that is, source and channel codes that consist of mapping blocks of nonoverlapping data into blocks of encoded data. Such codes (1) have undesirable probabilistic properties such as loss of stationarity and ergodicity, (2) do not include several practical communications devices which act instead as linear or nonlinear filters, and (3) require synchronization and buffers.
In this paper the Kolmogorov-Ornstein Isomorphism Theorem of Ergodic Theory is shown to easily yield a noiseless source coding theorem for a non-block class of codes called sliding-block codes which consist of nonlinear, time-invariant, finite memory and finite delay filters. This result is coupled with the sliding-block source coding with a fidelity criterion theorem [the author, D. L. Neuhoff and P. C. Shields, Ann. Probab. 3, 315–328 (1975; Zbl 0304.94025)] to obtain a general sliding-block source coding theorem: As an example, Meshalkin’s isomorphism technique [L. D. Meshalkin, Dokl. Akad. Nauk SSSR 128, 41–44 (1959; Zbl 0099.12301)] is interpreted as a sliding-block \(\varepsilon\)-noiseless source code.

Reviewer: Robert M. Gray

MSC:

94A29

Source coding

Keywords:

Kolmogorov-Ornstein Isomorphism Theorem; noiseless source coding theorem; non-block class of codes

Citations:

Zbl 0304.94025; Zbl 0099.12301