On the data processing theorem in the semi-deterministic setting

TL;DR

This paper establishes data processing lower bounds on expected distortion in semi-deterministic settings, linking source complexity and decoder limitations, with implications for finite-state and linear encoding schemes.

Contribution

It introduces new lower bounds based on Lempel-Ziv complexity and extends results to linear encoders and decoders in continuous alphabets.

Findings

Lower bounds on expected distortion derived for semi-deterministic sources.

Bounds expressed via Lempel-Ziv complexity of source and reproduction sequences.

Extension of results to linear encoders and decoders in continuous alphabet scenarios.

Abstract

Data processing lower bounds on the expected distortion are derived in the finite-alphabet semi-deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder is subjected to various kinds of limitations, e.g., decoders implementable by finite-state machines, with or without counters, and with or without a restriction of common reconstruction with high probability. Some of our bounds are given in terms of the Lempel-Ziv complexity of the source sequence or the reproduction sequence. We also demonstrate how some analogous results can be obtained for classes of linear encoders and linear decoders in the continuous alphabet case.