Source-Channel Coding and Separation for Generalized Communication Systems

TL;DR

This paper explores generalized communication systems with non-ergodic channels and introduces new capacity and distortion metrics, revealing that classical separation may not always be optimal under these broader conditions.

Contribution

It extends the classical Shannon separation theorem by analyzing alternative capacity and distortion metrics in generalized, non-ergodic communication systems.

Findings

Different end-to-end distortion metrics affect separation optimality.

Classical separation theorem does not always hold in generalized systems.

New capacity definitions like capacity versus outage are introduced.

Abstract

We consider transmission of stationary and ergodic sources over non-ergodic composite channels with channel state information at the receiver (CSIR). Previously we introduced alternate capacity definitions to Shannon capacity, including the capacity versus outage and the expected capacity. These generalized definitions relax the constraint of Shannon capacity that all transmitted information must be decoded at the receiver. In this work alternate end-to-end distortion metrics such as the distortion versus outage and the expected distortion are introduced to relax the constraint that a single distortion level has to be maintained for all channel states. For transmission of stationary and ergodic sources over stationary and ergodic channels, the classical Shannon separation theorem enables separate design of source and channel codes and guarantees optimal performance. For generalized communication systems, we show that different end-to-end distortion metrics lead to different conclusions about separation optimality even for the same source and channel models.