Returning to Shannon's Original Meaning

TL;DR

This paper revisits Shannon theory to emphasize the essential role of ergodicity in channel capacity, challenging the common belief that slow fading channels have zero capacity in the strict Shannon sense.

Contribution

It demonstrates that ergodicity is crucial for defining channel capacity and refutes the notion that slow fading channels inherently have zero capacity within Shannon's framework.

Findings

Ergodicity is essential for channel capacity.

Generalized capacity can be negative, indicating limitations.

The assertion that slow fading channels have zero capacity is conceptually incorrect.

Abstract

Shannon theory is revisited to show that ergodicity is an indispensable element of channel capacity. The generalized channel capacity $C=\sup_{\bm{X}}\underline{I}(\bm{X}; \bm{Y})$ is checked with a negative conclusion and the popular assertion "the capacity of a slow fading channel is zero in strict Shannon sense" is found to be conceptually wrong.