Worst-Case Expected-Capacity Loss of Slow-Fading Channels

TL;DR

This paper characterizes the worst-case expected-capacity loss in slow-fading channels, providing precise measures for delay-limited communication scenarios and extending results to fading paper writing.

Contribution

It introduces a worst-case expected-capacity loss framework and derives exact characterizations for slow-fading channels and fading paper scenarios.

Findings

Exact characterization of worst-case additive and multiplicative capacity loss.

Extension of capacity loss analysis to fading paper writing.

Results within one bit per channel use for the fading paper case.

Abstract

For delay-limited communication over block-fading channels, the difference between the ergodic capacity and the maximum achievable expected rate for coding over a finite number of coherent blocks represents a fundamental measure of the penalty incurred by the delay constraint. This paper introduces a notion of worst-case expected-capacity loss. Focusing on the slow-fading scenario (one-block delay), the worst-case additive and multiplicative expected-capacity losses are precisely characterized for the point-to-point fading channel. Extension to the problem of writing on fading paper is also considered, where both the ergodic capacity and the additive expected-capacity loss over one-block delay are characterized to within one bit per channel use.