Opportunistic capacity and error exponent regions for compound channel with feedback

TL;DR

This paper explores variable length feedback communication over compound channels, defining an opportunistic capacity region that adapts to the channel, and provides bounds on the error exponent region, enhancing understanding of reliable communication in uncertain environments.

Contribution

It introduces an opportunistic capacity region for compound channels with feedback and derives lower bounds for the error exponent region, advancing the theoretical framework.

Findings

Opportunistic capacity region characterized for compound channels with feedback.

Lower bounds established for the error exponent region.

Communication rate adapts to the channel chosen by nature.

Abstract

Variable length communication over a compound channel with feedback is considered. Traditionally, capacity of a compound channel without feedback is defined as the maximum rate that is determined before the start of communication such that communication is reliable. This traditional definition is pessimistic. In the presence of feedback, an opportunistic definition is given. Capacity is defined as the maximum rate that is determined at the end of communication such that communication is reliable. Thus, the transmission rate can adapt to the channel chosen by nature. Under this definition, feedback communication over a compound channel is conceptually similar to multi-terminal communication. Transmission rate is a vector rather than a scalar; channel capacity is a region rather than a scalar; error exponent is a region rather than a scalar. In this paper, variable length communication over a compound channel with feedback is formulated, its opportunistic capacity region is characterized, and lower bounds for its error exponent region are provided..