New Bounds for the Capacity Region of the Finite-State Multiple Access Channel

TL;DR

This paper derives exact capacity bounds for finite-state multiple access channels with feedback, particularly in stationary, ergodic, and indecomposable cases, providing explicit results for specific scenarios.

Contribution

It introduces a sequence of inner and outer bounds that coincide, establishing the capacity region for certain classes of FS-MACs with feedback.

Findings

Bounds coincide for stationary ergodic FS-MACs with feedback

Explicit capacity region results for indecomposable FS-MACs without feedback

Applicable to specific scenarios with multi-letter capacity expressions

Abstract

The capacity region of the Finite-State Multiple Access Channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We provided a sequence of inner and outer bounds for this region. These bounds are shown to coincide, and hence yield the capacity region, of FS-MACs where the state process is stationary and ergodic and not affected by the inputs, and for indecomposable FS-MAC when feedback is not allowed. Though the capacity region is `multi-letter' in general, our results yield explicit conclusions when applied to specific scenarios of interest.