Summary
This paper explores how much information multiple users can send together over different types of communication channels when there are limits on the input cost, like power or energy. The authors examine various channel models including Gaussian noise and fading effects, providing exact descriptions of achievable information rates for different levels of acceptable error. They also show when certain strong theoretical properties apply and explain how these results connect to known capacity concepts in wireless communication. Their work offers clearer mathematical understanding of multiuser communication limits under practical constraints.
What this means in practice
- •For wireless network engineers: Design multiuser wireless systems respecting power limits by using precise capacity regions derived for various channel state information scenarios.
- •For telecommunication system analysts: Evaluate the performance limits of fading multiuser channels under strict input constraints and error tolerance using the paper’s capacity characterizations.
A theory result. No direct application yet.
Abstract
We study the $\varepsilon$-capacity regions of mixed multiple-access channels (MACs) with general mixture where the channel inputs are subject to a cost constraint. We first determine the $\varepsilon$-capacity results for additive MACs. We next give a single-letterized inner bound on the $\varepsilon$-capacity region for mixed memoryless MACs, and furthermore establish a single-letterized $0$-capacity region of the mixed memoryless MAC with finite alphabets in terms of the essential infimum of mutual informations for component channels. We also show that the Gaussian MAC with additive Gaussian noise satisfies the strong converse property, which is stronger than the traditional strong converse theorem, via a simple proof based on the information spectrum method that does not require the well-known ``wringing'' technique. We then focus on the quasi-static fading Gaussian MAC, for which we derive the $\varepsilon$-capacity region and show that it, in the case specialized to single-users, exactly coincides with the traditional $\varepsilon$-outage capacity region, thereby providing a Shannon-theoretic operational interpretation of the latter. We further verify, via the information spectrum method, that the $\varepsilon$-capacity regions coincide across four scenarios of CSI availability (no-CSI, CSIR, CSIT, and CSIRT). We also demonstrate that this coincidence generally fails for mixed MACs with general (not necessarily stationary or ergodic) components, and give a counter example to prove it. Finally, we extend these results to the $K$-user quasi-static fading Gaussian MAC.