Many-Broadcast Channels: Definition and Capacity in the Degraded Case

TL;DR

This paper introduces the many-user paradigm in information theory, defining capacity for degraded many-broadcast channels where the number of users grows with blocklength, and analyzes Gaussian examples with positive asymptotic message lengths.

Contribution

It extends classical multiuser information theory to scenarios with a large, growing number of users, defining capacity and analyzing Gaussian degraded many-broadcast channels.

Findings

Capacity defined for many-user regimes

Gaussian degraded channel analyzed with positive message lengths

Numerical example demonstrates achievable rates

Abstract

Classical multiuser information theory studies the fundamental limits of models with a fixed (often small) number of users as the coding blocklength goes to infinity. Motivated by emerging systems with a massive number of users, this paper studies the new {\em many-user paradigm}, where the number of users is allowed to grow with the blocklength. The focus of this paper is the degraded many-broadcast channel model, whose number of users may grow as fast as linearly with the blocklength. A notion of capacity in terms of message length is defined and an example of Gaussian degraded many-broadcast channel is studied. In addition, a numerical example for the Gaussian degraded many-broadcast channel with fixed transmit power constraint is solved, where every user achieves strictly positive message length asymptotically.