Completion Time in Broadcast Channel and Interference Channel

TL;DR

This paper extends the concept of completion time from multi-access channels to broadcast and interference channels, deriving the completion time region for various Gaussian channel regimes to characterize user trade-offs.

Contribution

It introduces the completion time region for broadcast and interference channels, providing exact results for Gaussian broadcast channels and bounds for interference channels.

Findings

Exact CTR for Gaussian broadcast channel in strong/very strong regimes.

Achievable CTR and outer-bound for Gaussian interference channel in weak/mixed regimes.

Framework to analyze trade-offs between users' completion times.

Abstract

In a multi-user channel, completion time refers to the number of channel uses required for users, each with some given fixed bit pool, to complete the transmission of all their data bits. This paper extends the information theoretic formulation of multi-access completion time to broadcast channel and interference channel, enabling us to obtain the so-called completion time region (CTR), which, analogous to capacity region, characterizes all possible trade-offs between users' completion times. Specifically, for Gaussian broadcast channel (GBC) and Gaussian interference channel (GIC) in the strong/very strong regime, the exact CTR is obtained. For GIC in the weak/mixed regime, an achievable CTR based on the Etkin-Tse-Wang scheme and an outer-bound are obtained.