Completion Time in Two-user Channels: An Information-Theoretic Perspective

TL;DR

This paper introduces an information-theoretic framework for analyzing completion times in two-user channels, revealing trade-offs, achievable regions, and optimization strategies for different channel types.

Contribution

It develops a novel completion time region concept using constrained rates and characterizes it for multi-access, broadcast, and interference channels with practical phase-based transmission strategies.

Findings

Completion time region is achieved by two-phase operation.

The region may be non-convex in general.

Optimal weighted sum completion time can be minimized using the proposed framework.

Abstract

In a two-user channel, completion time refers to the number of channel uses spent by each user to transmit a bit pool with some given size. In this paper, the information-theoretic formulation of completion time is based on the concept of constrained rates, where users are allowed to employ different numbers of channel uses for transmission as opposed to the equal channel use of the standard information-theoretic formulation. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time region (or inner and outer bounds) is established for a Gaussian broadcast channel and a Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally an optimization problem of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel is solved, demonstrating the utility of the completion time approach.