An Information Theoretic Point of View to Contention Resolution

TL;DR

This paper models contention resolution in wireless networks using information theory, linking delay to entropy, and explores optimal threshold strategies for efficient user scheduling.

Contribution

It introduces an information-theoretic framework for contention resolution, relating delay to entropy and analyzing optimal threshold strategies in opportunistic scheduling.

Findings

Delay is related to the entropy of the threshold distribution.

Maximal probability allocation minimizes entropy and delay.

Framework applies to various network scenarios.

Abstract

We consider a slotted wireless network in an infrastructure setup with a base station (or an access point) and N users. The wireless channel gain between the base station and the users is assumed to be i.i.d., and the base station seeks to schedule the user with the highest channel gain in every slot (opportunistic scheduling). We assume that the identity of the user with the highest channel gain is resolved using a series of contention slots and with feedback from the base station. In this setup, we formulate the contention resolution problem for opportunistic scheduling as identifying a random threshold (channel gain) that separates the best channel from the other samples. We show that the average delay to resolve contention is related to the entropy of the random threshold. We illustrate our formulation by studying the opportunistic splitting algorithm (OSA) for i.i.d. wireless channel [9]. We note that the thresholds of OSA correspond to a maximal probability allocation scheme. We conjecture that maximal probability allocation is an entropy minimizing strategy and a delay minimizing strategy for i.i.d. wireless channel. Finally, we discuss the applicability of this framework for few other network scenarios.