Improved Target Acquisition Rates with Feedback Codes

TL;DR

This paper models target acquisition as a channel coding problem with feedback, proposing a two-stage adaptive search strategy and characterizing fundamental limits on acquisition rates, highlighting the benefits of adaptivity.

Contribution

It introduces an information theoretic framework for target search, proposes a novel two-stage adaptive strategy, and derives bounds on the benefits of adaptivity over non-adaptive methods.

Findings

The two-stage adaptive strategy approaches fundamental limits on acquisition rate.

Adaptive strategies outperform non-adaptive ones in various regimes.

Bounds on the adaptivity gain quantify the advantage of feedback-based search.

Abstract

This paper considers the problem of acquiring an unknown target location (among a finite number of locations) via a sequence of measurements, where each measurement consists of simultaneously probing a group of locations. The resulting observation consists of a sum of an indicator of the target's presence in the probed region, and a zero mean Gaussian noise term whose variance is a function of the measurement vector. An equivalence between the target acquisition problem and channel coding over a binary input additive white Gaussian noise (BAWGN) channel with state and feedback is established. Utilizing this information theoretic perspective, a two-stage adaptive target search strategy based on the sorted Posterior Matching channel coding strategy is proposed. Furthermore, using information theoretic converses, the fundamental limits on the target acquisition rate for adaptive and non-adaptive strategies are characterized. As a corollary to the non-asymptotic upper bound of the expected number of measurements under the proposed two-stage strategy, and to non-asymptotic lower bound of the expected number of measurements for optimal non-adaptive search strategy, a lower bound on the adaptivity gain is obtained. The adaptivity gain is further investigated in different asymptotic regimes of interest.