The Bee-Identification Problem: Bounds on the Error Exponent

Consider the problem of identifying a massive number of bees, uniquely labeled with barcodes, using noisy measurements. We formally introduce this “bee-identification problem”, define its error exponent, and derive efficiently computable upper and lower bounds for this exponent. We show that joint decoding of barcodes provides a significantly better exponent compared to separate decoding followed by permutation inference. For low rates, we prove that the lower bound on the bee-identification exponent obtained using typical random codes (TRC) is strictly better than the corresponding bound obtained using a random code ensemble (RCE). Further, as the rate approaches zero, we prove that the upper bound on the bee-identification exponent meets the lower bound obtained using TRC with joint barcode decoding.

I. Introduction

Consider a group of different bees, in which each bee is tagged with a unique barcode for identification purposes in order to understand interaction patterns in honeybee social networks [1]. Assume that a camera is employed to picture the beehive to study the interactions among bees. The image output (see Fig. 1) can be considered as a noisy and unordered set of barcodes. We formally pose the problem of bee-identification from a beehive image as an information-theoretic problem (Sec. I-B). Fig. 1.

Bees tagged with barcodes (adapted from [1]).