Bee-Identification Error Exponent with Absentee Bees

The "bee-identification problem" was formally defined by Tandon, Tan and Varshney [IEEE Trans. Commun., vol. 67, 2019], and the error exponent was studied. This work extends the results for the "absentee bees" scenario, where a small fraction of the bees are absent in the beehive image used for identification. For this setting, we present an exact characterization of the bee-identification error exponent, and show that independent barcode decoding is optimal, i.e., joint decoding of the bee barcodes does not result in a better error exponent relative to independent decoding of each noisy barcode. This is in contrast to the result without absentee bees, where joint barcode decoding results in a significantly higher error exponent than independent barcode decoding. We also define and characterize the `capacity' for the bee-identification problem with absentee bees, and prove the strong converse for the same.