  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.
