The Bee-Identification Problem: Bounds on the Error Exponent

Error Exponents in the Bee Identification Problem

“…They show that for any of the two decoders, the error exponent of the typical random code (TRC) is strictly higher than the random coding error exponent at relatively low coding rates, as is already known to happen in ordinary channel coding over a general DMC [7], [9]. In [14], a converse bound is also derived, which is proved to have the same value as the value of the TRC exponent under joint decoding at rate zero. In a different work [15], the same authors of [14] study the capacity and the error exponent of the bee identification problem, but when some fraction of the bees are assumed to be outside the beehive.…”

“…In [14], a converse bound is also derived, which is proved to have the same value as the value of the TRC exponent under joint decoding at rate zero. In a different work [15], the same authors of [14] study the capacity and the error exponent of the bee identification problem, but when some fraction of the bees are assumed to be outside the beehive. The authors provide an exact characterization of the error exponent and they prove that independent decoding is optimal.…”

“…Recently, the bee identification problem has been studied from the viewpoint of its exponential error bounds. In [14], the codebook is composed by binary codewords, which are permuted and fed into a binary symmetric channel (BSC). In that work, two different decoding techniques have been considered; independent decoding and joint decoding.…”

“…The focus of this work is on extensions and refinements of the error exponent analysis of the same decoding rules studied in [14]. In particular, the main contributions of this work are the following.…”

“…1. In naïve (independent) decoding, we adopt a slightly relaxed definition for the probability of error; while in [14], error counts even if a single bee is incorrectly decoded, here, we refer to an error event only when at least L bees are erroneously decoded. We believe that such a relaxed definition may be more suitable in this kind of problem (and others as well), which accounts for a massive amount of data.…”