  Motivated by applications of biometric identification and content
identification systems, we consider the problem of random coding for channels,
where each codeword undergoes lossy compression (vector quantization), and
where the decoder bases its decision only on the compressed codewords and the
channel output, which is in turn, the channel's response to the transmission of
an original codeword, before compression. For memoryless sources and memoryless
channels with finite alphabets, we propose a new universal decoder and analyze
its error exponent, which improves on an earlier result by Dasarathy and Draper
(2011), who used the classic maximum mutual information (MMI) universal
decoder. Further, we show that our universal decoder provides the same error
exponent as that of the optimal, maximum likelihood (ML) decoder, at least as
long as all single-letter transition probabilities of the channel are positive.
We conjecture that the same argument remains true even without this positivity
condition.
