  We study the problem of universal decoding for unknown discrete memoryless
channels in the presence of erasure/list option at the decoder, in the random
coding regime. Specifically, we harness a universal version of Forney's
classical erasure/list decoder developed in earlier studies, which is based on
the competitive minimax methodology, and guarantees universal achievability of
a certain fraction of the optimum random coding error exponents. In this paper,
we derive an exact single-letter expression for the maximum achievable
fraction. Examples are given in which the maximal achievable fraction is
strictly less than unity, which imply that, in general, there is no universal
erasure/list decoder which achieves the same random coding error exponents as
the optimal decoder for a known channel. This is in contrast to the situation
in ordinary decoding (without the erasure/list option), where optimum exponents
are universally achievable, as is well known. It is also demonstrated that
previous lower bounds derived for the maximal achievable fraction are not tight
in general. We then analyze a generalized random coding ensemble which
incorporate a training sequence, in conjunction with a suboptimal practical
decoder ("plug-in" decoder), which first estimates the channel using the known
training sequence, and then decodes the remaining symbols of the codeword using
the estimated channel. One of the implications of our results, is setting the
stage for a reasonable criterion of optimal training. Finally, we compare the
performance of the "plug-in" decoder and the universal decoder, in terms of the
achievable error exponents, and show that the latter is noticeably better than
the former.
