  The analysis of random coding error exponents pertaining to erasure/list
decoding, due to Forney, is revisited. Instead of using Jensen's inequality as
well as some other inequalities in the derivation, we demonstrate that an
exponentially tight analysis can be carried out by assessing the relevant
moments of a certain distance enumerator. The resulting bound has the following
advantages: (i) it is at least as tight as Forney's bound, (ii) under certain
symmetry conditions associated with the channel and the random coding
distribution, it is simpler than Forney's bound in the sense that it involves
an optimization over one parameter only (rather than two), and (iii) in certain
special cases, like the binary symmetric channel (BSC), the optimum value of
this parameter can be found in closed form, and so, there is no need to conduct
a numerical search. We have not found yet, however, a numerical example where
this new bound is strictly better than Forney's bound. This may provide an
additional evidence to support Forney's conjecture that his bound is tight for
the average code. We believe that the technique we suggest in this paper can be
useful in simplifying, and hopefully also improving, exponential error bounds
in other problem settings as well.
