  Universally achievable error exponents pertaining to certain families of
channels (most notably, discrete memoryless channels (DMC's)), and various
ensembles of random codes, are studied by combining the competitive minimax
approach, proposed by Feder and Merhav, with Chernoff bound and Gallager's
techniques for the analysis of error exponents. In particular, we derive a
single--letter expression for the largest, universally achievable fraction
$\xi$ of the optimum error exponent pertaining to the optimum ML decoding.
Moreover, a simpler single--letter expression for a lower bound to $\xi$ is
presented. To demonstrate the tightness of this lower bound, we use it to show
that $\xi=1$, for the binary symmetric channel (BSC), when the random coding
distribution is uniform over: (i) all codes (of a given rate), and (ii) all
linear codes, in agreement with well--known results. We also show that $\xi=1$
for the uniform ensemble of systematic linear codes, and for that of
time--varying convolutional codes in the bit-error--rate sense. For the latter
case, we also show how the corresponding universal decoder can be efficiently
implemented using a slightly modified version of the Viterbi algorithm which em
employs two trellises.
