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Universally achievable error exponents pertaining to certain families ofchannels (most notably, discrete memoryless channels (DMC's)), and variousensembles of random codes, are studied by combining the competitive minimaxapproach, proposed by Feder and Merhav, with Chernoff bound and Gallager'stechniques for the analysis of error exponents. In particular, we derive asingle--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 $\xi$ ispresented. To demonstrate the tightness of this lower bound, we use it to showthat $\xi=1$, for the binary symmetric channel (BSC), when the random codingdistribution is uniform over: (i) all codes (of a given rate), and (ii) alllinear codes, in agreement with well--known results. We also show that $\xi=1$for the uniform ensemble of systematic linear codes, and for that oftime--varying convolutional codes in the bit-error--rate sense. For the lattercase, we also show how the corresponding universal decoder can be efficientlyimplemented using a slightly modified version of the Viterbi algorithm which ememploys two trellises.

Competitive minimax universal decoding for several ensembles of random codes