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This paper presents an achievability bound that evaluates the exactprobability of error of an ensemble of random codes that are decoded by aminimum distance decoder. Compared to the state-of-the-art which demandsexponential computation time, this bound is evaluated in polynomial time. Thisimprovement in complexity is also attainable for the original random codingbound that utilizes an information density decoder. The general bound isparticularized for the binary symmetric channel, the binary erasure channel,and the Gaussian channel.

Efficient Evaluation of the Probability of Error of Random Coding Ensembles