Lower Bound for Ensemble-Average Error Probability for a Discrete Memoryless Channel

The article obtains a lower asymptotic bound for the average error probability over a standard ensemble of codes for the case of decoding using a list of fixed length $L\geq 1$ for a discrete memoryless channel. For all coding rates, this bound establishes the optimality of the exponent of the familiar Gallager upper bound [E. G. Gallager, Information Theory and Reliable Communication, Wiley, 1968].