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This paper studies the performance of block coding on an additive whiteGaussian noise channel under different power limitations at the transmitter.Lower bounds are presented for the minimum error probability of codessatisfying maximal and average power constraints. These bounds are tighter thanprevious results in the finite blocklength regime, and yield a betterunderstanding on the structure of good codes under an average power limitation.Evaluation of these bounds for short and moderate blocklengths is alsodiscussed.

Error Probability Bounds for Gaussian Channels under Maximal and Average Power Constraints