This paper studies the performance of block coding on an additive white
Gaussian noise channel under different power limitations at the transmitter.
Lower bounds are presented for the minimum error probability of codes
satisfying maximal and average power constraints. These bounds are tighter than
previous results in the finite blocklength regime, and yield a better
understanding on the structure of good codes under an average power limitation.
Evaluation of these bounds for short and moderate blocklengths is also
discussed.Comment: Submitted to the IEEE Transactions on Information Theory. This
article was presented in part at the 2019 IEEE International Symposium on
Information Theory, Paris, France (ISIT 2019) and at the 2020 International
Z\"urich Seminar on Communication and Information, Z\"urich, Switzerland (IZS
2020
