Optimizing the Meta-Converse for Power-Constrained Gaussian Channels

We study the channel-coding performance on an additive white Gaussian noise channel with different power limitations at the transmitter. While the meta-converse bound can be used to obtain lower bounds on the minimum error probability of the best coding scheme, it is required to solve an optimization problem over n-dimensional input distributions. This point hinders its application in several scenarios of interest. In this talk, we consider the optimization of the meta-converse bound with a certain auxiliary product distribution. Exploiting certain symmetries of the bound, we simplify and solve the optimization problem over input distributions for 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. While the results are specific for the power-constrained Gaussian channel, the techniques presented could be of interest in other settings.