Error probability bounds for Gaussian channels under maximal and average power constraints

Abstract

This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. New 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.This work was supported in part by the European Research Council (ERC) under Grant 714161, and in part by the Spanish Ministry of Economy and Competitiveness under Grant TEC2016-78434-C3 (AEI/FEDER, EU)