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

## TL;DR

This paper derives tighter error probability bounds for Gaussian channels with maximal and average power constraints, enhancing understanding of code performance in finite blocklength regimes.

## Contribution

It provides new lower bounds on error probability that improve upon previous results, especially for short and moderate blocklengths.

## Key findings

- Bounds are tighter than previous results.
- Better understanding of code structure under average power constraints.
- Evaluation applicable to short and moderate blocklengths.

## Abstract

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.