# The Reliability Function for the Additive White Gaussian Noise Channel at Rates above the Capacity

## TL;DR

This paper analyzes the error probability behavior of additive white Gaussian noise channels at rates exceeding capacity, establishing exponential decay and deriving the optimal error exponent using the information spectrum approach.

## Contribution

It introduces a new analysis of error probabilities above capacity and derives the optimal exponent function using the information spectrum method.

## Key findings

- Error probability tends to one exponentially for rates above capacity
- Derivation of the optimal error exponent function
- Demonstration of the usefulness of the information spectrum approach

## Abstract

We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.