# The Method of Types for the AWGN Channel

## TL;DR

This paper provides new ways to calculate error and decoding bounds for a communication channel using a method involving finite alphabets.

## Contribution

The paper introduces alternative derivations for error and decoding bounds using the method of types with sub-exponential complexity.

## Key findings

- Sphere-packing upper bound on the optimal block error exponent is derived using the method of types.
- A lower bound on the optimal correct-decoding exponent is also derived using similar techniques.
- The method uses finite alphabets with sizes dependent on block length n.

## Abstract

For the discrete-time AWGN channel with a power constraint, we give an alternative derivation for the sphere-packing upper bound on the optimal block error exponent and an alternative derivation for the analogous lower bound on the optimal correct-decoding exponent. The derivations use the method of types with finite alphabets of sizes depending on the block length n and with the number of types sub-exponential in n.