The Method of Types for the AWGN Channel

TL;DR

This paper introduces a new derivation of Shannon's sphere-packing bound and establishes a lower bound on the correct-decoding exponent for the AWGN channel using the method of types.

Contribution

It provides an alternative derivation of the sphere-packing bound and the first lower bound on the correct-decoding exponent for the AWGN channel.

Findings

Derived an alternative proof of Shannon's sphere-packing upper bound.

Proved a lower bound on the optimal correct-decoding exponent.

Utilized the method of types with finite alphabets depending on block length.

Abstract

For the discrete-time AWGN channel with a power constraint, we give an alternative derivation of Shannon's sphere-packing upper bound on the optimal block error exponent and prove for the first time an 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.