Diversity Order Vs Rate in an AWGN Channel

TL;DR

This paper analyzes the relationship between diversity order and data rate in AWGN channels, revealing exponential and subexponential error probability bounds across different rate regions and assessing practical code performance.

Contribution

It provides a comprehensive analysis of diversity order behavior across the entire capacity region for both theoretical bounds and practical codes in AWGN channels.

Findings

Gallager's bounds show exponential diversity at low and high rates.

Practical codes exhibit exponential diversity throughout the capacity region.

Gaussian input bounds approximate practical code performance well.

Abstract

We study the diversity order vs rate of an additive white Gaussian noise (AWGN) channel in the whole capacity region. We show that for discrete input as well as for continuous input, Gallager's upper bounds on error probability have exponential diversity in low and high rate region but only subexponential in the mid-rate region. For the best available lower bounds and for the practical codes one observes exponential diversity throughout the capacity region. However we also show that performance of practical codes is close to Gallager's upper bounds and the mid-rate subexponential diversity has a bearing on the performance of the practical codes. Finally we show that the upper bounds with Gaussian input provide good approximation throughout the capacity region even for finite constellation.