Approximately Universal Codes over Slow Fading Channels

TL;DR

This paper characterizes and constructs approximately universal codes that achieve optimal diversity-multiplexing tradeoff over various slow fading channels, unifying and extending existing coding schemes.

Contribution

It provides a precise characterization of approximately universal codes that are optimal for all fading distributions, and uses this to design and validate new and existing coding schemes.

Findings

Characterization of approximately universal codes

Construction of new coding schemes with optimal tradeoff

Validation of existing schemes' optimality

Abstract

Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. Our main contribution is a precise characterization of codes that are universally tradeoff-optimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. We denote this characterization as one of approximate universality where the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains, respectively. The characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space-time coding literature.