An algebraic look into MAC-DMT of lattice space-time codes

TL;DR

This paper analyzes the diversity-multiplexing trade-off of lattice space-time codes, providing bounds, recovering known results, and revealing connections to algebraic number theory, ultimately showing the optimality of certain codes in MAC.

Contribution

It introduces a DMT bound for restricted-dimension lattice codes and demonstrates the optimality of algebraic number field codes and Alamouti code in MAC.

Findings

Derived a DMT bound for restricted-dimension lattice codes.

Reproduced known DMT results for algebraic number field codes and Alamouti code.

Established the optimality of these codes in multiple access channels.

Abstract

In this paper we are concentrating on the diversity-multiplexing gain trade-off (DMT) of some space-time lattice codes. First we give a DMT bound for lattice codes having restricted dimension. We then recover the well known results of the DMT of algebraic number field codes and the Alamouti code by using the union bound and see that these codes do achieve the previously mentioned bound. During our analysis interesting connections to the Dedekind's zeta-function and to the unit group of algebraic number fields are revealed. Finally we prove that both the number field codes and Alamouti code are in some sense optimal codes in the multiple access channel (MAC).