Remarks on criteria for achieving the optimal diversity-multiplexing gain trade-off

TL;DR

This paper challenges the sufficiency of the non-vanishing determinant criterion for optimal DMT in asymmetric STBCs, contrasting recent findings and translating universality criteria into lattice theory with new conjectures.

Contribution

It demonstrates that NVD alone does not guarantee optimal DMT, and reformulates the universality criterion in lattice theory, proposing new conjectures.

Findings

NVD criterion is insufficient for asymmetric STBCs to achieve optimal DMT

Reformulation of universality criterion in lattice theory context

Proposes conjectures to clarify the criteria for optimal DMT

Abstract

In this short note we will prove that non-vanishing determinant (NVD) criterion is not enough for an asymmetric space-time block code (STBC) to achieve the optimal diversity-multiplexing gain trade-off (DMT). This result is in contrast to the recent result made by Srinath and Rajan. In order to clarify the issue further the approximately universality criterion by Tavildar and Viswanath is translated into language of lattice theory and some conjectures are given.