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

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.