Asymptotic-information-lossless designs and diversity-multiplexing tradeoff

It is well known that in the Zheng-Tse optimal diversity-multiplexing tradeoff curve, the Alamouti scheme meets the point corresponding to the maximum diversity gain only, whereas V-BLAST meets only the point corresponding to the maximum multiplexing gain. We define asymptotic-information-lossless (AILL) designs and obtain a necessary and sufficient condition under which a design is AILL. Analogous to the condition that full-rank designs achieve the point corresponding to the zero multiplexing gain of the optimal tradeoff, we show that it is a necessary and sufficient condition for a design to be AILL to achieve the point corresponding to the zero diversity gain of the optimal tradeoff curve. Also, we obtain a lower bound on the tradeoff achieved by the designs from field extensions and division algebras. The lower bound for the designs from division algebras indicates that they achieve both the extreme points (corresponding to the zero diversity gain and zero multiplexing gain) of the optimal tradeoff curve.