On the Successive Refinability of {MIMO} channels: {DMT} and Codes

Abstract

Diversity embedded space time codes are high rate codes that aredesigned such that they have a high diversity code embedded withinthem. A recent work by Diggavi and Tse characterizes theperformance limits that can be achieved by diversity embeddedspace-time codes in terms of the achievable Diversity MultiplexingTradeoff (DMT). In particular, they have shown that the trade off issuccessively refinable for rayleigh fading channels with one degreeof freedom using superposition coding and Successive InterferenceCancellation (SIC). However, for Multiple-Input Multiple-Output(MIMO) channels, the questions of successive refinability remainsopen.We consider MIMO Channels under superposition coding and SIC. Wederive an upper bound on the successive refinement characteristicsof the DMT. We then construct explicit space time codes that achievethe derived upper bound. These codes, constructed from cyclicdivision algebras, have minimal delay. Our results establish thatwhen the channel has more than one degree of freedom, the DMT is notsuccessive refinable using superposition coding and SIC. Thechannels considered in this work can have arbitrary fadingstatistics.