Optimum efficiently decodable layered space-time block codes

A class of layered space-time block codes is proposed for the slow Rayleigh fading multi-input multi-output (MIMO) channel. These codes consist of either orthogonal designs or uncoded symbols in each layer and therefore lend themselves to very low-complexity decoding using the idea of group decision feedback detection. The exact frame error probability (FEP) performance for such decoders is obtained without making any simplifying assumptions about the effects of error propagation. Given any finite signal-to-noise ratio and an overall rate in bits/channel use that is to be achieved, we propose to minimize the FEP to obtain optimal codes from the class of layered space-time block codes. The optimization is performed over the choice of the number of layers, the sizes of the layers, the allocation of rates to the different layers in the code, and over the allocation of powers across the transmit antennas. The resulting optimum codes are the first ones (to the best of our knowledge) that optimize the FEP as opposed to other less desirable criteria such as diversity order, worst-case pair-wise error probability, union bound on error probability, or mutual information. The optimization of FEP over the class of layered space-time codes allows us to implicitly (and optimally) trade-off diversity order and multiplexing gain while maintaining decoding complexity that is O(K/sup 2/) where K is the number of transmit antennae. We show that only special situations call for maximizing diversity order (as with orthogonal designs) or maximizing multiplexing gain (as with V-BLAST). In all other situations, very substantial improvements can be obtained by our minimum FEP codes over orthogonal designs and V-BLAST.