Information-Lossless Space-Time Block Codes From Crossed-Product Algebras

It is known that the Alamouti code is the only complex orthogonal design (COD) which achieves capacity and that too for the case of two transmit and one receive antenna only. Damen et al. proposed a design for 2 transmit antennas, which achieves capacity for any number of receive antennas, calling the resulting STBC when used with a signal set an informationlossless STBC. In this paper, using crossed-product central simple algebras, we construct STBCs for arbitrary number of transmit antennas over an apriori specified signal set. Alamouti code and quasi-orthogonal designs are the simplest special cases of our constructions. We obtain a condition under which these STBCs from crossed-product algebras are information lossless. We give some classes of crossed-product algebras, from which the STBCs obtained are information lossless and also of fullrank. We present some simulation results for two, three and four transmit antennas to show that our STBCs perform better than some of the best known STBCs and also that these STBCs are approximately 1 dB away from the capacity of the channel with QAM symbols as input.