High-rate information-lossless linear dispersion STBCs from group algebra

For multiple-input multiple-output (MIMO) channels, at high spectral efficiencies, space-time block codes (STBC) must be designed to maximize the mutual information between the transmit and receive signals. In an uncoiled scheme (spatial multiplexing or V-BLAST), it is well-known that the Gaussian input distribution maximizes the mutual information. Hassibi and Hochwald (2002) introduced a linear dispersion (LD) framework for designing space-time codes, wherein any transmit codeword is a linear combination of a fixed set of matrices called the weight matrices. A LD space-time block code is said to be information-lossless if it does not disturb the maximum mutual information between the transmit and receive signals. In other words, a MIMO scheme using information-lossless LD space-time block codes has the same capacity as the uncoded scheme. Through computer search, information-lossless LD codes with better diversity compared to the uncoded system were found by Hassibi et al., and also by Heath et al. (2002). We give a general algebraic construction of high-rate information-lossless STBC, both square and rectangular, by restricting the weight matrices to those which form a finite group under matrix multiplication.