Asymptotically-good, multigroup ML-decodable STBCs

For a family/sequence of Space-Time Block Codes (STBCs) \mbox{C₁,C₂,…}, with increasing number of transmit antennas N_i, with rates R_i complex symbols per channel use, \mbox{i=1,2,…}, the \emph{asymptotic normalized rate} is defined as \mbox{lim_i→∞R_i/N_i}. A family of STBCs is said to be \emph{asymptotically-good} if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas. An STBC C is said to be g-group ML-decodable if its information symbols can be partitioned into g groups, such that each group of symbols can be ML decoded independently of others. In this paper, for g≥2, we construct g-group ML-decodable codes with rates greater than one complex symbol per channel use. These codes are asymptotically good too. For g>2, these are the first instances of g-group ML-decodable codes, with rates greater than 1, presented in the literature. We also construct multigroup ML-decodable codes with the best known asymptotic normalized rates. Specifically, we propose delay-optimal 2-group ML-decodable codes for number of antennas N>1 with rate \mbox{N/4+1/N} for even N and rate \mbox{N/4+5/4N−1/2} for odd N. We construct delay optimal, g-group ML-decodable codes, g>2, for number of antennas N that are a multiple of \mbox{g^{2^[g−1/2]}} with rate \mbox{N/g^{2^g−1}+g²−g/2N}. We also construct non-delay-optimal g-group ML-decodable codes, g≥2, for number of antennas N that are a multiple of \mbox{2^⌊g−12⌋}, with delay g^N and rate \mbox{N/2^g−1+g−1/2N}