Asymptotically-Good, Multigroup ML-Decodable STBCs

For a family/sequence of Space-Time Block Codes (STBCs) C₁, C₂, ..., with increasing number of transmit antennas N_i, with rates R_i complex symbols per channel use, i = 1, 2,..., the asymptotic normalized rate is defined as lim_i→∞ R_i/N_i. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a nonzero 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 N/4 + 1/N for even N and rate N/4 + 5/4N - ½ for odd N. We construct delay optimal, g-group ML-decodable codes, g >; 2, for number of antennas N that are a multiple of g2^⌊g-1/2⌋ with rate N/^g2g-1 + g^2-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 2^⌊g-1/2⌋, with delay gN and rate N/2g-1 + g-1/2N.