Asymptotically-Good, Multigroup Decodable Space-Time Block Codes

For a family of Space-Time Block Codes (STBCs) C₁, C₂, ... , with increasing number of transmit antennas Ni, with rates Ri complex symbols per channel use, i = 1, 2, ... , we introduce the notion of asymptotic normalized rate which we define as lim_i→∞ R_i/N_i , and we say that a family of STBCs is Ri asymptotically-good if its 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 decodable, g ≥ 2, if the information symbols encoded by it can be partitioned into g groups, such that each group of symbols can be ML decoded independently of the others. In this paper we construct full-diversity g-group decodable codes with rates greater than one complex symbol per channel use for all g ≥ 2. Specifically, we construct delay-optimal, g-group decodable codes for number of transmit antennas N_t that are a multiple of g^2[g-1/2] with rate N_t/g^2g-1 + g²-g/2N_t . Using these new codes as building blocks, we then construct non-delay-optimal g-group decodable codes with rate roughly g times that of the delay-optimal codes, for number of antennas N^t that are a multiple of 2[g-1/2], with delay gN_t and rate N_t/2^g-1 +g-1/2N_t For each g ≥ 2, the new delay-optimal and nondelay-optimal families of STBCs are both asymptotically-good, with the latter family having the largest asymptotic normalized rates among all known families of multigroup decodable codes with delay T ≤ gN_t. Also, for g ≥ 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature.