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 limi → ∞RiNi, and we say that a family of STBCs is 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 Nt that are a multiple of g2LeftFloor;g-12 ⌋ with rate Ntg2g-1+g2-g2Nt. 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 Nt that are a multiple of 2Left Floor g-12, with delay gNt and rate Nt2g-1+g-12Nt. For each g ≥ 2, the new delay-optimal and non-delay-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 ≤ gNt. Also, for g ≥ 3, these are the first instances of g-group decodable codes with rates greater than 1 reported in the literature. © 2002-2012 IEEE.