Reduced-complexity ML decodable STBCs: Revisited design criteria

In this work, we revisit the structure of weight matrices for Linear Dispersion STBCs to admit ML decoding with low-complexity. We first propose novel sufficient design criteria for linear STBCs considering an arbitrary number of antennas and an arbitrary coding rate. Then we apply the derived criteria to three families of codes, multi-group decodable, fast decodable, and fast-group decodable codes. We provide analytical proofs showing that the ML-decoding complexity of such codes depends only on the weight matrices and their ordering and not on the channel gains or the number of antennas and explaining why the so far used Hurwitz-Radon theory-based approaches do not exactly determine the complexity of all classes of STBCs under ML decoding.