Multigroup-Decodable STBCs from Clifford Algebras

A Space-Time Block Code (STBC) in K symbols (variables) is called g-group decodable STBC if its maximum-likelihood decoding metric can be written as a sum of g terms such that each term is a function of a subset of the K variables and each variable appears in only one term. In this paper we provide a general structure of the weight matrices of multi-group decodable codes using Clifford algebras. Without assuming that the number of variables in each group to be the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal g-group decodable codes is presented for arbitrary number of antennas. For the special case of Nt = 2a we construct two subclass of codes: (i) A class of 2a-group decodable codes with rate a/2(a-1), which is, equivalently, a class of Single-Symbol Decodable codes, (ii) A class of (2a- 2)-group decodable with rate (a- 1)/2(a-2), i.e., a class of Double-Symbol Decodable codes. Simulation results show that the DSD codes of this paper perform better than previously known Quasi-Orthogonal Designs.