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 $N_t=2^a$ we construct two subclass of codes: (i) A class of $2a$-group decodable codes with rate $\frac{a}{2^{(a-1)}}$, which is, equivalently, a class of Single-Symbol Decodable codes, (ii) A class of $(2a-2)$-group decodable with rate $\frac{(a-1)}{2^{(a-2)}}$, 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.