Multigroup-decodable STBCs from Clifford algebras

Abstract

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 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.