A Novel Construction of 2-Group Decodable 4 x 4 Space-Time Block Codes

Fast Maximum Likelihood Decodable Space-Time Block Codes (STBCs) have recently gained a lot of interest for using in wireless communication systems. Several strategies have been introduced in the literature to build such codes, among them we mention the conditional detection strategy [1], [2], where the code matrix can be expressed as the sum of two Orthogonal STBCs by means of a unitary matrix. Thus, the decoder benefits from the orthogonality by estimating an orthogonal set of symbols assuming knowledge of the other set of symbols. Even if this strategy permits high rates, numerical optimization of the coding gain becomes unrealizable for high-order constellations. Another strategy has been proposed in the literature, the g-group decodable codes [3], [4], where the minimization of the Maximum Likelihood (ML) metric can be made over several independent subsets of symbols. Moreover, the g-group decodability strategy enables us to optimize the coding gain for each subset of symbols separately which permits the optimization of the coding gain for high-order constellations. On the other hand, the rate of g-group decodable codes is limited. In this paper, we reformulate the problem of finding Unitary Weight (UW)-2-group decodable codes in an alternative way based on necessary and sufficient conditions. Then, a simple routine is used to search for the desired code. We determine the maximum achievable rate for a specified type of weight matrices.