Minimum-decoding-complexity, maximum-rate space-time block codes from Clifford algebras

Abstract

It is well known that Alamouti code and, in general, Space-time Block Codes (STBCs) from Complex Orthogonal Designs (CODs) are Single-symbol decodable/symbol-by-symbol Decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes are obtainable from designs that are not CODs. Recently, two such classes of SSD codes have been studied: (i) Coordinate Interleaved Orthogonal Designs (CIODs) and (ii) Minimum-decoding-complexity (MDC) STBCs from Quasi-ODs (QODs). In this paper, we obtain SSD codes with unitary weight matrices (but not CODs) from matrix representations of Clifford algebras. Moreover, we derive an upper bound on the rate of SSD codes with unitary weight matrices and show that our codes meet this bound. Also, we present conditions on the signal sets which ensure full-diversity and give expressions for the coding gain.