Space - time block factorisation codes over Gaussian integers

A solution for the design of space time codes over a complex signal constellation is given. The Gaussian integer field is described and shown to produce a similar complex signal constellation as QAM for particular parameters. The mapping between the Galois field and the Gaussian integer field is shown to preserve the rank statistics of codeword matrices and thereby the diversity gain of the code. Factorisation space time codes, which have similarities to BCH codes, are constructed over a Galois field and then mapped to a Gaussian integer constellation. This construction is one example of how classical coding theory can be directly applied to space time code design. Statistical analysis of the Euclidean, geometric and rank metrics, is performed. The codeword error performance for different dimensions is shown to give full rank and to perform marginally better than a similar delay diversity code for the parameters considered.