In this work, the geometric relation between space time block code design for
the coherent channel and its non-coherent counterpart is exploited to get an
analogue of the information theoretic inequality I(X;S)≤I((X,H);S) in
terms of diversity. It provides a lower bound on the performance of
non-coherent codes when used in coherent scenarios. This leads in turn to a
code design decomposition result splitting coherent code design into two
complexity reduced sub tasks. Moreover a geometrical criterion for high
performance space time code design is derived.Comment: final version, 11 pages, two-colum