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Differential encoding is known to simplify receiver implementation because it by-passes channel estimation. Relying on linear constellation precoders designed in closed-from for coherent multi-antenna systems, we derive a non-constant modulus space-time differential scheme that enables diversity, does not sacrifice rate, and more interestingly, it allows for constellation designs with many degrees of freedom. Performance merits of this scheme are analyzed and compared with existing differential designs. Simulations corroborate our theoretical findings.