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Multi-antenna systems allow for a significant increase in transmission rates of coherent wireless transmissions over Rayleigh fading channels. Various multi-antenna designs have been developed in recent years targeting either high-performance or high rate. We design a layered space-time (ST) scheme equipped with linear complex field (LCF) coding, which enables full diversity with full rate, for any number of transmit- and receive-antennas through either flat or non-flat fading channels. Our theoretical claims are confirmed by simulations.