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This paper presents a practicable scheme for building a high-frequency, direct digital-to-RF transmitter. The transmitter uses a simple look-up table to generate a binary output stream which then is filtered to produce a radiated signal, so that there is no need for precise digital-to-analog converters. The look-up table entries are produced by a new constrained list decoding algorithm operating over the real alphabet. This all-digital transmitter can be a modulator only, or a combined encoder and modulator and supports the direct generation of RF signals using currently available high-speed CMOS. The paper concludes with spectra having carrier frequencies over 10 GHz and data rates up to 1200 Mbps.