This paper presents a practicable scheme for building a high-frequency direct-digitizing transmitter. The transmitter uses a simple look-up table to generate a binary output stream, which is then filtered to produce a radiated signal, so that there is no need for precise digital-to-analog converters. The data in the look-up table is produced by a new constrained-list-decoding algorithm operating over the real alphabet. The transmitter can only be a modulator, or a combined encoder and modulator. The technology presented in this paper supports the generation of RF signals for commercial applications. The 10-Gbit DSP architectures currently produced for ethernet, for e.g., can be used directly to transmit these binary sequences. The paper concludes with spectra and error vector magnitude measurements for Gaussian minimum shift keying (GMSK) and quadrature phase shift keying (QPSK) with frequencies over 10 GHz.