A 24-dimensional block code based on the Leech lattice is described for use in a 19200-b/s modem. Encoding (the process of converting binary data into message point coordinates) and detection (conversion of the received coordinates into the coordinates of the nearest code point of the lattice) are described. Decoding (the further conversion of these into binary data) is not described, since it consists of an easily achieved reversal of the encoding process. Block (1000-bit-length) error rates in the presence of white noise for baud rates of 2400 and 2743, the two baud rates at which the modem can operate, are presented. Encoding plus decoding was successfully programmed for an ADSP2100 signal processor requiring altogether slightly less than one half the processing capability.>

This paper attempts to present a comprehensive tutorial survey of the development of efficient modulation techniques for bandlimited channels, such as telephone channels. After a history of advances in commercial high-speed modems and a discussion of theoretical limits, it reviews efforts to optimize two-dimensional signal constellations and presents further elaborations of uncoded modulation. Its principal emphasis, however, is on coded modulation techniques, in which there is an explosion of current interest, both for research and for practical application. Both block-coded and trellis-coded modulation are covered, in a common framework. A few new techniques are presented.