The use of coding in digital communications, to be effective, requires that the modulation system be designed on an unconventional basis. Rather than using "error probability" as the modulation criterion, this paper argues that the appropriate modulation criterion is the "cut-off rate" R of the discrete channel which the modulation system creates. It is then shown that the R criterion leads to a rich "communication theory" of its own in which the optimality of the simplex signal set can be proved (rather than conjectured) and in which "soft decision" demodulators can be systematically designed. At the same time, the R criterion leads to a modulation system compatible with the use of effective coding techniques in an overall efficient digital communication system.