Theoretical basics of digital radio communication are developed for three decades. In the last decade are introduced individual systems into the praxis. Actual state is described as standard UMTS, and it is enhanced to be created basics of the next generations of systems. The mathematical description of tools devoted for digital signal transmission has its basics in the origin of quantising description of discrete signal. The source description of digital messages is based on the number characteristics of the speed of information of generating and their similarities to the ways of modulation. Described are modulations without memory as well as with memory. Derived are criterions of optimal receiving as well as the way of other modulations.