In this chapter, based on definitions of signal synthesizers and analysers, a general and generic scheme of a discrete communication system is developed in order to deduce practical systems as its special cases. The synthesizer is transferred into a discrete transmitter, and the analyser is used as a correlation receiver followed by an optimum detector. The system structure is presented in terms of mathematical operators and supported by exact mathematical expressions based on the theory of discrete-time stochastic processes. The likelihood function is derived, and the maximum likelihood rule is applied to specify the decision process and construct the optimum detector. A multilevel system and a quadrature phase-shift keying system are deduced as special cases, and the bit error probability expression is derived. For the sake of continuity and completeness in presenting communication systems theory, a generic digital communication system is developed and related to its discrete counterpart.