Coset codes. I. Introduction and geometrical classification

Practically all known good constructive coding techniques for bandlimited channels, including lattice codes and various trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition Lambda / Lambda ' and by a binary encoder C that selects a sequence of cosets of the lattice Lambda '. The fundamental coding gain of a coset code, as well as other important parameters such as the error coefficient, the decoding complexity, and the constellation expansion factor, are purely geometric parameters determined by C Lambda / Lambda '. The known types of coset codes, as well as a number of new classes that systematize and generalize known codes, are classified and compared in terms of these parameters.>