Coset codes-I: Introduction and geometrical classification

Practically all known good constructive coding techniques for band-limited channels, including lattice codes and various recently proposed trellis-coded modulation schemes, can be characterized as coset codes. A coset code is defined by a lattice partition A / A and by a binary encoder C that selects a sequence of cosets of the lattice A'. 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 and A/A. 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.