BLOCK-CODED PSK MODULATION USING 2-LEVEL GROUP CODES OVER DIHEDRAL GROUPS

A length n group code over a group G is a subgroup of G(n) under compo nent-wise group operation. Group codes over dihedral groups D-M, with 2M elements, that are two-level constructible using a binary code and a code over Z(M) residue class integer ring module M, as component cod es are studied for arbitrary M. A set of necessary and sufficient cond itions on the component codes for the two-level construction to result in a group code over D-M are obtained. The conditions differ for M od d and even. Using two-level group codes over D-M as label codes, perfo rmance of block-coded modulation scheme is discussed under all possibl e matched labelings of 2M-APSK and 2M-SPSK (asymmetric and symmetric P SK) signal sets in terms of the minimum squared Euclidean distance. Ma tched labelings that lead to Automorphic Euclidean Distance Equivalent codes are identified. It is shown that depending upon the ratio of Ha mming distances of the component codes some labelings perform better t han other. The best labeling is identified under a set of restrictive conditions. Finally, conditions on the component codes for phase rotat ional invariance properties of the signal space codes are discussed.