Block coset codes for M-ary phase shift keying

Aktract-Construction of efficient block-encoded M-ary phase shift keying (M-PSK) schemes is investigated in this paper. An algebraic approach is adopted in which the basic modulation signals are associated with the elements of a finite group. Using some of the properties of group partition chains, the algebraic properties of linear codes are investigated. From this analysis, a class of codes called block coset codes is introduced. Distance properties of the block coset codes are obtained in terms of the distance properties of the underlying group partition chain. A particular choice of coset representatives yields the standard block coset code construction, which is applicable to M-PSK for M of the form 2‘ x 3’. The standard block coset code construction is seen to be equivalent to block code constructions previously reported in the literature, and is modified to account for the fact that the 4 PSK constellation forms a Hamming space; the modification results in substantial improvements in some cases. A table of some examples of 2’ x 3‘ PSK block coset codes is included.