Block coset codes for M-ary phase shift keying

Construction of efficient block-encoded M-ary phase-shift-keying (M-PSK) schemes is investigated. 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 the linear codes are studied. From this analysis, a class of codes called blocked coset codes is obtained. 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 representations yields the standard block coset code construction, which is applicable to M-PSK for M of the form 2^k×3^l . The standard block coset code construction is seen to be equivalent to block code constructions previously reported in the literature, and it 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 ^k×3^l PSK block coset codes is included