Fully phase transparent multidimensional trellis-coded MPSK

A multidimensional trellis-code multiple shift keying (MPSK) system based on the coset code is proposed. The new configuration employs natural construction to design fully rotational invariant code. Codes of consistent structure are developed to enable the computer search of good multidimensional codes as well as the investigation of the sufficient conditions for set partitioning applied to the design of fully rotationally invariant codes. Such codes maintain a minimum amount of loss coding gains. However the associated set partitions of the good codes permit the development of fully rotationally invariant codes without expanding encoder complexity or decreasing coding gain. A variety of transmission rates is allowed within achievable minimum multidimensional signal space. Set partitioning and trellis design which guarantee full design procedure for fully rotationally invariant code is developed based on the subset- and state-rotation diagrams