A method of building systematically a multi-dimensional (n, D, L) circular trellis
coded modulation (CTCM)
encoder with properties of optimal energy efficiency, strong
tail biting and maximum
minimum distance (dmin) of trellis paths is disclosed. In addition, a communication
system for use in a power limited channel application is disclosed comprising a circular trellis
coded modulation (CTCM)
encoder with permuted
state structure for encoding based on a circular trellis path associated with a sequence of digital information bits and a set of simplexes identified for the path from a multi-dimensional
signal constellation; a
transmitter coupled to said CTCM
encoder for transmitting said sequence of channel symbols over said channel; a
receiver for receiving a transmission from said
transmitter including said sequence of channel symbols and any
noise induced therein; and a CTCM decoder coupled to said
receiver for decoding the received transmission without knowledge of the starting state of the circular trellis path of the CTCM encoder to recover the sequence of information bits. Apparatus and methods of encoding and decoding are also disclosed utilizing a combination of circular trellis-
coded modulation with permuted
state structure and simplex
signal constellation techniques for use in the digital communication
system.