Multidimensional trellis coding for MPSK

The use of multidimensional M-ary phase-shift keying (MPSK) signaling is considered for bandwidth and power efficient communication. Trellis-coded modulation is used to code N successive symbols (N-dimensional coding) of MPSK at one time to form a more complex signal than symbol-by-symbol coding, with the expectation of improved performance. In the general case, it is found that the allowed values of bandwidth efficiency (b.p.s./Hz or bits/symbol) are a discrete set, any integer plus J/N where J can have the integer values 0 through N-1. In all cases, the allowed values of M are smaller than those for symbol-by-symbol coding for the same bandwidth efficiency. Thus, the minimum distance between signal points is increased by N-dimensional coding, and this is an important factor in increasing the coding gain. A search of possible trellises and codes reveals that trellis coding of two 6 PSK symbols at a time for 2 b.p.s./Hz gives an asymptotic coding gain of 4.77 dB (as compared to uncoded 4 PSK) with a 16-state trellis