New rotationally invariant trellis codes for 8PSK modulation

With the help of two-dimensional (2-D) symbol constellations, 8PSK (phase-shift keying) trellis codes are presented that are rotationally invariant to phase shifts by multiples of π/4 without an increase in complexity over noninvariant codes. The use of 2-D symbol sets leads to the problem that an additional 2-D symbol synchronization is necessary. However, this can easily be achieved because each 2-D symbol comprises either two even or two odd 8PSK symbols, i.e. given the first 8PSK symbol of a 2-D symbol, the second one is chosen out of a 4PSK set, which can even be used to obtain better phase synchronization. Another advantage of applying 2-D codes is that Viterbi decoding has to be performed with only half the symbol rate, which can be desirable for high-speed applications. With the help of a novel arithmetic architecture, it is possible to design a 100-Mb/s Viterbi decoder. Two basic methods of deriving new codes are used: the application of multidimensional code symbols and the method of symbol-by-butterfly replacement