Minimal complexity design of analytically described trellis codes

G. Ungerboeck (1982) has shown how to specify trellis codes that have some power gain and the same bandwidth as their corresponding uncoded schemes. He realizes his trellis codes by a convolutional encoder followed by a mapping rule. R. Calderbank and J.E. Mazo (1984) have shown how to realize these two operations in a single-step procedure, thus yielding analytically described trellis codes. These ideas are extended to any number of dimensions and to rotationally invariant trellis codes. Design rules that yield minimal complexity for analytically described trellis codes are presented, and these rules generally provide a hand design for trellis codes. A 2-D and 4-D example are used to illustrate the author´s approach.<>