On the analytical representation of trellis codes

Abstract

The authors examine some of the features of an analytical representation for trellis-coded modulation (TCM), based on a single function f. They first consider the structure of the function, f, and observe that (i) it must be nonlinear, (ii) it can reflect certain phase-invariance properties of the code, and (iii) it can reflect the intrinsic parallel structure of the encoder. Then they provide a general parametric representation of f based on orthogonal Volterra series, and show some examples of code design for channels with intersymbol interference.<>