V.L. Tamp, V.N. Nosikov, M.Y. Mikhlin

One of the ways of increasing efficiency of systems of data transmission is coordination of work of a codec and a modem. As a result trellis coded modulation (TCM) in the signal space chosen is being shaped. The most widespread TCM is a design with trellis coding. At present empirical approaches are used to choose trellis coders with different variants of their descriptions. The existing approaches do not allow to analyse to the full extent their structure to develop devices with given features. The main ways of the analytical description of coder linear unceasing codes are their presentation as generating and checking matrixes. For displaying nonlinear trellis codes one uses trellis diagrams of R trellis coders which are presented as half-infinite graphs of the GR(V) type, describing the relation of the structure of coders with status of their registers and output sequence symbols. It is shown that interpretation of the graph in a matrix form definitely defines its internal structure (the position of edges and their orientation), but does not take into account changes in coder functioning. In this connection it is recommended to use together the incidence matrix and code the matrix in Hemming metrics, which allow to describe precisely the structure of a graph and interrelation between status of a coder and its output values. This approach to the description defines to the full extent the structure of the trellis coder.