Further error event diagram reduction using algorithmic techniques

Biglieri showed that a diagram with N/sup 2/ states can be used to compute the generating function for any trellis code with N states. Rouanne & Costello and Zehavi & Wolf showed that for quasi-regular trellis codes, an N-state diagram produces the correct generating function. Schlegel showed that application of a standard FSM (finite-state-machine) minimization algorithm reduces quasi-regular trellis code diagrams to at most N states and often reduces the number of states for non-quasi-regular trellis codes as well. In this paper we show that performing iteratively both a forward and a backward application of Schlegel's state reduction operation can further reduce the diagram produced by Schlegel's algorithm. We also found that the maximum required diagram size for linear trellis codes to be [(N/sup 2/ - N)/2] + 1.