Further error event diagram reduction using algorithmic techniques

Biglieri showed that a diagram with N² 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 [(N² - N)/2] + 1.