Reduced complexity trellis code transfer function computation

An appropriate transfer function T(W,I) allows computation of the distance spectra and union bounds on the bit error rate for 2/sup ve/-state trellis codes. Various state transition diagrams can yield the correct transfer function. Biglieri (1984) described a general algorithm using a 2/sup 2/spl nu/(e)/-state transition diagram. Rouanne and Costello (1989) and Zehavi and Wolf (1987) demonstrated that a 2/sup /spl nu/(e)/-state transition diagram is sufficient for quasi-regular codes. This paper computes the transfer function using a 2/sup /spl nu/(e)+/spl nu/(q)/-state transition diagram where /spl nu//sub q/ might be any integer between zero and /spl nu//sub e/. The particular value of /spl nu//sub q/ depends on the relationship between the constellation labeling and the convolutional encoder. For quasi-regular codes, /spl nu//sub q/=0 and the overall number of states is the same as with the technique of Rouanne et al. For codes that are not quasi-regular, the new technique often improves efficiency with /spl nu//sub q/