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^ve -state trellis codes. Various state transition diagrams can yield the correct transfer function. Biglieri (1984) described a general algorithm using a 2^2ν(e)-state transition diagram. Rouanne and Costello (1989) and Zehavi and Wolf (1987) demonstrated that a 2^ν(e)-state transition diagram is sufficient for quasi-regular codes. This paper computes the transfer function using a 2 ^ν(e)+ν(q)-state transition diagram where ν_q might be any integer between zero and ν_e. The particular value of ν_q depends on the relationship between the constellation labeling and the convolutional encoder. For quasi-regular codes, ν_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 ν _q<ν_e and sometimes ν_q=0