Using a new technique to obtain generating function for convolutional codes

For a large constraint length convolutional code or a typical convolutional projection code, which has a constraint length of 56, Viterbi's state-diagram technique cannot be used to obtain the generating function because of the extremely large number of computations involved. A new technique based on direct computation of the distance, the number of information bits, and the branch length of a path called the state equation calculation is developed to handle such large constraint length codes. A convolutional P3 rate 1/2 code's generating function was calculated by a computer program devised specially for the P3 convolutional projection code utilizing the new technique. The bit error probability upper and lower bounds are compared with the probability of error obtained by simulation.< >