A new technique to evaluate an expurgated bound on punctured turbo trellis coded modulation

This work presents an enumerative technique to evaluate the distance spectrum of punctured turbo trellis coded modulation (TuCM) composed of two trellis coded modulation (TCM) component encoders connected in parallel via an interleaver. A matrix-based transfer function approach is employed to find the multiplicities of Hamming and Euclidean distances of input and output strings (distance spectrum) of each component TCM encoders after puncturing. An expurgated union bound on the bit error rate of TuCM schemes over the AWGN channel is computed using the distance spectrum. Comparisons with simulation results shows that the bound is tight in the range of the signal to noise of interest.