On the asymptotic input-output weight distributions and thresholds of convolutional and turbo-like encoders

We present a general method for computing the asymptotic input-output weight distribution of convolutional encoders. In some instances, one can derive explicit analytic expressions. In general, though, to determine the growth rate of the input-output weight distribution for a particular normalized input weight κ and output weight ω, a system of polynomial equations has to be solved. This method is then used to determine the asymptotic weight distribution of various concatenated code ensembles and to derive lower bounds on the thresholds of these ensembles under maximum-likelihood (ML) decoding.