Hayman-like techniques for computing input-output weight distribution of convolutional encoders

In this paper we derive exact formulæ of the input-output weight enumerators for truncated convolutional encoders. Although explicit analytic expressions can be computed for relatively small code lengths, they become prohibitively complex to calculate as the truncation length increases. By applying Hayman-like techniques, we present an accurate and easy to compute approximation of the weight enumerators. One of our main results is the proof that the sequence of their exponential growths converges uniformly to the asymptotic growth rate. Finally, we estimate the speed of this convergence.