Fixed length analysis of turbo decoder

We propose an approach based on a message circulation concept for the convergence analysis of the turbo decoder. We define an interleaver ensemble as a set of all possible interleavers and a k-segment cycle in a given interleaver. Then a message-round probability on a k-segment cycle is derived on an interleaver ensemble. The result is very suggestive and allows the quantitative explanation of the convergence rate.