Analysis of the truncation biasing for importance sampling simulation of encoded systems

Importance sampling (IS) simulation of convolutionally encoded communication systems requires choosing code-words distinct of the transmitted one, called error-centers, in order to bent the simulation distribution along the direction of such that centers and so speed up simulation [1], [2]. As in practice it is mandatory to limit the number of error-centers the estimative turns up to be biased. We call truncation bias (Delta^T) the difference between the IS estimative using all error-centers and the IS estimative using a limited number of error-centers. In this paper we employ the results given by Urbanke et alli [3] on the asymptotic input-output weight distribution to analyze the asymptotic behaviour of E* [Delta^T] the expected value of the truncation bias.