On the Spread of Random Interleaver

Details On the Spread of Random Interleaver On the Spread of Random Interleaver

2005-10-23

arxiv.org/abs/cs/0510067v1

IEEE International Symposium on Information Theory 2005

Computer Science

Information Theory

5 pages, published in Proceedings of IEEE International Symposium on Information Theory 2005, Adelaide, Australia

Scientific paper

10.1109/ISIT.2005.1523372

For a given blocklength we determine the number of interleavers which have spread equal to two. Using this, we find out the probability that a randomly chosen interleaver has spread two. We show that as blocklength increases, this probability increases but very quickly converges to the value $1-e^{-2} \approx 0.8647$. Subsequently, we determine a lower bound on the probability of an interleaver having spread at least $s$. We show that this lower bound converges to the value $e^{-2(s-2)^{2}}$, as the blocklength increases.

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