On the Spread of Random Interleaver

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 ≈ 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 , as the blocklength increases.