Variance of the turbo-code performance bound over the interleavers

We evaluate the variance of the union performance bound for a turbo-code over all possible interleavers of length N. The asymptotic analysis (for large N) shows that the ratio of the standard deviation over the mean value of the bound remains constant with respect to N. Numerical results corresponding to turbo-codes with two-memory component codes indicate that this ratio increases with the signal to noise ratio. Theoretical and simulation results demonstrate that the majority of the interleavers result in performance bounds very close to the average value of the bound. This effect is stronger for larger interleaver lengths.