Variance of the turbo code performance bound over the interleavers

We evaluate the variance of the union performance bound for a rate-1/3 turbo code over all possible interleavers of length N, under the assumption of a maximum-likelihood (ML) decoder. Theoretical and simulation results for turbo codes with two-memory component codes indicate that the coefficient of variation of the bound increases with the signal-to-noise ratio and decreases with the interleaver length. Theoretical analysis for large interleaver lengths shows that the coefficient of variation asymptotically approaches a constant value. The results also demonstrate that the majority of the interleavers have performance bounds very close to the average value of the bound. This phenomenon is more palpable for larger interleaver lengths.