Reduced complexity interleaver growth algorithm for turbo codes

This paper is focused on the problem of significantly reducing the complexity of the recursive interleaver growth algorithm (IGA) with the goal of extending the range of applicability of the algorithm to significantly larger interleavers for a given CPU time and processor. In particular, we present two novel modifications to IGA changing the complexity order of the algorithm from O(N_max⁴) to O(N_max²), present several further minor modifications reducing the CPU time albeit not fundamentally changing the complexity order, and present a mixed mode strategy that combines the results of complexity reduction techniques that do not alter the algorithm outcome itself, with a novel transposition value set cardinality constrained design that does modify the optimization results. The mixed strategy can be used to further extend the range of interleaver sizes by changing the complexity order from O(N_max²) to O(N_max) (i.e., linear in the interleaver size). Finally, we present optimized variable length interleavers for the Universal Mobile Telecommunications System (UMTS) and Consultative Committee for Space Data Systems (CCSDS) standards outperforming the best interleavers proposed in the literature.