The use of quadratic permutation polynomials as interleavers for turbo codes is justified, among other things, by the fact that the quadratic permutation polynomials provide turbo codes of very good performance and simultaneously they support a specific conflict-free parallel access to extrinsic values in two different access orders. It is rather easy to write and read in parallel to and from multiple memories by one access order. Nevertheless, turbo decoders have to access the multiple memories at least by two different access orders. Then, parallel writes and reads lead to conflicts in accessing the multiple memories. Having only one conflict-free parallel access method for quadratic permutation polynomials restricts to design efficient flexible (multistandard) decoders for turbo codes at high data rates. We show that quadratic permutation polynomials with butterfly networks as interconnection networks between decoder units and memories support many kinds of flexible and variant conflict-free parallel access methods for turbo codes that are not known today. This result extends possibilities to implement high speed turbo decoders not only by application specific circuits but also by (general purpose) graphics processor units for (multistandard) modems.

A theoretical foundation for any turbo interleaver to be a contention-free interleaver to access data in parallel by a butterfly network is presented. A contention-free parallel access of multiple memories in parallel plays a crucial role for implementing high speed turbo decoders for high data rate applications. The presented theoretical analysis shows that a butterfly network has a sufficiently rich permutation structure to be a routing network between parallel decoder units and multiple memories. Thus turbo code design is independent of the designing of a contention-free parallel access by butterfly networks. In particular, a turbo interleaver needs not to provide a built-in contention-free parallel access for any parallel access by butterfly networks. We demonstrate how to apply this theory to turbo interleavers widely used in commercial telecommunication standards.

A near-far resistant iterative algorithm for multiuser signature sequence delay estimation is presented. It is shown that the maximum-likelihood delay estimator can be replaced by the so-called blind ML delay estimator which depends on delays only, not on transmitted symbols and complex channel coefficients. A variable projection type algorithm is presented to compute the blind ML estimator in an iterative way. According to the simulation results, the delays for all users can be estimated reliably both in AWGN and fading channels by using the scheme being proposed.