Optimum Distance Quadratic Permutation Polynomial-Based Interleavers for Turbo Codes

An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Also, the recently proposed quadratic permutation polynomial (QPP) based interleavers by Sun and Takeshita (IEEE Trans. Inform. Theory, Jan. 2005) provide excellent performance for short-to-medium block lengths. In this work the minimum distance of turbo codes with QPP-based interleavers is considered in detail. Large tables of optimum (in terms of turbo code minimum distance and multiplicity) QPPs for turbo codes with 8-state and 16-state constituent codes are presented. The minimum distances are compared to existing results in the literature on dithered relative prime (DRP) interleavers. The optimality of the new tables makes them an excellent source of information to advance the understanding of permutation polynomial (PP) based interleavers