On the Equivalence of Interleavers for Turbo Codes

Three of the most common interleavers for turbo codes (TCs) are dithered relative prime (DRP) interleavers, quadratic permutation polynomial (QPP) interleavers, and almost regular permutation (ARP) interleavers. In this paper, it is shown that DRP and QPP interleavers can be expressed in the ARP interleaver function form. Furthermore, QPP interleavers can be seen as a particular case of ARP interleavers, in which the values of the periodic shifts follow the quadratic term of the QPP interleaver function. Some application examples of the equivalent expressions are provided. Particularly, in the QPP interleaver case, the different instances in the Long-Term Evolution standard are considered. Obtained results are useful when investigating a suitable and general permutation model for TCs.