In this paper, we introduce a class of deterministic interleavers for turbo codes based on permutation polynomials over ZN. A search for interleavers has been performed based on a subset of error events with input weight 2m and the simulated performance is compared with S-random interleavers and Quadratic interleavers.

A typical Turbo code (TC) is constructed by parallel concatenating two convolutional codes via an interleaver. The design of the interleaver is critical to the performance of the turbo code. Interleavers for TC’s can in general be separated into random interleavers and deterministic interleavers. The basic random interleaver permutes the information bits in a pseudo-random manner. Near Shannon limit performance can be achieved with these interleavers for large frame sizes. The S-random interleaver proposed in [3] is an improvement to the random interleaver. Deterministic interleavers are constructed using deterministic rules. In [4], quadratic interleavers have been introduced. Quadratic interleavers achieve the average performance of random interleavers. However, they are still not as good as S-random interleavers. We propose another class of deterministic interleavers. They are based on permutation polynomials (PP) over ZN. A PP P (x)= Cc, aixi over ZN is a polynomial with integer coefficients such that, when computed modulo N, it permutes {O, 1,.... N-1). When N= 2”, the necessary and sufficient condition for a polynomial to be a PP is that a1 is odd and both a2+ a4+... and a3+ a5+... are even [2]. For general N, the condition is given in [l]. A PP-based interleaver can be constructed by mapping x to P (z). We will consider second degree polynomials only.