Permutation polynomial based deterministic interleavers for turbo codes

Abstract

In this paper, we introduce a class of deterministic interleavers for turbo codes based on permutation polynomials over ZN. A search for in- terleavers 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 con- catenating 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