An integral component of a turbo code is a carefully designed interleaver. Interleavers based on quadratic permutation polynomials (moduloN) were introduced by Sun and Takeshita. They have several good properties and have been selected to be used in a cellular phone system. Ryu and Takeshita later initiated the study of the related deinterleavers. Here we extend this latter work and introduce a very efficient method for computing the (degree of the) lowest degree polynomial giving the deinterleaver. Our approach is based on combining two techniques. The Chinese remainder theorem allows us to study one prime power factor ofNat a time. Our other technique is to first present the inverse function as a power series with integer coefficients. ModuloNthat series is actually a polynomial. The polynomials yielding the same function form a coset of the ideal of identically vanishing polynomials. With the aid of a known Gröbner basis of that ideal we then finally identify a minimal degree polynomial within the given coset.

Rapid frequency and frame synchronization scheme is proposed to minimize channel switching time and improve the synchronization performance during channel switching in IEEE 802.11p standard. As a measure of performance, theoretical formula for false alarm and detection probability is derived. It is shown that optimal threshold value is less than 0.5 dB and overall performance gain is given by the amount of the power gain of control channel, which is normally 10 dB

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. Sun and Takeshita have recently shown that the class of quadratic permutation polynomials over integer rings provides excellent performance for turbo codes. In this correspondence, a necessary and sufficient condition is proven for the existence of a quadratic inverse polynomial for a quadratic permutation polynomial over an integer ring. Further, a simple construction is given for the quadratic inverse. All but one of the quadratic interleavers proposed earlier by Sun and Takeshita are found to admit a quadratic inverse, although none were explicitly designed to do so. An explanation is argued for the observation that restriction to a quadratic inverse polynomial does not narrow the pool of good quadratic interleavers for turbo codes