4 research outputs found
Permutation Polynomial Interleaved Zadoff-Chu Sequences
Constant amplitude zero autocorrelation (CAZAC) sequences have modulus one
and ideal periodic autocorrelation function. Such sequences have been used in
communications systems, e.g., for reference signals, synchronization signals
and random access preambles. We propose a new family CAZAC sequences, which is
constructed by interleaving a Zadoff-Chu sequence by a quadratic permutation
polynomial (QPP), or by a permutation polynomial whose inverse is a QPP. It is
demonstrated that a set of orthogonal interleaved Zadoff-Chu sequences can be
constructed by proper choice of QPPs.Comment: Submitted to IEEE Transactions on Information Theor
Analysis of cubic permutation polynomials for turbo codes
Quadratic permutation polynomials (QPPs) have been widely studied and used as
interleavers in turbo codes. However, less attention has been given to cubic
permutation polynomials (CPPs). This paper proves a theorem which states
sufficient and necessary conditions for a cubic permutation polynomial to be a
null permutation polynomial. The result is used to reduce the search complexity
of CPP interleavers for short lengths (multiples of 8, between 40 and 352), by
improving the distance spectrum over the set of polynomials with the largest
spreading factor. The comparison with QPP interleavers is made in terms of
search complexity and upper bounds of the bit error rate (BER) and frame error
rate (FER) for AWGN and for independent fading Rayleigh channels. Cubic
permutation polynomials leading to better performance than quadratic
permutation polynomials are found for some lengths.Comment: accepted for publication to Wireless Personal Communications (19
pages, 4 figures, 5 tables). The final publication is available at
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On the Equivalence of Interleavers for Turbo Codes
International audienceThree 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 (LTE) standard are considered. Obtained results are useful when investigating a suitable and general permutation model for TCs