Analysis of Cubic Permutation Polynomials for Turbo Codes

Authors:
Lucian Trifina;Daniela Tarniceriu
Affiliations:
Faculty of Electronics, Telecommunications and Information Technology, "Gheorghe Asachi" Technical University of Iasi, Iasi, Romania 700506;Faculty of Electronics, Telecommunications and Information Technology, "Gheorghe Asachi" Technical University of Iasi, Iasi, Romania 700506
Venue:
Wireless Personal Communications: An International Journal
Year:
2013

Citing 7
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Abstract

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.