Improved QPP interleavers for LTE standard

Abstract

This paper proposes and proves a theorem which stipulates sufficient conditions the coefficients of two quadratic permutation polynomials (QPP) must satisfy, so that the permutations generated by them are identical. The result is used to reduce the search time of QPP interleavers with lengths given by Long Term Evolution (LTE) standard up to 512, by improving the distance spectrum over the set of polynomials with the largest spreading factor. Polynomials that lead to better performance compared to LTE standard are found for several lengths. Simulations show that 0.5 dB coding gains can be obtained compared to LTE standard.

The limitation of permutation polynomial interleavers for turbo codes and a scheme for dithering permutation polynomials

“…LTE-QPP and QPP from [6] have the weakest performance and CPP from [2] have performance closer to dithered LPP one, excepting for SNR = 5 dB. Table 7 Minimum distances (d min ), corresponding multiplicities of codewords (N d min ) and FER at high SNR for QPP from [2] or [7,8] and dithered LPP interleavers for lengths N ≥ 224. Generator matrix of recursive systematic convolutional codes and trellis termination are as in the LTE turbo code [5].…”

“…In [2,7,8] few methods for finding good QPP or CPP based interleavers are given. These methods also take into account other parameters of QPP/CPP based interleavers (such as D parameter or spread and refined nonlinearity degree).…”

“…These methods also take into account other parameters of QPP/CPP based interleavers (such as D parameter or spread and refined nonlinearity degree). In Tables 6 and 7, the our dithered LPPs are compared with the QPPs from [2] or [7,8] and the CPPs from [2], for some lengths, considering the simulated FER and the minimum distance. It is observed that for all reported lengths dithered LPPs lead to higher or equal minimum distances (excepting CPP of length 40 and QPPs of lengths 320, 560, 848 and 1008, respectively).…”

“…Permutation polynomial (PP) based interleavers over integer rings have been widely studied [1][2][3][6][7][8]. In particular quadratic permutation polynomial (QPP) based interleavers were emphasized due to their simple implementation [3] as well as excellent performance [1].…”

Novel Interleaver Design for Turbo Codes

“…A new non-linearity metric is investigated and a new interleaver metric that is a function of both the non-linearity metric and the spread factor is proposed. In [34] comparison between the QPP and ARQ interleavers is drawn and design and performance results for both are presented [35]. Proves a theorem to reduce the search time of QPP interleavers with lengths given by LTE standard up to 512, and gives sufficient conditions the coefficients of two QPPs must fulfil to generate identical permutations [36].…”