A Generalized Construction of Multiple Complete Complementary Codes and Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets

Abstract

In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can generate multiple sets of complete complementary codes (CCCs) over ZN , where N (N ≥ 3) is a positive integer of the form N = p e 0 0 p e 1 1 . . . p e n−1 n−1 , p0 < p1 < · · · < pn−1 are prime factors of N and e0, e1, · · · , en−1 are non-negative integers. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by N . When N is odd, the combination of the proposed CCCs results to a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic quasi-complementary sequence sets (QCSSs) with more flexible parameters.Index Terms-Complete complementary codes (CCCs), asymptotically optimal quasi-complementary sequence set (QCSSs), maximum aperiodic cross-correlation magnitude, multi-carrier code-division multiple-access (MC-CDMA).

Asymptotically Optimal and Near-optimal Aperiodic Quasi-Complementary Sequence Sets Based on Florentine Rectangles

“…Analysing closely the results of [32], [33] and [34] it is being observed that the number of CCC's and eventually the set size of the QCSS are small when N is 3 or have the smallest prime factor 3. Also it has been observed in all the previous constructions [32]- [34] that the optimal QCSS are designed over Z N , where N always a prime, power of prime or an odd integer, depending on the constructions. To overcome these problems, in search of new approaches to design QCSSs over any alphabet size N, we propose several sets of CCCs and eventually QCSSs using Florentine rectangles.…”

“…The main difference of this construction with all the previous constructions is that here we can construct asymptotically optimal and near-optimal QCSS over Z N for any N > 3, whereas previously N ≥ 5 was only odd integer [34], prime [32], [33] or power of prime [32]. For comparing the parameters with the exixting results, in Table VI, K prev and ρ prev denote the previous set size and the previously reported optimality factor, respectively, of the QCSS over Z N , for some values of N, when N has a prime factor 3.…”

“…In [33], Li et al designed a systematic framework to construct aperiodic asymptotically optimal QCSSs using several sets of CCCs having prime length sequences over the alphabet Z N , where N is a prime integer. Recently in 2020, Zhou et al [34] proposed a general construction of QCSS over Z N , for any odd integer N ≥ 3. Asymptotically optimal aperiodic QCSSs with corresponding parameters, reported till date, are given in Table I.…”

“…For comparing the parameters with the exixting results, in Table VI, K prev and ρ prev denote the previous set size and the previously reported optimality factor, respectively, of the QCSS over Z N , for some values of N, when N has a prime factor 3. The values of K prev and ρ prev are obtained from [34]. Compared with [32], [33] and [34], the uniqueness of our construction can be listed down as follows:…”

“…The values of K prev and ρ prev are obtained from [34]. Compared with [32], [33] and [34], the uniqueness of our construction can be listed down as follows:…”