Correlation and Set Size Bounds of Complementary Sequences with Low Correlation Zone

2013 IEEE International Symposium on Information Theory

Guan

Parampalli

et al. 2013

Self Cite

The Levenshtein bound, as a function of the weight vector, is only known to be tighter than the Welch bound on aperiodic correlation for K ≥ 4, N ≥ 2, where K and N denoting the set size and the sequence length, respectively. A quadratic weight vector is proposed in this paper which leads to a tighter Levenshtein bound for K ≥ 4, N ≥ 2 and K = 3, N ≥ 4. The latter case was left open by Levensthein.

Section: Ieee International Symposium On Information Theorymentioning

confidence: 87%

“…Next, we show the numerical comparison of the lower bounds in (12) and (9) in Fig. 1 for K ∈ {3, 4} and N = 128.…”

Section: Ieee International Symposium On Information Theorymentioning

confidence: 99%

See 1 more Smart Citation

Quadratic weight vector for tighter aperiodic Levenshtein bound

2013 IEEE International Symposium on Information Theory

Guan

Parampalli

et al. 2013

Self Cite

“…To illustrate the permutation π on Z N let us have the following example. 1,2,3,4,5,6,7,8,9,10,11,12,13,14] and π(Z 15 ) = [0, 8,4,6,2,10,3,14,1,12,5,13,9,11,7].…”

Section: Multiple Cccs With Low Maximum Inter-set Aperiodic Crosmentioning

confidence: 99%

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

Zhou

Adhikary

et al. 2020

IEEE Trans. Commun.

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).

“…Against such a backdrop, there have been two approaches aiming to provide a larger set size, i.e., K > M . The first approach is to design zeroor low-correlation zone (ZCZ/LCZ) based complementary sequence sets, called ZCZ-CSS [15], [16] or LCZ-CSS [17]. A ZCZ-CSS (LCZ-CSS) based MC-CDMA system is capable of achieving zero-(low-) interference performance but requires a closed-control loop to dynamically adjust the timings of all users such that the received signals can be quasi-synchronously aligned within the ZCZ (LCZ).…”

Section: Introductionmentioning

confidence: 99%

Asymptotically Locally Optimal Weight Vector Design for a Tighter Correlation Lower Bound of Quasi-Complementary Sequence Sets

IEEE Trans. Signal Process.

Guan

Mow

2017

Self Cite

Abstract-A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto-and cross-correlation sums. For multicarrier codedivision multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector w and is expressed in terms of three additional parameters associated with QCSS: the set size K, the number of channels M , and the sequence length N . It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition M ≥ 2 and K ≥ K + 1, where K is a certain function of M and N , is satisfied. A challenging research problem is to determine if there exists a weight vector which gives rise to a tighter GLB for all (not just some) K ≥ K + 1 and M ≥ 2, especially for large N , i.e., the condition is asymptotically both necessary and sufficient. To achieve this, we analytically optimize the GLB which is (in general) non-convex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the non-convex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions. Index Terms-Fractional quadratic programming, convex optimization, Welch Bound, Levenshtein Bound, perfect complementary sequence set (PCSS), quasi-complementary sequence set (QCSS), Golay complementary pair.