Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2109.13697

New Interleaving Constructions of Asymptotically Optimal Periodic Quasi-Complementary Sequence Sets

Gaojun Luo·Martianus Frederic Ezerman·San Ling
View original source ↗Read source document ↗Export metadata ↓

Abstract

The correlation properties of sequences form a focal point in the design of multiple access systems of communications. Such a system must be able to serve a number of simultaneous users while keeping interference low. A popular choice for the set of sequences to deploy is the quasi-complementary sequence set (QCSS). Its large set size enables the system to accommodate a lot of users. The set has low nontrivial correlation magnitudes within a zone around the origin. This keeps undue interference among users under control. A QCSS performs better than the perfect complementary sequence set (PCSS) does in schemes with fractional delays. The optimality of a set of periodic sequences is measured by its maximum periodic correlation magnitude, for which there is an established lower bound to aim at. For a fixed period, optimal sets are known only for very restricted parameters. Efforts have therefore been centered around the constructions of asymptotically optimal sets. Their periods are allowed to be as large as sufficient to establish optimality. In this paper we share an insight that a sequence set that asymptotically attains the Welch bound generates an asymptotically optimal periodic QCSS by interleaving. One can simply use known families of such sequence sets to construct the desired QCSSs. Seven families of QCSSs with specific parameters are shown as examples of this general construction. We build upon the insight to propose two new direct constructions of asymptotically optimal QCSSs with very flexible parameters without interleaving. The flexibility enhances their appeal for practical implementation. The mathematical tools come from the theory of groups in the form of additive and multiplicative characters of finite fields.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gaojun Luo, Martianus Frederic Ezerman, San Ling. 2021-09-28. New Interleaving Constructions of Asymptotically Optimal Periodic Quasi-Complementary Sequence Sets. https://arxiv.org/abs/2109.13697

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

cs.IT↗
arXiv2026

Sequence Reconstruction over the Deletion Channel

In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the minimum number of channel outputs (assuming that they are distinct) required to reconstruct a list of size $\ell-1$ of candidate sequences, one of which corresponds to the original transmitted sequence. More specifically, we determine the maximum possible size of the intersection of $\ell \geq 3$ deletion balls of radius $t$ centered at $x_1, x_2, \dots, x_{\ell}$, where $x_i \in \{0,1\}^n$ for all $i \in \{1,2,\dots,\ell\}$ and $x_i \neq x_j$ for $i \neq j$, with $ n \geq t+\ell-1$ and $t \geq 1$.

cs.IT↗
arXiv2026

A generalization of the map $χ$

The mapping $ χ_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=χ_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

cs.IT↗