Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

Damir, Mohamed Taoufiq; Karrila, Alex; Amorós, Laia; Gnilke, Oliver W.; Karpuk, David; Hollanti, Camilla

doi:10.1109/tit.2021.3059749

Cited by 10 publications

(17 citation statements)

References 46 publications

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“…To this end, well-rounded (sub)lattices should be utilized [20,19]. Nevertheless, the densest possible packing does not necessarily yield the best performance, as demonstrated in [13], but the kissing number also plays a role, and hence generic well-rounded lattices are of a particular interest.…”

Section: Secure Wireless Communicationsmentioning

confidence: 99%

“…Nevertheless, the construction of GWR lattices with arbitrary good packing density is something that, as far as we are aware, has not been done before. Further, such constructions provide good candidates for secure lattice codes according to [13] (see also discussion in Section 5).…”

Section: Proof a Basis For L (Rs) V1mentioning

confidence: 99%

“…The task of finding GWR lattices with good sphere packing density was motivated by the findings in e.g. [11], [13] where it was demonstrated, using fading wiretap channel simulations, that having a small kissing number and a high sphere packing density for the eavesdropper's lattice can lower the correct decoding probability for the eavesdropper for some relevant channel quality ranges.…”

Section: 3 When the Communication Channel Is Of Amentioning

confidence: 99%

“…One way to describe a lattice is via its theta series, which can be further related to the so-called flatness factor utilized in communications theory and smoothing parameter in cryptography. In [13], it was shown that well-rounded lattices yield promising candidates for lattice codes in wireless communications [26] and physical layer security [6]. In [2] a means to approximate theta functions was given, enabling efficient comparison of candidate lattice codes.…”

mentioning

confidence: 99%

“…In [2] a means to approximate theta functions was given, enabling efficient comparison of candidate lattice codes. It was also noted in [13] that the densest packings might not provide the best candidates due to their large kissing numbers, and hence a study on generic well-rounded lattices having minimal kissing numbers was proposed.…”

mentioning

confidence: 99%

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Dense generic well-rounded lattices

Hollanti¹,

Mantilla-Soler²,

Miller³

2021

Preprint

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It is well-known that the densest lattice sphere packings also typically have the largest kissing numbers. The sphere packing density maximization problem is known to have a solution among well-rounded lattices, of which the integer lattice Z n is the simplest example. The integer lattice is also an example of a generic well-rounded lattice, i.e., a well-rounded lattice with a minimal kissing number. However, the integer lattice has the worst density among well-rounded lattices. In this paper, the problem of constructing explicit generic well-rounded lattices with dense sphere packings is considered. To this end, so-called tame lattices recently introduced by Damir et al. are utilized. Tame lattices came to be as a generalization of the ring of integers of certain abelian number fields. The sublattices of tame lattices constructed in this paper are shown to always result in either a generic well-rounded lattice or the lattice An, with density ranging between that of Z n and An. Further, explicit deformations of some known densest lattice packings are constructed, yielding a family of generic well-rounded lattices with densities arbitrarily close to the optimum. In addition to being an interesting mathematical problem on its own, the constructions are also motivated from a more practical point of view. Namely, the constructed lattices provide good candidates for lattice codes used in secure wireless communications.

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Section: Secure Wireless Communicationsmentioning

confidence: 99%

Section: Proof a Basis For L (Rs) V1mentioning

confidence: 99%

Section: 3 When the Communication Channel Is Of Amentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Dense generic well-rounded lattices

Hollanti¹,

Mantilla-Soler²,

Miller³

2021

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How to discover consumer attention to design topics of fast fashion: a topic modeling approach

Pan,

Li,

Luo

et al. 2023

JFMM

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PurposeIt is widely known that fast-fashion retailers are struggling to keep up with consumer attention for quick responses within the fashion industry. With the advance of Internet and e-commerce, consumers prefer to purchase online. Online platform information has become an essential source for exploring consumer attention. However, there is often a mismatch between the information provided by retailers and the feedback received from consumers, leading to an imbalance between the supply side and demand side of online information. The purpose of this study is therefore to provide a unified approach to discover consumer attention from the design topic aspect by revealing the information imbalance between supply side and demand side.Design/methodology/approachTo address the issue of online information imbalance and discover consumer attention, this study proposed an approach that focuses on the design topic perspective. The design topic is a collection of design elements that represent a clothing-design feature more comprehensively and accurately compared to a single design element. The proposed approach begins with generating design topics through topic modeling based on online information provided by retailers on e-commerce platforms. Two indicators, influence degree and attention degree, are then used to quantify the intensity of supply information and consumer attention related to design topics. Finally, design topic strategy diagrams are constructed to reveal information imbalance and discover consumer attention.FindingsThe experimental case demonstrates the existence of information imbalance, indicating that the intensity of supply information and consumer attention from the perspective of design topics is not uniform, although both follow the Pareto principle. The results of consumer attention distribution with heavy power-law tails are consistent with current research findings. This further demonstrates that the proposed approach is capable of discovering consumer attention in the design topic strategy diagrams.Practical implicationsThe issue of information imbalance between retailers and consumers poses a challenge in keeping up with customer attention. The proposed approach offers a practical solution by visually identifying the symptoms of information imbalance and discovering consumer attention through design topic strategy diagrams. This approach provides fast-fashion retailers with a valuable reference to seize market opportunities, improve product design and adjust marketing or management strategies.Originality/valueThis study proposes a novel approach to disclose the issue of information imbalance between supply side and demand side and therefore to discover consumer attention from the perspective of design topics. In addition, guidelines for applying the proposed approach for fast-fashion marketing and management are presented.

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On the Secrecy Gain of Formally Unimodular Construction A₄ Lattices

Bollauf

Lin

Ytrehus

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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The theta series of a lattice has been extensively studied in the literature and is closely related to a critical quantity widely used in the fields of physical layer security and cryptography, known as the flatness factor, or equivalently, the smoothing parameter of a lattice. Both fields raise the fundamental question of determining the (globally) maximum theta series over a particular set of volume-one lattices, namely, the stable lattices. In this work, we present a property of unimodular lattices, a subfamily of stable lattices, to verify that the integer lattice Z n achieves the largest possible value of theta series over the set of unimodular lattices. Such a result moves towards proving the conjecture recently stated by Regev and Stephens-Davidowitz: any unimodular lattice, except for those lattices isomorphic to Z n , has a strictly smaller theta series than that of Z n . Our techniques are mainly based on studying the ratio of the theta series of a unimodular lattice to the theta series of Z n , called the secrecy ratio. We relate the Regev and Stephens-Davidowitz conjecture with another conjecture for unimodular lattices, known in the literature as the Belfiore-Solé conjecture. The latter assumes that the secrecy ratio of any unimodular lattice has a symmetry point, which is exactly where the global minimum of the secrecy ratio is achieved.Our technical contributions are three-fold.

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Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

Cited by 10 publications

References 46 publications

Dense generic well-rounded lattices

Dense generic well-rounded lattices

How to discover consumer attention to design topics of fast fashion: a topic modeling approach

On the Secrecy Gain of Formally Unimodular Construction A₄ Lattices

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Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

Cited by 10 publications

References 46 publications

Dense generic well-rounded lattices

Dense generic well-rounded lattices

How to discover consumer attention to design topics of fast fashion: a topic modeling approach

On the Secrecy Gain of Formally Unimodular Construction A4 Lattices

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Product

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On the Secrecy Gain of Formally Unimodular Construction A₄ Lattices