Publications related to Leech lattice

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New dense superball packings in three dimensions

Maria Margarethe Dostert

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...

WALTER DE GRUYTER GMBH2020

Automorphisms of even unimodular lattices and equivariant Witt groups

Eva Bayer Fluckiger

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

EUROPEAN MATHEMATICAL SOC2020

Sharp sphere packings

Maryna Viazovska

In this talk we will speak about recent progress on the sphere packing problem. The packing problem can be formulated for a wide class of metric spaces equipped with a measure. An interesting feature of this optimization problem is that a slight change of ...

World Scientific Publishing2018

Gaussian Multiple Access via Compute-and-Forward

Michael Christoph Gastpar, Jingge Zhu

Lattice codes used under the compute-and-forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): the receiver succes- sively decodes the integer linear combinations of the messages until it can invert and r ...

Institute of Electrical and Electronics Engineers2017

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W)

Oleg Yazyev, Gabriel Albert Autes

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different fr ...

Amer Physical Soc2016

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

Michael Christoph Gastpar, Jingge Zhu

A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of codewords, our scheme im ...

Institute of Electrical and Electronics Engineers2015

On lattice codes for Gaussian interference channels

Michael Christoph Gastpar, Jingge Zhu

The usefulness of lattice codes is investigated for two-user Gaussian interference channels (IC). A coding scheme based on the compute-and-forward technique is shown to achieve the capacity region of the Gaussian IC under strong interference. The proposed ...

2015

Gaussian (dirty) multiple access channels: a compute-and-forward perspective

Michael Christoph Gastpar, Jingge Zhu

Lattice codes are applied to the two-user Gaussian multiple access channel (MAC) combined with a modified compute-and-forward transmitting scheme. It is shown that non-corner points on the boundary of the capacity region can be achieved by decoding two int ...

IEEE2014

Leech lattice

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New dense superball packings in three dimensions

Automorphisms of even unimodular lattices and equivariant Witt groups

Sharp sphere packings

The sphere packing problem in dimension 24

Gaussian Multiple Access via Compute-and-Forward

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W)

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

On lattice codes for Gaussian interference channels

Gaussian (dirty) multiple access channels: a compute-and-forward perspective

On the number of lattice points in a small sphere and a recursive lattice decoding algorithm

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP2 (X = Mo, W)

New dense superball packings in three dimensions

Automorphisms of even unimodular lattices and equivariant Witt groups

The sphere packing problem in dimension 24

Sharp sphere packings

Gaussian Multiple Access via Compute-and-Forward

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

On the number of lattice points in a small sphere and a recursive lattice decoding algorithm

Gaussian (dirty) multiple access channels: a compute-and-forward perspective

On lattice codes for Gaussian interference channels