Lattices Applied to Coding for Reliable and Secure Communications

“…By exploiting the characteristics of the communications channel such as noise or fading, one can design lattice codes that minimize the probability of making decoding errors. For a nice introduction to the use of lattices for reliable and secure communications we refer the reader to [4].…”

Section: Introductionmentioning

confidence: 99%

Learning Optimal Lattice Codes for MIMO Communications

Amorós

Pitkänen

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…In this section, we will provide a short practical motivation for the construction of generic well-rounded lattices with large packing densities. We refer the interested reader to [26,3,6,9] and references therein for more details on reliable and secure wireless communications.…”

Section: Secure Wireless Communicationsmentioning

confidence: 99%

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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“…The torus layers spherical codes (TLSC) [7], while not asymptotically dense, have a more homogeneous structure and have been shown to compare favorably with other codes for non-asymptotic minimum distances. This method foliates the sphere S 2n−1 by flat manifolds S 1 × • • • × S 1 and distributes points using good packing density lattices in the half-dimension [8], [9]. Other recent contributions to this topic include codes obtained by partitioning the sphere into regions of equal area [10], bounds for constructible codes near the Shannon bound [11], commutative group codes [12], [13] and cyclic group codes [14].…”

Section: Introductionmentioning

confidence: 99%

“…with η i := π/4 + i∆η as in(6), t := t(d) as in(7), m i := m(d, η i ) as in(9) and n i := n(d, η i ) as in(12). To construct a code in R 8 with minimum distance d = 0.5 by our standard procedure, we consider the foliation of S 7 by (S 3 ×S 3 ) η and use Proposition 1 to choose the set of parameters η ∈ {0.5053, π/4, 1.2907}.…”

mentioning

confidence: 99%

Constructive spherical codes in 2^k dimensions

Miyamoto

Earp

Costa

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We present a new systematic approach to constructing spherical codes in dimensions 2 k , based on Hopf foliations. Using the fact that a sphere S 2n−1 is foliated by manifolds S n−1 cos η × S n−1 sin η , η ∈ [0, π/2], we distribute points in dimension 2 k via a recursive algorithm from a basic construction in R 4. Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between achieving a large number of codewords for a minimum given distance and effective constructiveness with low encoding computational cost. Bounds for the asymptotic density are derived and compared with other constructions. The encoding process has storage complexity O(n) and time complexity O(n log n). We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity O(n log n).

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Lattices Applied to Coding for Reliable and Secure Communications

Cited by 19 publications

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Learning Optimal Lattice Codes for MIMO Communications

Learning Optimal Lattice Codes for MIMO Communications

Dense generic well-rounded lattices

Constructive spherical codes in 2^k dimensions

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Lattices Applied to Coding for Reliable and Secure Communications

Cited by 19 publications

References 0 publications

Learning Optimal Lattice Codes for MIMO Communications

Learning Optimal Lattice Codes for MIMO Communications

Dense generic well-rounded lattices

Constructive spherical codes in 2k dimensions

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Constructive spherical codes in 2^k dimensions