Coverart for item
The Resource Lattices applied to coding for reliable and secure communications, Sueli I.R. Costa [and others], (electronic book)

Lattices applied to coding for reliable and secure communications, Sueli I.R. Costa [and others], (electronic book)

Label
Lattices applied to coding for reliable and secure communications
Title
Lattices applied to coding for reliable and secure communications
Statement of responsibility
Sueli I.R. Costa [and others]
Contributor
Editor
Subject
Language
eng
Summary
This book provides a first course on lattices - mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields
Member of
Cataloging source
YDX
Dewey number
511.33
Index
no index present
LC call number
QA171.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Costa, Sueli I. R.
Series statement
Springer briefs in mathematics
http://library.link/vocab/subjectName
  • Lattice theory
  • Data Encryption
Label
Lattices applied to coding for reliable and secure communications, Sueli I.R. Costa [and others], (electronic book)
Instantiates
Publication
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Intro; Contents; 1 Introduction; 2 Lattices and Applications; 2.1 Sphere Packing and Covering; 2.1.1 Equivalent Lattices; 2.2 Sublattices; 2.3 The Dual of a Lattice; 2.4 Important Lattices and Their Duals; 2.4.1 Table of Record Lattices; 2.5 Applications; 2.5.1 Coding; 2.5.2 Quantization; 2.5.3 Computational Problems and Cryptography; Exercises; 3 Lattices from Codes; 3.1 Construction A; 3.2 Relevant Distances in Codes and Lattices; 3.2.1 q-ary Lattice Decoding; 3.3 Wiretap Coding and Theta Series; Exercises; 4 Ideal Lattices; 4.1 Ideal Lattices from Quadratic Fields
  • 4.1.1 Lattice Constructions4.1.2 Some Sublattices; 4.1.3 Coding Applications; 4.1.4 High-Dimensional Lattices; 4.2 Ideal Lattices for Cryptography; Exercises; 5 Lattices and Spherical Codes; 5.1 Spherical and Geometrically Uniform Codes; 5.2 Flat Tori; 5.3 Commutative Group Codes, Flat Tori, and Lattices; 5.3.1 Commutative Group Codes; 5.3.2 Lattice Connections; 5.3.3 Approaching the Bound: Good and Optimum Commutative Group Codes; 5.3.4 Commutative Group Codes and Codes on Graphs; 5.4 Spherical Codes on Layers of Tori; 5.4.1 Codes for the Gaussian Channel
  • 5.4.2 Application: Coding for Continuous Alphabet Sources6 Lattices and Index Coding; 6.1 Introduction; 6.2 Voronoi Constellations; 6.3 Index Coding in AWGN Channel; 6.4 Voronoi Constellations for Index Coding: An Illustration; 6.5 Lattice Index Codes; 6.5.1 An Upper Bound on the Side Information Gain; 6.6 A Construction of Lattice Index Codes Using the Chinese Remainder Theorem; 6.7 Discussion; References; Index
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319678818
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-67882-5
Specific material designation
remote
System control number
  • on1030601547
  • (OCoLC)1030601547
Label
Lattices applied to coding for reliable and secure communications, Sueli I.R. Costa [and others], (electronic book)
Publication
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Intro; Contents; 1 Introduction; 2 Lattices and Applications; 2.1 Sphere Packing and Covering; 2.1.1 Equivalent Lattices; 2.2 Sublattices; 2.3 The Dual of a Lattice; 2.4 Important Lattices and Their Duals; 2.4.1 Table of Record Lattices; 2.5 Applications; 2.5.1 Coding; 2.5.2 Quantization; 2.5.3 Computational Problems and Cryptography; Exercises; 3 Lattices from Codes; 3.1 Construction A; 3.2 Relevant Distances in Codes and Lattices; 3.2.1 q-ary Lattice Decoding; 3.3 Wiretap Coding and Theta Series; Exercises; 4 Ideal Lattices; 4.1 Ideal Lattices from Quadratic Fields
  • 4.1.1 Lattice Constructions4.1.2 Some Sublattices; 4.1.3 Coding Applications; 4.1.4 High-Dimensional Lattices; 4.2 Ideal Lattices for Cryptography; Exercises; 5 Lattices and Spherical Codes; 5.1 Spherical and Geometrically Uniform Codes; 5.2 Flat Tori; 5.3 Commutative Group Codes, Flat Tori, and Lattices; 5.3.1 Commutative Group Codes; 5.3.2 Lattice Connections; 5.3.3 Approaching the Bound: Good and Optimum Commutative Group Codes; 5.3.4 Commutative Group Codes and Codes on Graphs; 5.4 Spherical Codes on Layers of Tori; 5.4.1 Codes for the Gaussian Channel
  • 5.4.2 Application: Coding for Continuous Alphabet Sources6 Lattices and Index Coding; 6.1 Introduction; 6.2 Voronoi Constellations; 6.3 Index Coding in AWGN Channel; 6.4 Voronoi Constellations for Index Coding: An Illustration; 6.5 Lattice Index Codes; 6.5.1 An Upper Bound on the Side Information Gain; 6.6 A Construction of Lattice Index Codes Using the Chinese Remainder Theorem; 6.7 Discussion; References; Index
Dimensions
unknown
Extent
1 online resource.
Form of item
online
Isbn
9783319678818
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-67882-5
Specific material designation
remote
System control number
  • on1030601547
  • (OCoLC)1030601547

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