Lattices applied to coding for reliable and secure communications. ([2017])

• Record Type: Book
• Further Information: Note: Sueli I.R. Costa [and others].
• Editors: Costa, Sueli I. R
• 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 511.33; Mathematics; Lattice theory; MATHEMATICS -- General; Lattice theory; Computers -- Information Theory; Computers -- Security -- General; Coding theory & cryptology; Data encryption; Discrete groups; Coding theory; Data encryption (Computer science); Mathematics -- Geometry -- Analytic; Algebraic geometry; Electronic books
• Languages: English
• ISBNs: 9783319678825; 3319678825
• Related ISBNs: 9783319678818; 3319678817
• Notes: Note: Online resource; title from PDF title page (EBSCO, viewed April 10, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.