Nonuniform Fuchsian codes for noisy channels

DOI10.1016/j.jfranklin.2014.08.012zbMath1307.93112arXiv1403.2912OpenAlexW2152202694MaRDI QIDQ2263947

Montserrat Alsina, Iván Blanco-Chacón, Camilla Hollanti, Dionís Remón

Publication date: 19 March 2015

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.2912

zbMATH Keywords

additive white Gaussian noisy (AWGN) channelsFuchsian groups from rational quaternion algebra

Mathematics Subject Classification ID

Other types of codes (94B60) Channel models (including quantum) in information and communication theory (94A40)

Related Items (5)

On geometrically uniform codes and topological quantum MDS codes ⋮ Fuchsian codes with arbitrarily high code rates ⋮ Uniformization of hyperelliptic curves as a systematic approach to establishing decision regions of hyperbolic signal sets ⋮ A new method of coding geodesics on surfaces whose fundamental regions consist of the union of elementary triangles derived from the Farey series ⋮ Complete hyperbolic lattices derived from tessellations of type {4g,4g}

Cites Work

• Unnamed Item
• Unnamed Item
• Edge-pairing isometries and counting Dirichlet domains on the densest tessellation \(\{12g-6,3\}\) for signal set design
• Arithmetic Fuchsian groups and space time block codes
• A reduction point algorithm for cocompact Fuchsian groups and applications
• Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
• Attainability of the minimal exponent of exponential growth for some Fuchsian groups.
• Signal constellations in the hyperbolic plane: a proposal for new communication systems
• The combinatorial structure of cocompact discrete hyperbolic groups
• Presentations of the unit group of an order in a non-split quaternion algebra.
• Construction of class fields and zeta functions of algebraic curves
• Cyclic Division Algebras: A Tool for Space-Time Coding
• Algebraic Number Theory and Code Design for Rayleigh Fading Channels
• Full-diversity, high-rate space-time block codes from division algebras
• Solving quadratic equations using reduced unimodular quadratic forms
• A universal lattice code decoder for fading channels
• Quaternion Orders, Quadratic Forms, and Shimura Curves
• Excellent codes from modular curves

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