• Kirkman Equiangular Tight Fram...

Result: Kirkman Equiangular Tight Frames and Codes

Title:
Kirkman Equiangular Tight Frames and Codes
Authors:
JASPER, John, MIXON, Dustin G, FICKUS, Matthew
Source:
IEEE transactions on information theory. 60(1):170-181
Publisher Information:
New York, NY: Institute of Electrical and Electronics Engineers, 2014.
Publication Year:
2014
Physical Description:
print, 32 ref
Original Material:
INIST-CNRS
Subject Terms:
Telecommunications, Télécommunications, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Théorie de l'information, du signal et des communications, Information, signal and communications theory, Théorie de l'information, Information theory, Théorie du signal et des communications, Signal and communications theory, Codage, codes, Coding, codes, Echantillonnage, quantification, Sampling, quantization, Code binaire, Binary code, Código binario, Cohérence, Coherence, Coherencia, Espace euclidien, Euclidean space, Espacio euclidiano, Harmonique, Harmonic, Armónica, Méthode combinatoire, Combinatorial method, Método combinatorio, Transformation Fourier discrète, Discrete Fourier transformation, Transformación Fourier discreta, Echantillonnage parcimonieux, Compressed sensing, Equiangular tight frame, Grey-Rankin bound, Welch bound equality sequence, Welch bound
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, University of Missouri, Columbia, MO 65211, United States
Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433, United States
ISSN:
0018-9448
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=28149714
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Telecommunications and information theory
Accession Number:
edscal.28149714
Database:
PASCAL Archive

Further Information

An equiangular tight frame (ETF) is a set of unit vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications, such as waveform design and compressed sensing. At the moment, there are only two known flexible methods for constructing ETFs: harmonic ETFs are formed by carefully extracting rows from a discrete Fourier transform; Steiner ETFs arise from a tensor-like combination of a combinatorial design and a regular simplex. These two classes seem very different: the vectors in harmonic ETFs have constant amplitude, whereas Steiner ETFs are extremely sparse. We show that they are actually intimately connected: a large class of Steiner ETFs can be unitarily transformed into constant-amplitude frames, dubbed Kirkman ETFs. Moreover, we show that an important class of harmonic ETFs is a subset of an important class of Kirkman ETFs. This connection informs the discussion of both types of frames: some Steiner ETFs can be transformed into constant-amplitude waveforms making them more useful in waveform design; some harmonic ETFs have low spark, making them less desirable for compressed sensing. We conclude by showing that real-valued constant-amplitude ETFs are equivalent to binary codes that achieve the Grey―Rankin bound, and then construct such codes using Kirkman ETFs.