The golden ratio encoder

Ingrid Daubechies; C. Sinan Güntürk; Yang Wang; Özgr Yilmaz

doi:10.1109/TIT.2010.2059750

The golden ratio encoder

Ingrid Daubechies, C. Sinan Güntürk, Yang Wang, Özgr Yilmaz

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ =(1+ √5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed.

Original language	English (US)
Article number	5571869
Pages (from-to)	5097-5110
Number of pages	14
Journal	IEEE Transactions on Information Theory
Volume	56
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2010.2059750
State	Published - Oct 2010

Keywords

Analog-to-digital conversion
beta encoders
beta expansions
golden ratio
quantization
robustness

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2010.2059750

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title = "The golden ratio encoder",

abstract = "This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ =(1+ √5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed.",

keywords = "Analog-to-digital conversion, beta encoders, beta expansions, golden ratio, quantization, robustness",

author = "Ingrid Daubechies and G{\"u}nt{\"u}rk, {C. Sinan} and Yang Wang and {\"O}zgr Yilmaz",

note = "Funding Information: Manuscript received August 31, 2008; revised February 20, 2010. Date of current version September 15, 2010. I. Daubechies was supported in part by the NSF Grant DMS-0504924. C. S. G{\"u}nt{\"u}rk was supported in part by NSF Grant CCF-0515187, in part by an Alfred P. Sloan Research Fellowship, and in part by an NYU Goddard Fellowship. Y. Wang was supported in part by NSF Grant DMS-0410062. {\"O}. Yılmaz was supported in part by an NSERC Discovery Grant.",

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doi = "10.1109/TIT.2010.2059750",

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AU - Yilmaz, Özgr

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N2 - This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ =(1+ √5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed.

AB - This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ =(1+ √5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed.

KW - Analog-to-digital conversion

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KW - beta expansions

KW - golden ratio

KW - quantization

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The golden ratio encoder

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Keywords

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