Topic
Beta encoder
About: Beta encoder is a research topic. Over the lifetime, 5 publications have been published within this topic receiving 83 citations.
Papers
TL;DR: A method to implement beta-encoders so that they are also robust with respect to uncertainties of the value of beta, and it is shown that this can be done without a priori knowledge of beta by the transmitting party.
Abstract: Beta-encoders with error correction were introduced by Daubechies, DeVore, Guumlntuumlrk and Vaishampayan as an alternative to pulse-code modulation (PCM) for analog-to-digital conversion. An N-bit beta-encoder quantizes a real number by computing one of its N-bit truncated beta-expansions where betaisin(1,2) determines the base of expansion. These encoders have (almost) optimal rate-distortion properties like PCM; furthermore, they exploit the redundancy of beta-expansions and thus they are robust with respect to quantizer imperfections. However, these encoders have the shortcoming that the decoder needs to know the value of the base of expansion beta, a gain factor in the circuit used by the encoder, which is an impractical constraint. We present a method to implement beta-encoders so that they are also robust with respect to uncertainties of the value of beta. The method relies upon embedding the value of beta in the encoded bitstream. We show that this can be done without a priori knowledge of beta by the transmitting party. Moreover the algorithm still works if the value of beta changes (slowly) during the implementation
44 citations
TL;DR: A formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed, based on a robust implementation of a beta-encoder with β = φ = (1 + √5)/2, the golden ratio.
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
30 citations
TL;DR: In this article, the authors present a method whereby exponentially precise approximations to the value of beta in both GREs and beta encoders can be recovered amidst imprecise circuit components from the truncated beta expansions of a rdquotestrdquo number x testisin[-1, 1] and its negative counterpart -x test.
Abstract: The beta encoder was recently proposed as a quantization scheme for analog-to-digital (A/D) conversion; in contrast to classical binary quantization, in which each analog sample xisin[-1, 1] is mapped to the first N bits of its base-2 expansion, beta encoders replace each sample x with its expansion in a base beta between 1
12 citations
TL;DR: This paper introduces a new class of parameterized number systems, namely the generalized Phi number system (GPNS), which derives the traditional PhiNumber system, binary number system, beta encoder, and other commonly used number systems by selecting appropriate parameters.
Abstract: Technologies and applications of the field-programmable gate array (FPGAs) and digital signal processing (DSP)
require both new customizable number systems and new data formats. This paper introduces a new class of
parameterized number systems, namely the generalized Phi number system (GPNS). By selecting appropriate
parameters, the new system derives the traditional Phi number system, binary number system, beta encoder, and other
commonly used number systems. GPNS also creates new opportunities for developing customized number systems,
multimedia security systems, and image decomposition and enhancement systems. A new image enhancement algorithm
is also developed by integrating the GPNS-based bit-plane decomposition with Parameterized Logarithmic Image
Processing (PLIP) models. Simulation results are given to demonstrate the GPNS's performance.
5 citations
TL;DR: This paper introduces a more general encoder called the βα-encoder, that can offer more flexibility in design and robustness without any significant drawback on the exponential rate of convergence of the obtained expansion.
Abstract: The β-encoder, introduced as an alternative to binary encoding in A/D conversion,
creates a quantization scheme robust with respect to quantizer imperfections by
the use of a β-expansion, where 1 < β < 2. In this paper we introduce a more general encoder
called the βα-encoder, that can offer more flexibility in design and robustness without
any significant drawback on the exponential rate of convergence of the obtained expansion.
Although an extra multiplication is introduced, it needs not be very accurate. Mathematically,
the βα-encoder gives rise to a dynamical system that is both very interesting and
challenging.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2011 | 1 |
| 2010 | 1 |
| 2008 | 1 |
| 2007 | 1 |
| 2006 | 1 |