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On limits of wireless communications in a fading environment when using multiple antennas
 Wireless Personal Communications
, 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (M ..."
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Cited by 1526 (7 self)
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Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signaltonoise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99%
Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
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Cited by 519 (18 self)
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Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. `Occam's razor' is automatically embodied by this framework. The way in which Bayes infers the values of regularising constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling. 1 Data modelling and Occam's razor In science, a central task is to develop and compare models to a...
Actionable Information in Vision
"... I propose a notion of visual information as the complexity not of the raw images, but of the images after the effects of nuisance factors such as viewpoint and illumination are discounted. It is rooted in ideas of J. J. Gibson, and stands in contrast to traditional information as entropy or coding l ..."
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Cited by 7 (6 self)
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I propose a notion of visual information as the complexity not of the raw images, but of the images after the effects of nuisance factors such as viewpoint and illumination are discounted. It is rooted in ideas of J. J. Gibson, and stands in contrast to traditional information as entropy or coding length of the data regardless of its use, and regardless of the nuisance factors affecting it. The noninvertibility of nuisances such as occlusion and quantization induces an “information gap ” that can only be bridged by controlling the data acquisition process. Measuring visual information entails early vision operations, tailored to the structure of the nuisances so as to be “lossless ” with respect to visual decision and control tasks (as opposed to data transmission and storage tasks implicit in traditional Information Theory). I illustrate these ideas on visual exploration, whereby a “Shannonian Explorer ” guided by the entropy of the data navigates unaware of the structure of the physical space surrounding it, while a “Gibsonian Explorer ” is guided by the topology of the environment, despite measuring only images of it, without performing 3D reconstruction. The operational definition of visual information suggests desirable properties that a visual representation should possess to best accomplish visionbased decision and control tasks. 1.
The Strength of Statistical Evidence for Composite Hypotheses: Inference to the Best Explanation
, 2010
"... A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors o ..."
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Cited by 6 (4 self)
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A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with a reduced likelihood function on the interest parameter space. Unlike the Bayes factor and unlike the pvalue under interpretations that extend its scope, the weight of evidence is coherent in the sense that it cannot support a hypothesis over any hypothesis that it entails. Further, when comparing the hypothesis that the parameter lies outside a nontrivial interval to the hypothesis that it lies within the interval, the proposed method of weighing evidence almost always asymptotically favors the correct hypothesis
1 Actionable Information in Vision
"... Summary. A notion of visual information is introduced as the complexity not of the raw images, but of the images after the effects of nuisance factors such as viewpoint and illumination are discounted. It is rooted in ideas of J. J. Gibson, and stands in contrast to traditional information as entrop ..."
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Summary. A notion of visual information is introduced as the complexity not of the raw images, but of the images after the effects of nuisance factors such as viewpoint and illumination are discounted. It is rooted in ideas of J. J. Gibson, and stands in contrast to traditional information as entropy or coding length of the data regardless of its use, and regardless of the nuisance factors affecting it. The noninvertibility of nuisances such as occlusion and quantization induces an “information gap ” that can only be bridged by controlling the data acquisition process. Measuring visual information entails early vision operations, tailored to the structure of the nuisances so as to be “lossless ” with respect to visual decision and control tasks (as opposed to data transmission and storage tasks implicit in communications theory). The definition of visual information suggests desirable properties that a visual representation should possess to best accomplish visionbased decision and control tasks. 1.1 Preamble This paper discusses the role visual perception plays in the “signaltosymbol barrier ” problem.
unknown title
"... © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to s ..."
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© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. 1 Estimating information from image colors: an application to digital cameras and natural scenes