2016
Vazquez-Vilar, Gonzalo; Campo, Adria Tauste; i Fabregas, Albert Guillen; Martinez, Alfonso
Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds Are Tight Artículo de revista
En: IEEE Transactions on Information Theory, vol. 62, no 5, pp. 2324–2333, 2016, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing
@article{Vazquez-Vilar2016,
title = {Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verd\'{u}-Han Bounds Are Tight},
author = {Gonzalo Vazquez-Vilar and Adria Tauste Campo and Albert Guillen i Fabregas and Alfonso Martinez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7434042},
doi = {10.1109/TIT.2016.2542080},
issn = {0018-9448},
year = {2016},
date = {2016-05-01},
journal = {IEEE Transactions on Information Theory},
volume = {62},
number = {5},
pages = {2324--2333},
abstract = {Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verd\'{u}-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.},
keywords = {Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing},
pubstate = {published},
tppubtype = {article}
}
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.
2014
A, Pastore; Koch, Tobias; Fonollosa, Javier Rodriguez
A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information Artículo de revista
En: IEEE Transactions on Information Theory, vol. 60, no 7, pp. 4266–4285, 2014, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound
@article{Pastore2014a,
title = {A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information},
author = {Pastore A and Tobias Koch and Javier Rodriguez Fonollosa},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6832779 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60(7).pdf http://arxiv.org/pdf/1301.6120.pdf},
issn = {0018-9448},
year = {2014},
date = {2014-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {60},
number = {7},
pages = {4266--4285},
publisher = {IEEE},
abstract = {As shown by M\'{e}dard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat {H})) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat {H})) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying M\'{e}dard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than M\'{e}dard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat {H}) tends to zero as the SNR tends to infinity.},
keywords = {channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound},
pubstate = {published},
tppubtype = {article}
}
As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input (X) as the sum of two independent Gaussian variables (X_1) and (X_2) and by applying Médard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity.
2010
Djuric, Petar M; Miguez, Joaquin
Assessment of Nonlinear Dynamic Models by Kolmogorov–Smirnov Statistics Artículo de revista
En: IEEE Transactions on Signal Processing, vol. 58, no 10, pp. 5069–5079, 2010, ISSN: 1053-587X.
Resumen | Enlaces | BibTeX | Etiquetas: Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov–Smirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control
@article{Djuric2010a,
title = {Assessment of Nonlinear Dynamic Models by Kolmogorov\textendashSmirnov Statistics},
author = {Petar M Djuric and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5491124},
issn = {1053-587X},
year = {2010},
date = {2010-01-01},
journal = {IEEE Transactions on Signal Processing},
volume = {58},
number = {10},
pages = {5069--5079},
abstract = {Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method.},
keywords = {Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov\textendashSmirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control},
pubstate = {published},
tppubtype = {article}
}
Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method.