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source resolvability and Intrinsic Randomness: Two Random Number Generation Problems With Respect to a Subclass of f-Divergences

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第12期66卷 7588-7601页

作者： Nomura, Ryo Waseda Univ Ctr Data Sci Tokyo 1698050 Japan

This paper deals with two typical random number generation problems in information theory. One is the source resolvability problem (resolvability problem for short) and the other is the intrinsic randomness problem. In the literature, optimum achievable rates in these two problems with respect to the variational distance as well as the Kullback-Leibler (KL) divergence have already been analyzed. On the other hand, in this study we consider these two problems with respect to f-divergences. The f-divergence is a general non-negative measure between two probabilistic distributions on the basis of a convex function f. The class of f-divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to f-divergences. In this paper, we impose some conditions on the function f so as to simplify the analysis, that is, we consider a subclass of f-divergences. Then, we first derive general formulas of the first-order optimum achievable rates with respect to f-divergences. Next, we particularize our general formulas to several specified functions f. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. The second-order optimum achievable rates and optimistic optimum achievable rates have also been investigated.

关键词： f-divergence general source intrinsic randomness Kullback-Leibler divergence information-spectrum methods source resolvability variational distance

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source resolvability of Spatial-Smoothing-Based Subspace Methods: A Hadamard Product Perspective

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第10期67卷 2543-2553页

作者： Yang, Zai Stoica, Petre Tang, Jinhui Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Uppsala Univ Dept Informat Technol S-75105 Uppsala Sweden Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Jiangsu Peoples R China

A major drawback of subspace methods for directionof-arrival estimation is their poor performance in the presence of coherent sources. Spatial smoothing is a common solution that can be used to restore the performance of these methods in such a case at the cast of increased array size requirement. In this paper, a Hadamard product perspective of the source resolvability problem of spatial-smoothing-based subspace methods is presented. The array size that ensures resolvability is derived as a function of the source number, the rank of the source covariance matrix, and the source coherency structure. This new result improves upon previous ones and recovers them in special cases. It is obtained by answering a long-standing question first asked explicitly in 1973 as to when the Hadamard product of two singular positive-semidefinite matrices is strictly positive definite. The problem of source identifiability is discussed as an extension. Numerical results are provided that corroborate our theoretical findings.

关键词： Direction-of-arrival (DOA) estimation spatial-smoothing-based subspace methods source resolvability source identifiability Hadamard product Khatri-Rao product

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Relationship Between source resolvability with Normalized f-Divergence and Fixed-Length Coding

Relationship Between Source Resolvability with Normalized <i...

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IEEE Information Theory Workshop (ITW)

作者： Nomura, Ryo Waseda Univ Ctr Data Sci Tokyo Japan

ISBN: (纸本)9781728159621

This paper deals with the relationship between the source resolvability problem (or resolvability problem for short) and the fixed-length source coding problem. In the literature, optimum achievable rates in the resolvability problem (optimum resolvability rate) with respect to the variational distance as well as the Kullback-Leibler (KL) divergence, have already been analyzed. The relationship between the optimum resolvability rate and the optimum rate of the fixed-length source coding has also been clarified in each cases. In particular, it has been reported that the optimum source resolvability rate with respect to the normalized KL divergence has a close relationship with the optimum fixed-length source coding rate with the correct decoding exponent. Recently, the optimum resolvability rate with respect to a class of f-divergences has been analyzed. This result can be considered as a generalization of the optimum resolvability rate with respect to the unnormalized KL divergence. However, unnormalized f-divergences has not been considered yet in the resolvability problem. Hence, in this paper, we consider the resolvability problem with respect to a class of unnormalized f-divergences. In particular, we derive the relationship between the optimum resolvability rate with a class of normalized f-divergences and the optimum rate of the fixed-length source coding.

关键词： f-divergence Fixed-length Coding General source Random number generation source resolvability

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HADAMARD PRODUCT PERSPECTIVE ON source resolvability OF SPATIAL-SMOOTHING-BASED SUBSPACE METHODS 44

HADAMARD PRODUCT PERSPECTIVE ON SOURCE RESOLVABILITY OF SPAT...

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44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Yang, Zai Stoica, Petre Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Jiangsu Peoples R China Uppsala Univ Dept Informat Technol SE-75105 Uppsala Sweden

ISBN: (纸本)9781479981311

Spatial smoothing is a common preprocessing scheme for subspace methods that resolves their sensitivity to coherent sources. The source resolvability problem of spatial smoothing -based subspace methods has been extensively investigated using different analysis techniques. In this paper, a unified Hadamard product technique is provided to recover these results. This is done by answering a long-standing question in linear algebra as to under what conditions the Hadamard product of two singular positive-semidefinite matrices is positive definite.

关键词： DOA estimation subspace methods spatial smoothing source resolvability Hadamard product

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