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Strong Converse Using Change of Measure Arguments

IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第2期66卷 689-703页

作者： Tyagi, Himanshu Watanabe, Shun Indian Inst Sci Dept Elect Commun Engn Bangalore 560012 Karnataka India Tokyo Univ Agr & Technol Dept Comp & Informat Sci Tokyo 1848588 Japan

The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we develop a general and simple recipe for proving strong converse that is applicable for distributed problems as well. Heuristically, our proof of strong converse mimics the standard steps for proving a weak converse, except that we apply those steps to a modified distribution obtained by conditioning the original distribution on the event that no error occurs. A key component of our recipe is the replacement of the hard Markov constraints implied by the distributed nature of the problem with a soft information cost using a variational formula introduced by Oohama. We illustrate our method by providing a short proof of the strong converse for the Wyner-Ziv problem and strong converse theorems for interactive function computation, common randomness and secret key agreement, and the wiretap channel;the latter three strong converse problems were open prior to this work.

关键词： Strong converse wiretap channel function computation secret key agreement measure change

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Energy-Efficient Over-the-Air computation Scheme for Densely Deployed IoT Networks

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2020年第5期16卷 3558-3565页

作者： Basaran, Semiha Tedik Kurt, Gunes Karabulut Chatzimisios, Periklis Istanbul Tech Univ Dept Commun & Elect Engn TR-34469 Istanbul Turkey Alexander Technol Educ Inst Thessaloniki Dept Informat Thessaloniki 57400 Greece

In this article, we propose a spatial sampling approach to reduce energy consumption for over-the-air (function) computation (AirComp) scheme by utilizing the cross-correlations among sensor readings. Since the conventional AirComp scheme leads to a reduction in total transmission time and latency thanks to the joint communication and computation processes, it is especially well-suited to Internet of Things (IoT) monitoring systems. AirComp lets simultaneous transmissions of all nodes by exploiting the superposition property of wireless channel;however, it does not overcome the high energy consumption paradigm, which is a fundamental problem of densely deployed IoT monitoring systems. We present a minimum mean square error (MMSE) estimation scheme while a small number of observations are available for densely deployed networks. The proposed MMSE estimator provides a significant mean squared error improvement with reducing energy consumption compared to the conventional estimator. Since the network lifetime of IoT monitoring systems can be almost doubled, the proposed estimator provides flexibility for the dense deployment of nodes. The simulation results verify the theoretical expressions.

关键词： function computation Internet of Things (IoT) over-the-air computation

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Data Privacy for a ρ-Recoverable function

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第6期65卷 3470-3488页

作者： Nageswaran, Ajaykrishnan Narayan, Prakash Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Maryland Syst Res Inst College Pk MD 20742 USA

A user's data is represented by a finite-valued random variable. Given a function of the data, a querier is required to recover, with at least a prescribed probability, the value of the function based on a query response provided by the user. The user devises the query response, subject to the recoverability requirement, so as to maximize privacy of the data from the querier. Privacy is measured by the probability of error incurred by the querier in estimating the data from the query response. We analyze single and multiple independent query responses, with each response satisfying the recoverability requirement, which provide maximum privacy to the user. In the former setting, we also consider privacy for a predicate of the user's data. Achievability schemes with explicit randomization mechanisms for query responses are given and their privacy compared with converse upper bounds.

关键词： Chernoff radius function computation predicate privacy privacy recoverability

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Communication Versus computation: Duality for Multiple-Access Channels and Source Coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第1期65卷 292-301页

作者： Zhu, Jingge Lim, Sung Hoon Gastpar, Michael Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA Korean Inst Ocean Sci & Technol ICT Convergence Unit Busan 49111 South Korea Ecole Polytech Fed Sch Comp & Commun Sci CH-1015 Lausanne Switzerland

computation codes in network information theory are designed for scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. Korner and Marton showed for distributed source coding (DSC) that such function decoding can be achieved more efficiently than decoding the full information sources. Compute-forward has shown that function decoding, in combination with network coding ideas, is a useful building block for end-to-end communication over a network. In both cases, good computation codes are the key component in the coding schemes. Could these same codes simultaneously also enable full message decoding over a sufficiently strong multiple-access channel (MAC)? This work establishes a partial negative answer and converse result. Specifically, for any code that is known to be a good computation code for some MAC, we characterize a class of MACs for which that code cannot enable full message decoding (and vice versa). Finally, an analogous duality result is established for a related DSC problem.

关键词： function computation code duality multiple access channel compute-forward multi-terminal source coding structured code

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Interactive Source Coding for function computation in Collocated Networks

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第7期58卷 4289-4305页

作者： Ma, Nan Ishwar, Prakash Gupta, Piyush Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94709 USA Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA Alcatel Lucent Bell Labs Murray Hill NJ 07974 USA

A problem of interactive function computation in a collocated network is studied in a distributed block source coding framework. With the goal of computing samples of a desired function of sources at the sink, the source nodes exchange messages through a sequence of error-free broadcasts. For any function of independent sources, a computable characterization of the set of all feasible message coding rates-the rate region-isderived in terms of single-letter information measures. In the limit as the number of messages tends to infinity, the infinite-message minimum sum rate, viewed as a functional of the joint source probability mass function, is characterized as the least element of a partially ordered family of functionals having certain convex-geometric properties. This characterization leads to a family of lower bounds for the infinite-message minimum sum rate and a simple criterion to test the optimality of any achievable infinite-message sum rate. An iterative algorithm for evaluating the infinite-message minimum sum-rate functional is proposed and is demonstrated through an example of computing the minimum function of three Bernoulli sources. Based on the characterizations of the rate regions, it is shown that when computing symmetric functions of binary sources, the sink will inevitably learn certain additional information that is not demanded in computing the function. This conceptual understanding leads to new improved bounds for the minimum sum rate. The new bounds are shown to be orderwise better than those based on cut-sets as the network scales. The scaling law of the minimum sum rate is explored for different classes of symmetric functions and source parameters.

关键词： Collocated networks communication complexity distributed source coding function computation interactive coding

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Multi-Precision Table-Addition Designs for Computing Nonlinear functions in Deep Neural Networks 15

Multi-Precision Table-Addition Designs for Computing Nonline...

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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)/ IEEE Asia Pacific Conference on Post Graduate Research in Microelectronics and Electronics (PrimeAsia)

作者： Hsiao, Shen-Fu Huang, Kuey-Chin Chen, Yu-Hong Natl Sun Yat Sen Univ Dept Comp Sci & Engn Kaohsiung Taiwan

ISBN: (纸本)9781728129402

computation of non-linear functions such as hyperbolic tangent and sigmoid is critical in machine learning. Furthermore, precision requirement varies across different layers in deep neural networks. Thus it is beneficial to design multi-precision function computation units. Since many function computation methods require lookup tables (LUT) along with simple arithmetic components, we propose a dual-precision architecture with shared LUT based on a recently proposed table-bound algorithm. Experimental results show that the proposed dual-precision designs has smaller area compared with the design with separate single-precision modules.

关键词： function computation non-linear activation function lookup tables machine learning computer arithmetic

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Towards an Algebraic Network Information Theory: Distributed Lossy computation of Linear functions

Towards an Algebraic Network Information Theory: Distributed...

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IEEE International Symposium on Information Theory (ISIT)

作者： Lim, Sung Hoon Feng, Chen Pastore, Adrian Nazer, Bobak Gastpar, Michael KIOST Seoul South Korea Univ British Columbia Vancouver BC Canada CTTC CERCA Boston MA USA Boston Univ Boston MA 02215 USA Ecole Polytech Fed Lausanne Lausanne Switzerland

ISBN: (纸本)9781538692912

Consider the important special case of the K-user distributed source coding problem where the decoder only wishes to recover one or more linear combinations of the sources. The work of Korner and Marton demonstrated that, in some cases, the optimal rate region is attained by random linear codes, and strictly improves upon the best-known achievable rate region established via random i.i.d. codes. Recent efforts have sought to develop a framework for characterizing the achievable rate region for nested linear codes via joint typicality encoding and decoding. Here, we make further progress along this direction by proposing an achievable rate region for simultaneous joint typicality decoding of nested linear codes. Our approach generalizes the results of Korner and Marton to computing an arbitrary number of linear combinations and to the lossy computation setting.

关键词： Nested linear codes joint decoding distributed source-coding function computation

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Predicate Privacy and List Privacy for a ρ-Recoverable function

Predicate Privacy and List Privacy for a ρ-Recoverable Func...

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IEEE International Symposium on Information Theory (ISIT)

作者： Nageswaran, Ajaykrishnan Narayan, Prakash Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Maryland Inst Syst Res College Pk MD 20742 USA

ISBN: (纸本)9781538692912

For a given function of user data, a querier must recover with at least a prescribed probability, the value of the function based on a user-provided query response. Subject to this requirement, the user forms its query response so as to maximize probability of error-based predicate privacy or list privacy of the data from the querier. Achievability schemes with explicit randomization mechanisms for query responses are given and their privacies compared with converse upper bounds.

关键词： Add-noise query response data privacy function computation list privacy predicate privacy recoverability

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Optimal function computation in Directed and Undirected Graphs

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第6期58卷 3407-3418页

作者： Kowshik, Hemant Kumar, P. R. IBM India Res Lab Next Generat Syst Grp Bangalore 560045 Karnataka India Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA

We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs and undirected graphs. We study how the structure of the function affects the encoding strategies and the effect of interactive information exchange. Depending on the application, there could be a designated collector node, or every node might want to compute the function. We begin by considering a directed graph G = (V, E) on the sensor nodes, where the goal is to determine the optimal encoders on each edge which achieve function computation at the collector node. Our goal is to characterize the rate region in R-vertical bar E vertical bar, i.e., the set of points for which there exist feasible encoders with given rates which achieve zero-error computation for asymptotically large block length. We determine the solution for directed trees, specifying the optimal encoder and decoder for each edge. For general directed acyclic graphs, we provide an outer bound on the rate region by finding the disambiguation requirements for each cut, and describe examples where this outer bound is tight. Next, we address the scenario where nodes are connected in an undirected tree network, and every node wishes to compute a given symmetric Boolean function of the sensor data. Undirected edges permit interactive computation, and we therefore study the effect of interaction on the aggregation and communication strategies. We focus on sum-threshold functions and determine the minimum worst case total number of bits to be exchanged on each edge. The optimal strategy involves recursive in-network aggregation which is reminiscent of message passing. In the case of general graphs, we present a cut-set lower bound and an achievable scheme based on aggregation along trees. For complete graphs, we prove that the complexity of this scheme is no more than twice

关键词： Communication complexity function computation in-network computation

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Sum-Networks From Incidence Structures: Construction and Capacity Analysis

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第5期64卷 3461-3480页

作者： Tripathy, Ardhendu Ramamoorthy, Aditya Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA

A sum-network is an instance of a function computation problem over a directed acyclic network, in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of the well-studied multiple unicast network communication problem also hold for sum-networks, due to a known reduction between the two problems. In this paper, we describe an algorithm to construct families of sum-network instances using incidence structures. The computation capacity of several of these sum-network families is evaluated. Unlike the coding capacity of a multiple unicast problem, the computation capacity of sum-networks depends on the characteristic of the finite field over which the sum is computed. This dependence is very strong;we show examples of sum-networks that have a rate-1 solution over one characteristic but a rate close to zero over a different characteristic. In addition, a sum-network can have arbitrarily different computation capacities for different alphabets.

关键词： Network coding function computation sum-networks characteristic incidence structures

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