Multi-Session Function Computation and Multicasting in Undirected Graphs

Kannan, Sreeram; Viswanath, Pramod

doi:10.1109/jsac.2013.130408

Cited by 22 publications

(20 citation statements)

References 38 publications

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“…• Induction step: Suppose that the first k − 1 inequalities in (16) hold for some W * 1 , · · · , W * k−1 that satisfy conditions (3) and (4), and such that W * u , 1 ≤ u ≤ k − 1, take values over the maximal independent sets of…”

Section: Inner and Outer Bound Match: Inductionmentioning

confidence: 99%

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Distributed Function Computation Over a Rooted Directed Tree

Sefidgaran

Tchamkerten

2016

IEEE Trans. Inform. Theory

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This paper establishes the rate region for a class of source coding function computation setups where sources of information are available at the nodes of a tree and where a function of these sources must be computed at the root.The rate region holds for any function as long as the sources' joint distribution satisfies a certain Markov criterion.This criterion is met, in particular, when the sources are independent.This result recovers the rate regions of several function computation setups. These include the point-to-point communication setting with arbitrary sources, the noiseless multiple access network with "conditionally independent sources," and the cascade network with Markovian sources.

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Section: Inner and Outer Bound Match: Inductionmentioning

confidence: 99%

“…The following claim, whose proof is deferred to Appendix E, says that the graph entropy term on the right-hand side of the k-th inequality in (16) is equal to another graph entropy that we shall analyze here below:…”

Section: Inner and Outer Bound Match: Inductionmentioning

confidence: 99%

Distributed Function Computation Over a Rooted Directed Tree

Sefidgaran

Tchamkerten

2016

IEEE Trans. Inform. Theory

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“…In a classic function computation scenario, the nodes exchange messages through authenticated, noiseless, and public communication links, which results in undesired information leakage about the computed function [ 3 , 4 , 5 ]. Furthermore, it is possible to reduce the amount of public communication [ 6 , 7 ] by using distributed lossless or lossy source coding methods; see [ 8 , 9 , 10 , 11 , 12 ] for several extensions. The former method uses Slepian-Wolf (SW) coding [ 13 ] constructions, and the latter allows the computed function to be a distorted version of the target function and applies Wyner-Ziv (WZ) coding [ 14 ] methods, which result in further reductions compared to the former.…”

Section: Introductionmentioning

confidence: 99%

Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints

Günlü

2022

Entropy

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The problem of reliable function computation is extended by imposing privacy, secrecy, and storage constraints on a remote source whose noisy measurements are observed by multiple parties. The main additions to the classic function computation problem include (1) privacy leakage to an eavesdropper is measured with respect to the remote source rather than the transmitting terminals’ observed sequences; (2) the information leakage to a fusion center with respect to the remote source is considered a new privacy leakage metric; (3) the function computed is allowed to be a distorted version of the target function, which allows the storage rate to be reduced compared to a reliable function computation scenario, in addition to reducing secrecy and privacy leakages; (4) two transmitting node observations are used to compute a function. Inner and outer bounds on the rate regions are derived for lossless and lossy single-function computation with two transmitting nodes, which recover previous results in the literature. For special cases, including invertible and partially invertible functions, and degraded measurement channels, exact lossless and lossy rate regions are characterized, and one exact region is evaluated as an example scenario.

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“…However, we have different definitions of the estimate random variables for leaves and non-leaf nodes ((29) and (30)) but the same definition of description random variables. Note that the Gaussian test channel (31) and the definitions in (29) and (30) involve linear transformations. Therefore, all estimate random variables U TC i 's and description random variables V TC i 's are scalar Gaussian random variables with zero mean.…”

Section: A Notation On Typicality-based Codingmentioning

confidence: 99%

Rate Distortion for Lossy In-Network Linear Function Computation and Consensus: Distortion Accumulation and Sequential Reverse Water-Filling

Yang

Grover

Kar

2017

IEEE Trans. Inform. Theory

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We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying the accumulation of information loss in distributed computing, we obtain fundamental limits on network computation rate as a function of incremental distortions (and hence incremental loss of information) along the edges of the network. The above characterization, based on quantifying distortion accumulation, offers an improvement over classical cut-set type techniques which are based on overall distortions instead of incremental distortions. This quantification of information loss qualitatively resembles information dissipation in cascaded channels [1]. Surprisingly, this accumulation effect of distortion happens even at infinite blocklength. Combining this observation with an inequality on the dominance of mean-square quantities over relative-entropy quantities, we obtain outer bounds on the rate distortion function that are tighter than classical cut-set bounds by a difference which can be arbitrarily large in both data aggregation and consensus. We also obtain inner bounds on the optimal rate using random Gaussian coding, which differ from the outer bounds by, where D is the overall distortion. The obtained inner and outer bounds can provide insights A preliminary version of this work was presented in part at the 53rd Annual Allerton Conference on Communication, Control and Computing, 2015.2 on rate (bit) allocations for both the data aggregation problem and the consensus problem. We show that for tree networks, the rate allocation results have a mathematical structure similar to classical reverse water-filling for parallel Gaussian sources. I. INTRODUCTIONThe phenomenon of information dissipation [1]- [6] has been of increasing interest recently from an information-theoretic viewpoint. These results characterize and quantify the gradual loss of information as it is transmitted through cascaded noisy channels. This study has also yielded data processing inequalities that are stronger than those used classically [2], [5].The dissipation of information cannot be quantified easily using classical information-theoretic tools that rely on the law of large numbers, because the dissipation of information is often due to finite-length of codewords and power constraints on the channel inputs [1]. In many classical network information theory problems, such as relay networks, the dissipation of information is not observed because it can be suppressed by use of asymptotically infinite blocklengths [1],[7] 1 . However, information dissipation does happen in many problems of communications and computation. For example, in [4], Evans and Schulman obtain bounds on the information dissipation in noisy circuits, and in [1], Polyanskiy and Wu examine a similar problem in cascaded AWGN channels with power-constrained inputs. Our earlier works [8], [9] show that under some conditions, error-corre...

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Multi-Session Function Computation and Multicasting in Undirected Graphs

Cited by 22 publications

References 38 publications

Distributed Function Computation Over a Rooted Directed Tree

Distributed Function Computation Over a Rooted Directed Tree

Function Computation under Privacy, Secrecy, Distortion, and Communication Constraints

Rate Distortion for Lossy In-Network Linear Function Computation and Consensus: Distortion Accumulation and Sequential Reverse Water-Filling

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