A nested linear codes approach to distributed function computation over subspaces

Lalitha, V.; Prakash, Naveen; Vinodh, K.; Kumar, P. Vijay; Pradhan, S. Sandeep

doi:10.1109/allerton.2011.6120304

Cited by 7 publications

(22 citation statements)

References 6 publications

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“…Note that this distribution keeps the marginals (21) (due to the Markov chain (20)) and (22). Moreover, Definition (23) yields the following Markov chains…”

Section: Roots(k)mentioning

confidence: 99%

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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“…Note that this distribution keeps the marginals (21) (due to the Markov chain (20)) and (22). Moreover, Definition (23) yields the following Markov chains…”

Section: Roots(k)mentioning

confidence: 99%

Distributed Function Computation Over a Rooted Directed Tree

Sefidgaran

Tchamkerten

2016

IEEE Trans. Inform. Theory

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“…They show that such an approach leads to optimality. However, if the objective is to have the complete reconstruction of both the sources at the decoder (Slepian-Wolf setting), then it has been shown that for certain sources, using identical binning can be strictly suboptimal [9]. In general, to achieve the Slepian-Wolf performance limit, one needs to use either binning of the two sources using two independent linear codes or use independent unstructured binning of the two sources.…”

Section: Introductionmentioning

confidence: 99%

Quasi Linear Codes: Application to point-to-point and multi-terminal source coding

Shirani

Heidari

Pradhan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under addition. We argue that these codes provide gains in terms of achievable Rate-Distortions (RD) in different multi-terminal source coding problems. We derive the necessary covering bounds for analyzing the performance of QLC's. We then consider the Multiple-Descriptions (MD) problem, and prove through an example that the application of QLC's gives an improved achievable RD region for this problem. Finally, we derive an inner bound to the achievable RD region for the general MD problem which strictly contains all of the previous known achievable regions.

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“…. , X m and receiver that is interested in decoding the s dimensional subspace W corresponding to the space spanned by the set {Z i } of random variables defined in (1). Then minimum symmetric rate under the CC approach is given by…”

Section: A Rate Region Under the CC Approachmentioning

confidence: 99%

“…, X m and a receiver that is interested in decoding the s dimensional subspace W . Let W (0) W (1) . .…”

Section: A Identifying the Optimal Subspace Under The Ss Approachmentioning

confidence: 99%

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Linear Coding Schemes for the Distributed Computation of Subspaces

Lalitha

Prakash

Vinodh

et al. 2013

IEEE J. Select. Areas Commun.

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Let $X_1, ..., X_m$ be a set of $m$ statistically dependent sources over the common alphabet $\mathbb{F}_q$, that are linearly independent when considered as functions over the sample space. We consider a distributed function computation setting in which the receiver is interested in the lossless computation of the elements of an $s$-dimensional subspace $W$ spanned by the elements of the row vector $[X_1, \ldots, X_m]\Gamma$ in which the $(m \times s)$ matrix $\Gamma$ has rank $s$. A sequence of three increasingly refined approaches is presented, all based on linear encoders. The first approach uses a common matrix to encode all the sources and a Korner-Marton like receiver to directly compute $W$. The second improves upon the first by showing that it is often more efficient to compute a carefully chosen superspace $U$ of $W$. The superspace is identified by showing that the joint distribution of the $\{X_i\}$ induces a unique decomposition of the set of all linear combinations of the $\{X_i\}$, into a chain of subspaces identified by a normalized measure of entropy. This subspace chain also suggests a third approach, one that employs nested codes. For any joint distribution of the $\{X_i\}$ and any $W$, the sum-rate of the nested code approach is no larger than that under the Slepian-Wolf (SW) approach. Under the SW approach, $W$ is computed by first recovering each of the $\{X_i\}$. For a large class of joint distributions and subspaces $W$, the nested code approach is shown to improve upon SW. Additionally, a class of source distributions and subspaces are identified, for which the nested-code approach is sum-rate optimal.Comment: To appear in IEEE Journal of Selected Areas in Communications (In-Network Computation: Exploring the Fundamental Limits), April 201

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A nested linear codes approach to distributed function computation over subspaces

Cited by 7 publications

References 6 publications

Distributed Function Computation Over a Rooted Directed Tree

Distributed Function Computation Over a Rooted Directed Tree

Quasi Linear Codes: Application to point-to-point and multi-terminal source coding

Linear Coding Schemes for the Distributed Computation of Subspaces

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