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Linear Coding Schemes for the Distributed Computation of Subspaces

Lalitha, V and Prakash, N and Vinodh, K and Kumar, Vijay P and Pradhan, Sandeep S (2013) Linear Coding Schemes for the Distributed Computation of Subspaces. In: IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 31 (4). pp. 678-690.

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Official URL: http://dx.doi.org/10.1109/JSAC.2013.130406


Let X-1,..., X-m be a set of m statistically dependent sources over the common alphabet 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,..., X-m]Gamma in which the (m x 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.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, USA.
Keywords: Distributed function computation; nested codes; normalized entropy; source compression; linear encoders
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 20 May 2013 07:08
Last Modified: 20 May 2013 07:08
URI: http://eprints.iisc.ac.in/id/eprint/46487

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