A nested linear codes approach to distributed function computation over subspaces

Lalitha, V and Prakash, N and Kumar, Vijay P and Pradhan, Sandeep Sande and Vinodh, K (2011) A nested linear codes approach to distributed function computation over subspaces. In: 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 28-30 Sept. 2011, Monticello, IL, USA.

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Abstract

In this paper, we consider a distributed function computation setting, where there are m distributed but correlated sources X1,...,Xm and a receiver interested in computing an s-dimensional subspace generated by [X1,...,Xm]Γ for some (m × s) matrix Γ of rank s. We construct a scheme based on nested linear codes and characterize the achievable rates obtained using the scheme. The proposed nested-linear-code approach performs at least as well as the Slepian-Wolf scheme in terms of sum-rate performance for all subspaces and source distributions. In addition, for a large class of distributions and subspaces, the scheme improves upon the Slepian-Wolf approach. The nested-linear-code scheme may be viewed as uniting under a common framework, both the Korner-Marton approach of using a common linear encoder as well as the Slepian-Wolf approach of employing different encoders at each source. Along the way, we prove an interesting and fundamental structural result on the nature of subspaces of an m-dimensional vector space V with respect to a normalized measure of entropy. Here, each element in V corresponds to a distinct linear combination of a set {Xi}im=1 of m random variables whose joint probability distribution function is given.

Item Type:	Conference Paper
Publisher:	IEEE
Additional Information:	Copyright of this article belongs to IEEE.
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	01 Apr 2013 07:04
Last Modified:	01 Apr 2013 07:04
URI:	http://eprints.iisc.ac.in/id/eprint/46132

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