An Edge Reduction Lemma for linear network coding and an application to two-unicast networks

Weifei Zeng, Viveck Ramesh Cadambe, Muriel Medard

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

Abstract

In this paper, we study linear network coding over a wireline network of orthogonal capacitated links represented by a directed acyclic graph. Applying the algebraic framework for linear network coding over Koetter-Médard, we recover an Edge Reduction Lemma - a fundamental connection between edge deletion and the network transfer matrix in the context of the algebraic framework. We study the two-unicast network capacity problem where there are two independent sources and two independent destinations. Using the Edge Reduction Lemma, we make a connection between the linear transfer matrices in the two-unicast setting and the Generalized Network Sharing edge cut bound. Finally, using random linear network coding, we also derive an achievable rate region for the two-unicast problem that is computable purely from the various min-cuts in the graph.

Original languageEnglish (US)
Title of host publication2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Pages509-516
Number of pages8
DOIs
StatePublished - Dec 1 2012
Event2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012 - Monticello, IL, United States
Duration: Oct 1 2012Oct 5 2012

Publication series

Name2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012

Other

Other2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
CountryUnited States
CityMonticello, IL
Period10/1/1210/5/12

Fingerprint

Linear networks
Network coding

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications

Cite this

Zeng, W., Cadambe, V. R., & Medard, M. (2012). An Edge Reduction Lemma for linear network coding and an application to two-unicast networks. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012 (pp. 509-516). [6483261] (2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012). https://doi.org/10.1109/Allerton.2012.6483261
Zeng, Weifei ; Cadambe, Viveck Ramesh ; Medard, Muriel. / An Edge Reduction Lemma for linear network coding and an application to two-unicast networks. 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. pp. 509-516 (2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012).
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Zeng, W, Cadambe, VR & Medard, M 2012, An Edge Reduction Lemma for linear network coding and an application to two-unicast networks. in 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012., 6483261, 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012, pp. 509-516, 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012, Monticello, IL, United States, 10/1/12. https://doi.org/10.1109/Allerton.2012.6483261

An Edge Reduction Lemma for linear network coding and an application to two-unicast networks. / Zeng, Weifei; Cadambe, Viveck Ramesh; Medard, Muriel.

2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. p. 509-516 6483261 (2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Zeng W, Cadambe VR, Medard M. An Edge Reduction Lemma for linear network coding and an application to two-unicast networks. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. p. 509-516. 6483261. (2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012). https://doi.org/10.1109/Allerton.2012.6483261