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(Secure) Linear network coding multicast

A theoretical minimum and some open problems

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Abstract

We introduce network coding in an elementary way, through a combinatorial/algebraic framework, and discuss connections with classical coding theory. We also present a selection of emerging areas and long-standing open problems.

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Notes

  1. The minimum number of edges whose removal disconnects the sources from the receiver.

  2. Note that \(B_j\setminus \{c(f_{\leftarrow }^j({\delta _k}))\}\) forms a hyperplane, i.e., an \(h-1\) dimensional subspace, of an h-dimensional space that can be uniquely described by the associated orthogonal vector.

  3. Formally, the joint entropy of the keys Eve observes equals the joint entropy of the original keys—it is as if these were uniform at random keys for her.

  4. The outer bounds as well can also be expressed as Linear Programs. We refer the interested reader to [14, 15, 18].

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Acknowledgments

C. Fragouli was supported by the NSF Grant 1321120.

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Authors and Affiliations

  1. UCLA, Los Angeles, CA, USA

    Christina Fragouli

  2. Bell Labs, Murray Hill, NJ, USA

    Emina Soljanin

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  1. Christina Fragouli
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  2. Emina Soljanin
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Correspondence to Emina Soljanin.

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This is one of several papers published in Designs, Codes and Cryptography comprising the 25th Anniversary Issue.

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Fragouli, C., Soljanin, E. (Secure) Linear network coding multicast. Des. Codes Cryptogr. 78, 269–310 (2016). https://doi.org/10.1007/s10623-015-0155-6

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