Single-Unicast Secure Network Coding and Network Error Correction are as Hard as Multiple-Unicast Network Coding

Document Type

Conference Proceeding

Publication Date

6-1-2018

Abstract

This paper reduces multiple-unicast network coding to single-unicast secure network coding and single-unicast network error correction. Specifically, we present reductions that map an arbitrary multiple-unicast network coding instance to a unicast secure network coding instance in which at most one link is eavesdropped, or a unicast network error correction instance in which at most one link is erroneous, such that a rate tuple is achievable in the multiple-unicast network coding instance if and only if a corresponding rate is achievable in the unicast secure network coding instance, or in the unicast network error correction instance. Conversely, we show that an arbitrary unicast secure network coding instance in which at most one link is eavesdropped can be reduced back to a multiple-unicast network coding instance. In addition, we show that the capacity of a unicast network error correction instance in general is not (exactly) achievable.

Identifier

85044726592 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/TIT.2018.2820686

ISSN

00189448

First Page

4496

Last Page

4512

Issue

6

Volume

64

Grant

CCF-1526771

Fund Ref

National Science Foundation

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