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

Huang, Wentao and Ho, Tracey and Langberg, Michael and Kliewer, Jörg (2018) Single-Unicast Secure Network Coding and Network Error Correction are as Hard as Multiple-Unicast Network Coding. IEEE Transactions on Information Theory, 64 (6). pp. 4496-4512. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20180606-110229670

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TIT.2018.2820686DOIArticle
ORCID:
AuthorORCID
Huang, Wentao0000-0003-0963-3624
Langberg, Michael0000-0002-7470-0718
Additional Information:© 2018 IEEE. Manuscript received January 14, 2016; revised January 6, 2017; accepted February 28, 2018. Date of publication March 29, 2018; date of current version May 18, 2018. This work was supported in part by NSF under Grant CCF-1526771 and Grant CNS-1526547 and in part by the Caltech Lee Center. This paper was presented in part at the 2013 International Symposium on Network Coding [1], the 2014 Allerton Conference on Communication, Control and Computing [2], and the 2015 IEEE International Symposium on Information Theory [3].
Funders:
Funding AgencyGrant Number
NSFCCF-1526771
NSFCNS-1526547
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Network coding, equivalence, security, error correction, capacity
Issue or Number:6
Record Number:CaltechAUTHORS:20180606-110229670
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180606-110229670
Official Citation:W. Huang, T. Ho, M. Langberg and J. Kliewer, "Single-Unicast Secure Network Coding and Network Error Correction are as Hard as Multiple-Unicast Network Coding," in IEEE Transactions on Information Theory, vol. 64, no. 6, pp. 4496-4512, June 2018. doi: 10.1109/TIT.2018.2820686
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86837
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Jun 2018 18:11
Last Modified:03 Oct 2019 19:49

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