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

2018; Institute of Electrical and Electronics Engineers; Volume: 64; Issue: 6 Linguagem: Inglês

10.1109/tit.2018.2820686

1557-9654

Wentao Huang, Tracey Ho, Michael Langberg, Jörg Kliewer,

Wireless Communication Security Techniques

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.