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      Reliable and Secure Multishot Network Coding using Linearized Reed-Solomon Codes

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          Abstract

          Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with limitless computational resources may inject erroneous packets in up to \(t\) links, erase up to \(\rho\) packets, and wire-tap up to \(\mu\) links, all throughout \(\ell\) shots of a (random) linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of \( \ell n^\prime - 2t - \rho - \mu \) packets, where \( n^\prime \) is the number of outgoing links, for any packet length \( m \geq n^\prime \) (largest possible range), with only the restriction that \( \ell < q \) (size of the base field). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length \(n = \ell n^\prime \), and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication.

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          Network information flow

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            Polynomial Codes Over Certain Finite Fields

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              Linear network coding

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                Author and article information

                Journal
                09 May 2018
                Article
                1805.03789
                c2ed4e42-77ea-4525-b0e8-ada4a569a5a1

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                cs.IT math.IT

                Numerical methods,Information systems & theory
                Numerical methods, Information systems & theory

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