# An Equivalence between Secure Network and Index Coding

@article{Ong2016AnEB, title={An Equivalence between Secure Network and Index Coding}, author={Lawrence Ong and Badri N. Vellambi and J{\"o}rg Kliewer and Phee Lep Yeoh}, journal={2016 IEEE Globecom Workshops (GC Wkshps)}, year={2016}, pages={1-6} }

We extend the equivalence between network coding and index coding by Effros, El Rouayheb, and Langberg to the secure communication setting in the presence of an eavesdropper. Specifically, we show that the most general versions of secure network-coding setup by Chan and Grant and the secure index- coding setup by Dau, Skachek, and Chee, which also include the randomised encoding setting, are equivalent.

## 7 Citations

Secure Network and Index Coding Equivalence: The Last Piece of the Puzzle

- Computer Science2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

This paper proves the last direction, thereby completing the equivalence between secure network coding and secure index coding, which allows for a network code for any given network-coding instance to be translated to an index code for a suitably constructed index-c coding instance.

Secure Network-Index Code Equivalence: Extension to Non-zero Error and Leakage

- Computer Science2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

The equivalence between secure index coding and secure network coding is generalised to include non-zero decoding error and non- zero leakage.

A Code and Rate Equivalence Between Secure Network and Index Coding

- Computer ScienceIEEE Journal on Selected Areas in Information Theory
- 2021

This article extends the existing equivalence to one between secure index coding and secure network coding, where eavesdroppers are present in the network, and establishes a rate equivalence between these two problems.

Optimal Weakly Secure Linear Codes for Some Classes of the Two-Sender Index Coding Problem

- Computer ScienceArXiv
- 2019

This work provides constructions of weakly secure linear codes for different classes of the two-sender unicast index coding problem, using those of its sub-problems.

Private Index Coding

- Computer Science2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

It is shown that scalar coding is optimal for up to three receivers and scalar linear codes are sub-optimal for four receivers, and when no keys are available, a weaker notion of privacy analogous to weak security is considered.

Code Equivalences Between Network Codes With Link Errors and Index Codes With Side Information Errors

- Computer ScienceIEEE Access
- 2019

New code equivalence relationships between a network code and an index code are studied and results are generalized to erroneous cases for both a given network coding instance and a given index coding instance.

Optimal-Rate Characterisation for Pliable Index Coding using Absent Receivers

- Computer Science2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

We characterise the optimal broadcast rate for a few classes of pliable-index-coding problems. This is achieved by devising new lower bounds that utilise the set of absent receivers to construct…

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