# A Code Equivalence between Secure Network and Index Coding

@article{Ong2018ACE, title={A Code Equivalence between Secure Network and Index Coding}, author={Lawrence Ong and J{\"o}rg Kliewer and Badri N. Vellambi and Phee Lep Yeoh}, journal={ArXiv}, year={2018}, volume={abs/1804.09888} }

A code equivalence between index coding and network coding was established, which shows that any index-coding instance can be mapped to a network-coding instance, for which any index code can be translated to a network code with the same decoding-error performance, and vice versa. Also, any networkcoding instance can be mapped to an index-coding instance with a similar code translation. In this paper, we extend the equivalence to secure index coding and secure network coding, where…

## 3 Citations

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.

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.

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…

## References

SHOWING 1-10 OF 16 REFERENCES

An Equivalence Between Network Coding and Index Coding

- Computer ScienceIEEE Trans. Inf. Theory
- 2015

It is shown that the network coding and index coding problems are equivalent and one can determine the capacity region of a given network coding instance with colocated sources by studying the capacity area of a corresponding index coding instance.

Secure Network Coding on a Wiretap Network

- Computer ScienceIEEE Transactions on Information Theory
- 2011

This paper proposes a model, call the wiretap network, that incorporates information security with network coding, and presents a construction of secure linear network codes that can be used provided a certain graph-theoretic condition is satisfied.

Secure index coding: Existence and construction

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

It is proved that random keys do not promote security in three classes of index-coding instances.

On secure network coding with uniform wiretap sets

- Computer Science2013 International Symposium on Network Coding (NetCod)
- 2013

It is shown that, when network nodes can independently generate randomness, determining the secrecy capacity is at least as difficult as the k-unicast network coding problem and a low-complexity linear optimization-based achievable strategy is proposed involving global random keys that can be generated anywhere in the network.

Weakly Secure Network Coding

- Computer Science
- 2005

This work shows that under the new security requirements communication is possible at the multicast capacity and if random coding scheme is used the probability of the system being secure can be made arbitrarily close to one by coding over a large enough field.

Capacity bounds for secure network coding

- Computer Science2008 Australian Communications Theory Workshop
- 2008

We consider the problem of how to securely communicate over networks subject to presence of eavesdroppers. We obtain inner and outer bounds for the set of rate-capacity tuples at which data can be…

On the capacity region for index coding

- Computer Science2013 IEEE International Symposium on Information Theory
- 2013

A new inner bound on the capacity region of the general index coding problem is established, which relies on a random coding scheme and optimal decoding, and has a simple polymatroidal single-letter expression.

On the Security of Index Coding With Side Information

- Computer ScienceIEEE Transactions on Information Theory
- 2012

It is proved that for sufficiently large Q, an optimal linear index code which is strongly secure against such an adversary has length κ<sub>q</sub>+μ+2δ .

On the Index Coding Problem and Its Relation to Network Coding and Matroid Theory

- Computer ScienceIEEE Transactions on Information Theory
- 2010

It is shown that vectorlinear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions.

A rate-distortion approach to index coding

- Computer ScienceITA
- 2014

By applying network-information-theoretic tools, this work finds the optimal rate for the special case in which each source bit is present at either all of the decoders, none of theDecoder, all but one of the Decoder, or all but two of the Decoders.