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Register a new userOn the Capacity Region for Secure Index Coding
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Added by
Parastoo Sadeghi
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region.
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We investigate the construction of weakly-secure index codes for a sender to send messages to multiple receivers with side information in the presence of an eavesdropper. We derive a sufficient and necessary condition for the existence of index codes that are secure against an eavesdropper with access to any subset of messages of cardinality $t$, for any fixed $t$. In contrast to the benefits of using random keys in secure network coding, we prove that random keys do not promote security in three classes of index-coding instances.
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 gener
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 network-coding 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 eavesdroppers are present in the networks, and any code construction needs to guarantee security constraints in addition to decoding-error performance.
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