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Broadcast channels with confidential messages

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TLDR
Given two discrete memoryless channels (DMC's) with a common input, a single-letter characterization is given of the achievable triples where R_{e} is the equivocation rate and the related source-channel matching problem is settled.
Abstract
Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver 1 rate R_{1} and common messages to both receivers at rate R_{o} , while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R_{1},R_{e},R_{o}) where R_{e} is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Korner-Marton on the broadcast Channel.

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Citations
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References
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Journal ArticleDOI

The wire-tap channel

TL;DR: This paper finds the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission, and implies that there exists a Cs > 0, such that reliable transmission at rates up to Cs is possible in approximately perfect secrecy.
Book

Information Theory and Reliable Communication

TL;DR: This chapter discusses Coding for Discrete Sources, Techniques for Coding and Decoding, and Source Coding with a Fidelity Criterion.
Journal ArticleDOI

The rate-distortion function for source coding with side information at the decoder

TL;DR: The quantity R \ast (d) is determined, defined as the infimum ofrates R such that communication is possible in the above setting at an average distortion level not exceeding d + \varepsilon .
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Broadcast channels

TL;DR: This work introduces the problem of a single source attempting to communicate information simultaneously to several receivers and determines the families of simultaneously achievable transmission rates for many extreme classes of channels to lead to a new approach to the compound channels problem.
Journal ArticleDOI

Source coding with side information and a converse for degraded broadcast channels

TL;DR: In Section H of the paper, a characterization of the capacity region for degraded broadcast channels (DBC's) is given, which was conjectured by Bergmans and is somewhat sharper than the one obtained by Gallager.