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arXiv:1109.2766

Secure Broadcasting With Side-Information

Kyatsandra G. Nagananda, Chandra R. Murthy, Shalinee Kishore

Published Sep 13, 2011• 3 citations
arXivHTMLPDF

Abstract

In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.

DOI
10.48550/arxiv.1109.2766

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In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.
We studyinformation-theoretic securityfor discrete memorylessinterferenceandbroadcastchannels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers while ensuring mutual information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved byrandom binningtechniques. For the broadcast channel, adouble-binningcoding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as theswitchchannel, derived bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to createartificial noiseis proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.
This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.
In this study, we obtain an outer bound on the secrecy capacity region of a two-user semi-deterministic discrete memoryless broadcast channel with considering side-information available at the transmitter, where, the sender contain two independent confidential messages, each one is deliberated for one of the receivers but is kept entirely secret from the other. Further, we compare obtained outer bound via the specified secrecy capacity outer bound of the semi-deterministic broadcast channel without side information and without secrecy constraint; specifically, the side information impact on the outer bound is explained.
This paper studies the problem of secure communication over the broadcast channel with receiver-side information under the lens of individual secrecy constraints, that is, the transmitter wants to send two independent messages to two receivers, which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user.
We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers with perfect secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. This approach was first introduced by Wyner in 1975 for the wiretap channel model. In this paper, we investigate the secrecy capacity region bounds for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to the broadcast channel when one sender jointly encodes both messages and to the interference channel when two senders offer independent inputs to the channel. We consider a switch channel model which is a special case of the interference channel and show that the derived outer and inner bounds meet in this case. Finally, we focus on Gaussian interference channels with confidential messages and describe several transmission schemes and their achievable rate regions under the prefect secrecy requirement.
We study secret communication for broadcast channels with two legitimate receivers and one eavesdropper. The transmitter sends two independent confidential messages to the legitimate receivers which have to be kept secret from the eavesdropper. Here, each legitimate receiver is interested in one confidential message having the other one already as side information available. This problem arises for example in the broadcast phase in a bidirectional relay network, where a relay node establishes a bidirectional communication between two nodes while keeping the communication secure from an eavesdropper outside the network. We provide achievable rate regions and an outer bound on the secrecy capacity region.