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arXiv:0805.4374 · IEEE Transactions on Information Theory

Capacity Bounds for Broadcast Channels With Confidential Messages

Jin Xu, Yi Cao, Biao Chen

Published Sep 16, 2009• 82 citations
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Abstract

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.

DOI
10.1109/tit.2009.2027500

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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 paper, we consider non-degraded discrete memoryless broadcast channels where two private messages as well as a common message are transmitted at rate R1, R2and Rorespectively. The common message is for both receivers to decode; the private message is only for its intended receiver of which the other receiver shall be kept as ignorant as possible. Measuring ignorance by equivocation, we propose an achievable rate region (R1, R2, Ro, Re1, Re2) for this channel where Re1and Re2are the equivocation rates for the two receivers respectively. This result generalizes Csiszar and Kornerpsilas capacity region for broadcast channels with single private message, Liu et alpsilas result for broadcast channels with perfect secrecy, Gelpsilafand and Pinskerpsilas achievable rate region for broadcast channels with common message, and Martonpsilas achievable rate region for general broadcast channels.
We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Removing the secrecy constraint, this outer bound can also be served as a new outer bound for the relay broadcast channel. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages (no common message). Inner and outer bounds on the capacity-equivocation region are provided. Then, we study the Gaussian case, and find that with the help of the relay node, the achievable secrecy rate region of the Gaussian broadcast channels with two confidential messages is enhanced. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. This work generalizes Lai-Gamals work on the relay-eavesdropper channel by considering an additional common message for both the legitimate receiver and the eavesdropper. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszár-Körner’s work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.
A discrete memoryless multiple-access channel (MAC) with confidential messages is studied, where two users attempt to transmit common information to a destination and each user also has private (confidential) information intended for the destination. This channel generalizes the classical MAC model in that each user also receives channel outputs, and hence may obtain the confidential information sent by the other user from the channel output it receives. However, each user views the other user as a wiretapper or eavesdropper, and wishes to keep its confidential information as secret as possible from the other user. The level of secrecy of the confidential information is measured by the equivocation rate, i.e., the entropy rate of the confidential information conditioned on channel outputs at the wiretapper (the other user). The performance measure is the rate-equivocation tuple that includes the common rate, two private rates, and two equivocation rates as components. The set that includes all achievable rate-equivocation tuples is referred to as the capacity-equivocation region. The case of perfect secrecy is particularly of interest, in which each user's confidential information is perfectly hidden from the other user. The set that includes all achievable rates with perfect secrecy is referred to as the secrecy capacity region. For the MAC with two confidential messages, in which both users have confidential messages for the destination, inner bounds on the capacity-equivocation region, and secrecy capacity region are obtained. It is demonstrated that there is a tradeoff between the two equivocation rates (secrecy levels) achieved for the two confidential messages. For the MAC with one confidential message, in which only one user (user 1) has private (confidential) information for the destination, inner and outer bounds on the capacity-equivocation region are derived. These bounds match partially, and hence the capacity-equivocation region is partially characterized. Furthermore, the outer bound provides a tight converse for the case of perfect secrecy, and hence establishes the secrecy capacity region. A class of degraded MACs with one confidential message is further studied, and the capacity-equivocation region and the secrecy capacity region are established. These results are further explored via two example channels: the binary and Gaussian MACs. For both channels, the capacity-equivocation regions and the secrecy capacity regions are obtained.
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.
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.