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Mathematical Problems of Computer Science

Random Coding Bound for Secrecy E-capacity Region of the Broadcast Channel With Two Confidential Messages

Nasrin Afshar, Evgueni Haroutunian, Mariam E. Haroutunian

Published Apr 25, 2012• 0 citations
OpenAlex

Abstract

We study secrecy E-capacity region of the discrete memoryless broadcast channel with two independent confidential messages sent to two receivers (BC-2CM). The system involves two sources, one encoder, two discrete memoryless channels and two receivers. Each private message is sent to the corresponding receiver while keeping the other receiver in total ignorance of it. The level of ignorance is measured by the equivocation rate. E-capacity region is the set of rate pairs R1; R2 of codes with given error probability exponents (reliabilities) E1; E2 at respective receivers. We derived a random coding bound for secrecy E-capacity region of the BC-2CM. When error probability exponents are going to zero, this bound coincides with the inner bound of secrecy capacity region of the BC-2CM obtained by R. Liu, I. Maric, P. Spasojevic and R. Yates.

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We study secrecy E-capacity region of the discrete memoryless broadcast channel with two independent confidential messages sent to two receivers (BC-2CM). The system involves two sources, one encoder, two discrete memoryless channels and two receivers. Each private message is sent to the corresponding receiver while keeping the other receiver in total ignorance of it. The level of ignorance is measured by the equivocation rate. E-capacity region is the set of rate pairs R1; R2 of codes with given error probability exponents (reliabilities) E1; E2 at respective receivers. We derived a random coding bound for secrecy E-capacity region of the BC-2CM. When error probability exponents are going to zero, this bound coincides with the inner bound of secrecy capacity region of the BC-2CM obtained by R. Liu, I. Maric, P. Spasojevic and R. Yates.
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.
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.
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.
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as secret superposition scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma.