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IEEE International Symposium on Information Theory (ISIT)

The capacity region of a class of 3-receiver broadcast channels with two eavesdroppers

Sadaf Salehkalaibar, Mohammad Reza Aref

Published Jul 1, 2011• 4 citations
Publisher

Abstract

In this paper, we consider the 3-receiver broadcast channel with one common and two confidential messages. One of the confidential messages is sent to the first and second receivers and kept secret from the third receiver (eavesdropper). The other confidential message is sent to the first receiver and kept secret from the second and third receivers (eavesdroppers). The common message is decoded by all receivers. We study some special cases of the model and determine their secrecy capacity regions.

DOI
10.1109/isit.2011.6034283

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In this paper, we consider the 3-receiver broadcast channel with one common and two confidential messages. One of the confidential messages is sent to the first and second receivers and kept secret from the third receiver (eavesdropper). The other confidential message is sent to the first receiver and kept secret from the second and third receivers (eavesdroppers). The common message is decoded by all receivers. We study some special cases of the model and determine their secrecy capacity regions.
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In this paper, we consider the secrecy of the one-receiver, two-eavesdropper Broadcast Channel (BC) with three degraded message sets. There is a three-receiver BC where the common message is decoded by all receivers. The first confidential message is decoded by the first and the second receivers and is kept secret from the third receiver (eavesdropper). The second confidential message is decoded by the first receiver and is kept secret from the second and the third receivers (eavesdroppers). We propose an achievable scheme to find an inner bound to the secrecy capacity region of a class of one-receiver, two-eavesdropper BCs with three degraded message sets. We also compare our inner bound with another existing achievable region.
This paper establishes inner bounds on the secrecy capacity regions for the general three-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.
In this study, the authors consider the secrecy of a one‐receiver, two‐eavesdropper broadcast channel (BC) with three degraded message sets. Consider a three‐receiver BC with three messages, where the first message is decoded by all the receivers. The second message is decoded by the first and the second receivers and is to be kept secret from the third receiver. The third message is decoded by the first receiver and is to be kept secret from the second and the third receivers. The authors consider the imperfect secrecy condition at the second receiver, that is, it is allowed to partially decode the third message. However, the perfect secrecy condition at the third receiver, does not allow it to decode the confidential messages. The coding scheme for this model requires decoding strategy for finding the messages at different destinations. The authors propose a coding scheme which uses indirect decoding. The authors also obtain an outer bound and use it to determine the secrecy capacity region of some classes of one‐receiver, two‐eavesdropper BCs with three degraded message sets. The authors extend our results to the Gaussian case and evaluate the achievable region.
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.