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IEEE International Symposium on Information Theory (ISIT)

3-Receiver broadcast channels with common and confidential messages

Yeow-Khiang Chia, Abbas El Gamal

Published Jun 1, 2009• 30 citations
Publisher

Abstract

Achievable secrecy rate regions for the general 3-receiver broadcast channel with one common and one confidential message sets are established. We consider two setups: (i) when the confidential message is to be sent to two of the receivers and the third receiver is an eavesdropper; and (ii) when the confidential message is to be sent to one of the receivers and the other two receivers are eavesdroppers. We show that our secrecy rate regions are optimum for some special cases.

DOI
10.1109/isit.2009.5205421

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Achievable secrecy rate regions for the general 3-receiver broadcast channel with one common and one confidential message sets are established. We consider two setups: (i) when the confidential message is to be sent to two of the receivers and the third receiver is an eavesdropper; and (ii) when the confidential message is to be sent to one of the receivers and the other two receivers are eavesdroppers. We show that our secrecy rate regions are optimum for some special cases.
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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.
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 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.
We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.
In this paper, bounds to the secrecy capacity region for the general 3-receiver broadcast channel with 3 degraded message sets, are presented for confidential messages sent to be kept secret from one of the receivers. This model is a more general model than 2-receiver broadcast channels with confidential messages with an external wiretapper, and recently studied 3-receiver degraded broadcast channels with confidential messages, since the conditions on the receivers are general and wiretapper receives the common message. Wyner’s code partitioning combined with double-binning is used to show achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The proof for the outer bound is shown for three cases: the general case; under the condition that receiver 1 is less noisy than receiver 3, the wiretapper; and under the condition that both receivers 1 and 2 are less noisy than the wiretapper, where the inner and outer bounds coincide, giving the secrecy capacity of the special case of a 3-receiver BC with 2 degraded message sets. I.