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Mathematical Problems in Engineering

A Class of Three-Receiver Broadcast Channels with Degraded Message Sets and Side Information

Fangbiao Li, Zhi Xue

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We study a class of three-receiver discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information. We derive achievable rate region for this three-receive DM-BC with side information noncausally available at the transmitter. When the receivers follow a degradedness order, we determine the perfect secrecy capacity region of this class of three-receiver DM-BC with three degraded message sets and side information noncausally available at both the transmitter and the receiver. The achievable secrecy region of this paper subsumes Steinberg’s rate region for two-receiver degraded BC with the side information and the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.

DOI
10.1155/2013/406826

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We study a class of three-receiver discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information. We derive achievable rate region for this three-receive DM-BC with side information noncausally available at the transmitter. When the receivers follow a degradedness order, we determine the perfect secrecy capacity region of this class of three-receiver DM-BC with three degraded message sets and side information noncausally available at both the transmitter and the receiver. The achievable secrecy region of this paper subsumes Steinberg’s rate region for two-receiver degraded BC with the side information and the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.
In this paper, a three-receiver (named as one-receiver two-eavesdropper) discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information is studied. The main objective of this paper is to present a theorem so as to give an achievable secrecy region for this one-receiver two-eavesdropper DM-BC with the side information available at the transmitter. In the achievability proof scheme, we use the superposition coding scheme to divide the available randomness into different levels for misleading the eavesdroppers. We establish the achievable secrecy region by using a combination of Gelfand-Pinsker binning scheme and rate splitting technique. Achievability in this case also follows from the new idea of Nair-El Gamal indirect decoding. The achievable secrecy region of this paper subsumes the steinberg rate region for two-receiver degraded BC with the side information as well as the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.
In this paper, we study the one-receiver two-eavesdropper Broadcast Channel (BC) with three degraded message sets. A common message is sent to three receivers. Another message is sent to the first and second receivers and needs to be kept secret from the third receiver (second eavesdropper). The third message is sent to the first receiver and needs to be kept secret from the second and third receivers (first and second eavesdroppers). First, we consider perfect secrecy conditions at the eavesdroppers, where we find an achievable perfect secrecy region. In the achievability scheme, we use superposition coding which divides the available randomness into different levels. These levels are used to mislead the eavesdroppers. The proposed coding scheme determines the perfect secrecy capacity region of the one-receiver two-eavesdropper BC with three degraded message sets, when the receivers exhibit a degradedness order. Next, we find an achievable rate-equivocation region using the rate splitting technique and indirect decoding. We show that for the two-receiver one-eavesdropper BC with three degraded message sets where we relax the secrecy condition at the second receiver, our coding scheme is optimal when the second receiver is a degraded version of the first receiver and it is less noisy than the third receiver.
In this paper, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with noncausal side information, and Csiszár and Körner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity-equivocation region composed of all achievable rates-equivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy.
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.
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 consider a two-user broadcast channel (BC) with two-degraded message sets where a common message M2is intended for both receivers and a private message M1is intended for receiver one. There is an eavesdropper whose channel is stochastically degraded with respect to both receivers and both messages must be kept confidential from the eavesdropper. However, we do not assume any form of degradedness between the two receivers. We first characterize the capacity region of this class of discrete memoryless BC. Next, we consider the two-user Gaussian MIMO BC with two-degraded message sets and an eavesdropper. We characterize the capacity region for the case where the eavesdropper is only required to be stochastically degraded with respect to receiver one. We make use of the channel enhancement technique as well as an extremal entropy inequality of Liu et al. that was derived using the generalized Costa's entropy power inequality (EPI).