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Iran Workshop on Communication and Information Theory (IWCIT)

An achievable scheme for the one-receiver, two-eavesdropper broadcast channel

Sadaf Salehkalaibar, Mohammad Reza Aref

Published May 1, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iwcit.2014.6842505

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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.
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 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 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.
This paper establishes inner bounds on the secrecy capacity regions for the general 3-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, 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.