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, 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.
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, 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.
A three-receiver degraded broadcast channel with secrecy outside of a bounded range is studied, in which the channel quality gradually degrades from receiver 3 to receiver 1. The transmitter has three messages intended for the receivers with receiver 3 decoding all messages, receiver 2 decoding the first two messages, and receiver 1 decoding only the first message. Furthermore, the third message should be kept secure from receiver 1. The discrete memoryless channel is studied and the secrecy capacity region is characterized. The achievable scheme is based on superposition coding and random binning, in which one superposition layer and random binning together provide secrecy. The converse proof is derived based on the insight obtained from the achievable scheme so that manipulations of terms yield tight rate bounds.
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 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.
This paper considers a three-receiver broadcast channel with degraded message sets and message cognition. The model consists of a common message for all three receivers, a private common message for only two receivers and two additional private messages for these two receivers, such that each receiver is only interested in one message, while being fully cognizant of the other one. First, this model is investigated without any secrecy constraints, where the capacity region is established, showing that the straightforward extension of the Körner and Marton inner bound to the investigated scenario is optimal. In particular, this agrees with Nair and Wang's result, which states that the idea of indirect decoding - introduced to improve the Körner and Marton inner bound - does not provide a better region for this scenario. Further, some secrecy constraints are introduced by letting the private messages to be confidential ones. Two different secrecy criteria are considered: joint secrecy and individual secrecy. For both criteria, a general achievable rate region is provided. Moreover, the joint and individual secrecy capacity regions are established, if the two legitimate receivers are more capable than the eavesdropper. The established capacity regions indicate that the individual secrecy criterion can provide a larger capacity region as compared to the joint one, because each cognizant message can be used as a secret key for the other individual message. Further, the joint secrecy capacity is established for a more general class of more capable channels, where only one of the two legitimate receivers is more capable than the eavesdropper. This was done by showing that principle of indirect decoding introduced by Nair and El Gamal is optimal for this class of channels. This result is in contrast with the nonsecrecy case, where the indirect decoding does not provide any gain.