We study the degraded compound multi-receiver wiretap channel (DCMRWC). DCMRWC consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multiple-input multiple-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario we study, the transmitter sends a confidential message to users in the first group which needs to be kept confidential from the second group of users and the eavesdroppers. Moreover, the transmitter sends a different confidential message to users in the second group which needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. As in the first scenario, we obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we establish the secrecy capacity region when there is only one user in the second group.
We study the degraded compound multi-receiver wiretap channel (DCMRWC). DCMRWC consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multiple-input multiple-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario we study, the transmitter sends a confidential message to users in the first group which needs to be kept confidential from the second group of users and the eavesdroppers. Moreover, the transmitter sends a different confidential message to users in the second group which needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. As in the first scenario, we obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we establish the secrecy capacity region when there is only one user in the second group.
We study the degraded compound multi-receiver wiretap channel, which consists of two groups of users and a group of eavesdroppers. We consider two different communication scenarios. In both scenarios, the transmitter sends two confidential messages, one for each group of users. In the first scenario, both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the general discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multi-input multi-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario, the message sent to the first group of users needs to be kept confidential from both the second group of users and eavesdroppers, whereas the message sent to the second group of users needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. We find the secrecy capacity region for the general discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we obtain the secrecy capacity region when there is only one user in the second group.
We study the degraded multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The legitimate users and the eavesdropper satisfy a certain degradation order. In this paper, we study this channel model for the scenario where the transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. First, we obtain an inner bound for the capacity region of the discrete memoryless channel by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound for the capacity region of the degraded discrete memoryless channel. We show that this outer bound partially matches the inner bound. Consequently, we provide a partial characterization of the capacity region of the degraded discrete memoryless channel. Finally, we consider the degraded Gaussian multi-input multi-output (MIMO) wiretap channel with public and confidential messages. We show that, to evaluate both the inner and outer bounds for the Gaussian MIMO case, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds provided earlier for the degraded discrete memoryless channel partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel.
We study the multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless multi-receiver wiretap channel as well as its Gaussian multi-input multi-output (MIMO) instance. First, we consider the degraded discrete memoryless channel, and obtain an inner bound for the capacity region by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound, and show that this outer bound partially matches the inner bound, providing a partial characterization for the capacity region of the degraded channel model. Second, we obtain an inner bound for the general, not necessarily degraded, discrete memoryless channel by using Marton's inner bound, superposition coding, rate-splitting and binning. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel. Finally, we provide an inner bound for the capacity region of the general, not necessarily degraded, Gaussian MIMO multi-receiver wiretap channel.
This paper considers the compound wiretap channel, which generalizes Wyner's wiretap model to allow the channels to the (legitimate) receiver and to the eavesdropper to take a number of possible states. No matter which states occur, the transmitter guarantees that the receiver decodes its message and that the eavesdropper is kept in full ignorance about the message. The compound wiretap channel can also be viewed as a multicast channel with multiple eavesdroppers, in which the transmitter sends information to all receivers and keeps the information secret from all eavesdroppers. For the discrete memoryless channel, lower and upper bounds on the secrecy capacity are derived. The secrecy capacity is established for the degraded channel and the semideterministic channel with one receiver. The parallel Gaussian channel is further studied. The secrecy capacity and the secrecy degree of freedom ( ) are derived for the degraded case with one receiver. Schemes to achieve the for the case with two receivers and two eavesdroppers are constructed to demonstrate the necessity of a prefix channel in encoder design. Finally, the multi-antenna (i.e., MIMO) compound wiretap channel is studied. The secrecy capacity is established for the degraded case and an achievable is given for the general case.
We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multi-receiver wiretap channels with public and confidential messages, and iii) compound wiretap channels. The BCC is a broadcast channel with two users, where in addition to the common message sent to both users, a private message, which needs to be kept hidden as much as possible from the other user, is sent to each user. In this model, each user treats the other user as an eavesdropper. The multi-receiver wiretap channel is a broadcast channel with two legitimate users and an external eavesdropper, where the transmitter sends a pair of public and confidential messages to each legitimate user. Although there is no secrecy concern about the public messages, the confidential messages need to be kept perfectly secret from the eavesdropper. The compound wiretap channel is a compound broadcast channel with a group of legitimate users and a group of eavesdroppers. In this model, the transmitter sends a common confidential message to the legitimate users, and this confidential message needs to be kept perfectly secret from all eavesdroppers. In this paper, we provide a survey of the existing information-theoretic results for these three forms of secure broadcasting problems, with a closer look at the Gaussian multiple-input multiple-output (MIMO) channel models. We also present the existing results for the more general discrete memory-less channel models, as they are often the first step in obtaining the capacity results for the corresponding Gaussian MIMO channel models.
We study the multi-receiver wiretap channel (MR-WC) with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless MR-WC as well as its Gaussian multi-input multi-output (MIMO) counterpart. First, we propose an inner bound for the general, not necessarily degraded, discrete memoryless MR-WC by using Marton's inner bound and rate splitting in conjunction with superposition coding and binning. Second, we specialize this inner bound for the degraded discrete memoryless case. This specialized form of the inner bound can be obtained by using superposition coding and binning only. Next, we obtain an outer bound for the capacity region of the degraded channel, which matches the inner bound for some special cases. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Similar to the discrete memoryless case, for the Gaussian MIMO case as well, these bounds match for some special cases.