Results 1  10
of
15
The Secrecy Capacity Region of the Gaussian MIMO MultiReceiver Wiretap Channel
, 2009
"... In this paper, we consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this ch ..."
Abstract

Cited by 70 (23 self)
 Add to MetaCart
(Show Context)
In this paper, we consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the singleinput singleoutput (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimummeansquareerror and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semidefinite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirtypaper coding with Gaussian signals.
Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper
"... We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. Characterizing the secrecy capacity region of this channel in its most general form is difficult, because the version of this problem without any secr ..."
Abstract

Cited by 33 (16 self)
 Add to MetaCart
(Show Context)
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. Characterizing the secrecy capacity region of this channel in its most general form is difficult, because the version of this problem without any secrecy constraints, is the broadcast channel with an arbitrary number of receivers, whose capacity region is open. Consequently, to have progress in understanding secure broadcasting, we resort to studying several special classes of channels, with increasing generality. As the first model, we consider the degraded multireceiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multireceiver wiretap channel with a less noisiness order in each subchannel, where this order is not necessarily the same for all subchannels. Consequently, this parallel multireceiver wiretap channel is not as restrictive as the degraded multireceiver wiretap channel, because the overall channel does not exhibit a
Degraded Compound Multireceiver Wiretap Channels
, 2009
"... In this paper, we study the degraded compound multireceiver wiretap channel. The degraded compound multireceiver wiretap channel 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 ..."
Abstract

Cited by 22 (11 self)
 Add to MetaCart
(Show Context)
In this paper, we study the degraded compound multireceiver wiretap channel. The degraded compound multireceiver wiretap channel 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 general discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multipleinput multipleoutput (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. Furthermore, 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 general 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.
Secrecy Capacity Region of the Gaussian MultiReceiver Wiretap Channel
"... Abstract — We consider the Gaussian multireceiver wiretap channel and evaluate its secrecy capacity region. This evaluation requires the identification of underlying auxiliary random variables. For this purpose, we first visit the converse proof of the scalar Gaussian broadcast channel, and show th ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
(Show Context)
Abstract — We consider the Gaussian multireceiver wiretap channel and evaluate its secrecy capacity region. This evaluation requires the identification of underlying auxiliary random variables. For this purpose, we first visit the converse proof of the scalar Gaussian broadcast channel, and show that this proof cannot be extended to this secrecy context. The failure of this extension comes from the insufficiency of the entropypower inequality to resolve the ambiguity regarding the auxiliary random variables. Instead, we provide two converse proofs. The first one uses the alternative representation of the mutual information as an integration of the minimummeansquareerror (MMSE) along with the properties of the MMSE. The second one uses the relationship between the differential entropy and the Fisher information via the de Bruin identity along with the properties of the Fisher information. I.
The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel
, 2009
"... In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wiretapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wiretapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wiretapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to nondegraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channel is not degraded. we develop an Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, We investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.
Secure Broadcasting Using Multiple Antennas
"... Abstract: We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multireceiver wiretap channels with public and confidential messages, and iii) compound wiretap channels. The BCC is a broadcast channel with two users, where ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
(Show Context)
Abstract: We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multireceiver 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 multireceiver 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 informationtheoretic results for these three forms of secure broadcasting problems, with a closer look at the Gaussian multipleinput multipleoutput (MIMO) channel models. We also present the existing results for the more general discrete memoryless channel models, as they are often the first step in obtaining the capacity results for the corresponding Gaussian MIMO channel models. Index Terms: Broadcast channels, information theoretic security, multiple antennas.
On Gaussian MIMO Compound Wiretap Channels
"... Abstract — We study the twouser oneeavesdropper discrete memoryless compound wiretap channel, where the transmitter sends a common confidential message to both users, which needs to be kept perfectly secret from the eavesdropper. We provide a new achievable secrecy rate which is shown to be potent ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract — We study the twouser oneeavesdropper discrete memoryless compound wiretap channel, where the transmitter sends a common confidential message to both users, which needs to be kept perfectly secret from the eavesdropper. We provide a new achievable secrecy rate which is shown to be potentially better than the best known lower bound for the secrecy capacity of this compound wiretap channel. We next consider the twouser oneeavesdropper Gaussian multipleinput multipleoutput (MIMO) compound wiretap channel. We obtain an achievable secrecy rate for the Gaussian MIMO compound wiretap channel by using dirtypaper coding (DPC) in the achievable scheme we provided for the discrete memoryless case. We show that the corresponding achievable secrecy rate achieves at least half of the secrecy capacity of the twouser oneeavesdropper Gaussian MIMO wiretap channel. We also obtain the secrecy capacity of the twouser oneeavesdropper Gaussian MIMO compound wiretap channel when the eavesdropper is degraded with respect to one of the two users. I.
Gaussian MIMO multireceiver wiretap channel
, 2009
"... Abstract — We consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel, and derive the secrecy capacity region of this channel for the most general case. We first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same num ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
Abstract — We consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel, and derive the secrecy capacity region of this channel for the most general case. We first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices exhibit a positive semidefinite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that a variant of dirtypaper coding with Gaussian signals is optimal. I.
Secure Degrees of Freedom of KUser Gaussian Interference Channels: A Unified View
, 2013
"... We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM), and 3) ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM), and 3) Kuser interference channel with confidential messages and one external eavesdropper (ICCMEE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K−1) 2K−1. We show converses for ICEE and ICCM, which imply a converse for ICCMEE. We show achievability for ICCMEE, which implies achievability for ICEE and ICCM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers’ observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller subspace at every receiver, in order to attain the optimum sum secure d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly.
Secrecy Capacity Region of the Degraded Compound Multireceiver Wiretap Channel
"... Abstract—We study the degraded compound multireceiver 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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We study the degraded compound multireceiver 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 multiinput multioutput (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. I.