arXiv subjects

Sennur Ulukus

Publications and source records attributed to Sennur Ulukus.

323 records · Page 18Linked to original sources

arXiv2010

An Alternative Proof for the Capacity Region of the Degraded Gaussian MIMO Broadcast Channel

We provide an alternative proof for the capacity region of the degraded Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof does not use the channel enhancement technique as opposed to the original proof of Weingertan {\it et. al.} and the alternative proof of Liu {\it et. al}. Our proof starts with the single-letter description of the capacity region of the degraded broadcast channel, and directly evaluates it for the degraded Gaussian MIMO broadcast channel by using two main technical tools. The first one is the generalized de Bruijn identity due to Palomar \emph{et. al.} which provides a connection between the differential entropy and the Fisher information matrix. The second tool we use is an inequality due to Dembo which lower bounds the differential entropy in terms of the Fisher information matrix.

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arXiv2010

Gaussian MIMO Broadcast Channels with Common and Confidential Messages

We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user which is kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between the capacity region we obtained for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private messages, which is not known completely.

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arXiv2009

Degraded Compound Multi-receiver Wiretap Channels

In this paper, we study the degraded compound multi-receiver wiretap channel. The degraded compound multi-receiver 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 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. 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.

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arXiv2009

The Secrecy Capacity Region of the Gaussian MIMO Multi-receiver Wiretap Channel

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver 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 single-input single-output (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 minimum-mean-square-error 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 semi-definite 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 dirty-paper coding with Gaussian signals.

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arXiv2008

Dependence Balance Based Outer Bounds for Gaussian Networks with Cooperation and Feedback

We obtain new outer bounds on the capacity regions of the two-user multiple access channel with generalized feedback (MAC-GF) and the two-user interference channel with generalized feedback (IC-GF). These outer bounds are based on the idea of dependence balance which was proposed by Hekstra and Willems [1]. To illustrate the usefulness of our outer bounds, we investigate three different channel models. We first consider a Gaussian MAC with noisy feedback (MAC-NF), where transmitter $k$, $k=1,2$, receives a feedback $Y_{F_{k}}$, which is the channel output $Y$ corrupted with additive white Gaussian noise $Z_{k}$. As the feedback noise variances become large, one would expect the feedback to become useless, which is not reflected by the cut-set bound. We demonstrate that our outer bound improves upon the cut-set bound for all non-zero values of the feedback noise variances. Moreover, in the limit as $σ_{Z_{k}}^{2}\to \infty$, $k=1,2$, our outer bound collapses to the capacity region of the Gaussian MAC without feedback. Secondly, we investigate a Gaussian MAC with user-cooperation (MAC-UC), where each transmitter receives an additive white Gaussian noise corrupted version of the channel input of the other transmitter [2]. For this channel model, the cut-set bound is sensitive to the cooperation noises, but not sensitive enough. For all non-zero values of cooperation noise variances, our outer bound strictly improves upon the cut-set outer bound. Thirdly, we investigate a Gaussian IC with user-cooperation (IC-UC). For this channel model, the cut-set bound is again sensitive to cooperation noise variances but not sensitive enough. We demonstrate that our outer bound strictly improves upon the cut-set bound for all non-zero values of cooperation noise variances.

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arXiv2008

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. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver 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 multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.

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arXiv2008

A New Upper Bound on the Capacity of a Class of Primitive Relay Channels

We obtain a new upper bound on the capacity of a class of discrete memoryless relay channels. For this class of relay channels, the relay observes an i.i.d. sequence $T$, which is independent of the channel input $X$. The channel is described by a set of probability transition functions $p(y|x,t)$ for all $(x,t,y)\in \mathcal{X}\times \mathcal{T}\times \mathcal{Y}$. Furthermore, a noiseless link of finite capacity $R_{0}$ exists from the relay to the receiver. Although the capacity for these channels is not known in general, the capacity of a subclass of these channels, namely when $T=g(X,Y)$, for some deterministic function $g$, was obtained in [1] and it was shown to be equal to the cut-set bound. Another instance where the capacity was obtained was in [2], where the channel output $Y$ can be written as $Y=X\oplus Z$, where $\oplus$ denotes modulo-$m$ addition, $Z$ is independent of $X$, $|\mathcal{X}|=|\mathcal{Y}|=m$, and $T$ is some stochastic function of $Z$. The compress-and-forward (CAF) achievability scheme [3] was shown to be capacity achieving in both cases. Using our upper bound we recover the capacity results of [1] and [2]. We also obtain the capacity of a class of channels which does not fall into either of the classes studied in [1] and [2]. For this class of channels, CAF scheme is shown to be optimal but capacity is strictly less than the cut-set bound for certain values of $R_{0}$. We also evaluate our outer bound for a particular relay channel with binary multiplicative states and binary additive noise for which the channel is given as $Y=TX+N$. We show that our upper bound is strictly better than the cut-set upper bound for certain values of $R_{0}$ but it lies strictly above the rates yielded by the CAF achievability scheme.

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arXiv2008

Capacity of a Class of Diamond Channels

We study a special class of diamond channels which was introduced by Schein in 2001. In this special class, each diamond channel consists of a transmitter, a noisy relay, a noiseless relay and a receiver. We prove the capacity of this class of diamond channels by providing an achievable scheme and a converse. The capacity we show is strictly smaller than the cut-set bound. Our result also shows the optimality of a combination of decode-and-forward (DAF) and compress-and-forward (CAF) at the noisy relay node. This is the first example where a combination of DAF and CAF is shown to be capacity achieving. Finally, we note that there exists a duality between this diamond channel coding problem and the Kaspi-Berger source coding problem.

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arXiv2008

Outer Bounds for Multiple Access Channels with Feedback using Dependence Balance

We use the idea of dependence balance to obtain a new outer bound for the capacity region of the discrete memoryless multiple access channel with noiseless feedback (MAC-FB). We consider a binary additive noisy MAC-FB whose feedback capacity is not known. The binary additive noisy MAC considered in this paper can be viewed as the discrete counterpart of the Gaussian MAC-FB. Ozarow established that the capacity region of the two-user Gaussian MAC-FB is given by the cut-set bound. Our result shows that for the discrete version of the channel considered by Ozarow, this is not the case. Direct evaluation of our outer bound is intractable due to an involved auxiliary random variable whose large cardinality prohibits an exhaustive search. We overcome this difficulty by using functional analysis to explicitly evaluate our outer bound. Our outer bound is strictly less than the cut-set bound at all points on the capacity region where feedback increases capacity. In addition, we explicitly evaluate the Cover-Leung achievable rate region for the binary additive noisy MAC-FB in consideration. Furthermore, using the tools developed for the evaluation of our outer bound, we also explicitly characterize the boundary of the feedback capacity region of the binary erasure MAC, for which the Cover-Leung achievable rate region is known to be tight. This last result confirms that the feedback strategies developed by Kramer for the binary erasure MAC are capacity achieving.

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arXiv2007

A New Achievability Scheme for the Relay Channel

In this paper, we propose a new coding scheme for the general relay channel. This coding scheme is in the form of a block Markov code. The transmitter uses a superposition Markov code. The relay compresses the received signal and maps the compressed version of the received signal into a codeword conditioned on the codeword of the previous block. The receiver performs joint decoding after it has received all of the B blocks. We show that this coding scheme can be viewed as a generalization of the well-known Compress-And-Forward (CAF) scheme proposed by Cover and El Gamal. Our coding scheme provides options for preserving the correlation between the channel inputs of the transmitter and the relay, which is not possible in the CAF scheme. Thus, our proposed scheme may potentially yield a larger achievable rate than the CAF scheme.

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arXiv2007

Towards the Secrecy Capacity of the Gaussian MIMO Wire-tap Channel: The 2-2-1 Channel

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.

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arXiv2006

Dense Gaussian Sensor Networks: Minimum Achievable Distortion and the Order Optimality of Separation

We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those measurement samples to a collector node in a cooperative multiple access channel with potential feedback, and reconstruct the entire random process at the collector node. We provide lower and upper bounds for the minimum achievable expected distortion when the underlying random process is Gaussian. When the Gaussian random process satisfies some general conditions, we evaluate the lower and upper bounds explicitly, and show that they are of the same order for a wide range of power constraints. Thus, for these random processes, under these power constraints, we express the minimum achievable expected distortion as a function of the power constraint. Further, we show that the achievability scheme that achieves the lower bound on the distortion is a separation-based scheme that is composed of multi-terminal rate-distortion coding and amplify-and-forward channel coding. Therefore, we conclude that separation is order-optimal for the dense Gaussian sensor network scenario under consideration, when the underlying random process satisfies some general conditions.

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arXiv2006

The Capacity Region of a Class of Discrete Degraded Interference Channels

We provide a single-letter characterization for the capacity region of a class of discrete degraded interference channels (DDICs). The class of DDICs considered includes the discrete additive degraded interference channel (DADIC) studied by Benzel. We show that for the class of DDICs studied, encoder cooperation does not increase the capacity region, and therefore, the capacity region of the class of DDICs is the same as the capacity region of the corresponding degraded broadcast channel.

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arXiv2006

Optimal Distortion-Power Tradeoffs in Gaussian Sensor Networks

We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those measurement samples to a collector node in a cooperative multiple access channel with imperfect feedback, and reconstruct the entire random process at the collector node. We provide lower and upper bounds for the minimum achievable expected distortion when the underlying random process is Gaussian. In the case where the random process satisfies some general conditions, we evaluate the lower and upper bounds explicitly and show that they are of the same order for a wide range of sum power constraints. Thus, for these random processes, under these sum power constraints, we determine the achievability scheme that is order-optimal, and express the minimum achievable expected distortion as a function of the sum power constraint.

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arXiv2006

Optimal Distortion-Power Tradeoffs in Sensor Networks: Gauss-Markov Random Processes

We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those measurement samples to a collector node in a cooperative multiple access channel with feedback, and reconstruct the entire random process at the collector node. We provide lower and upper bounds for the minimum achievable expected distortion when the underlying random process is stationary and Gaussian. In the case where the random process is also Markovian, we evaluate the lower and upper bounds explicitly and show that they are of the same order for a wide range of sum power constraints. Thus, for a Gauss-Markov random process, under these sum power constraints, we determine the achievability scheme that is order-optimal, and express the minimum achievable expected distortion as a function of the sum power constraint.

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arXiv2006

Power Control for User Cooperation

For a fading Gaussian multiple access channel with user cooperation, we obtain the optimal power allocation policies that maximize the rates achievable by block Markov superposition coding. The optimal policies result in a coding scheme that is simpler than the one for a general multiple access channel with generalized feedback. This simpler coding scheme also leads to the possibility of formulating an otherwise non-concave optimization problem as a concave one. Using the channel state information at the transmitters to adapt the powers, we demonstrate significant gains over the achievable rates for existing cooperative systems.

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arXiv2006

Mutual Information Games in Multi-user Channels with Correlated Jamming

We investigate the behavior of two users and one jammer in an AWGN channel with and without fading when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. Under various assumptions on the channel characteristics, and the extent of information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer. In all the cases where the channel is non-fading, we show that the game has a solution, and the optimal strategies are Gaussian signalling for the users and linear jamming for the jammer. In fading channels, we envision each player's strategy as a power allocation function over the channel states, together with the signalling strategies at each channel state. We reduce the game solution to a set of power allocation functions for the players and show that when the jammer is uncorrelated, the game has a solution, but when the jammer is correlated, a set of simultaneously optimal power allocation functions for the users and the jammer does not always exist. In this case, we characterize the max-min user power allocation strategies and the corresponding jammer power allocation strategy.

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