arXiv subjects

Chandra R. Murthy

Publications and source records attributed to Chandra R. Murthy.

51 records · Page 3Linked to original sources

arXiv2016

On the Secrecy Capacity Region of the 2-user Z Interference Channel with Unidirectional Transmitter Cooperation

In this work, the role of unidirectional limited rate transmitter cooperation is studied in the case of the 2-user Z interference channel (Z-IC) with secrecy constraints at the receivers, on achieving two conflicting goals simultaneously: mitigating interference and ensuring secrecy. First, the problem is studied under the linear deterministic model. The achievable schemes for the deterministic model use a fusion of cooperative precoding and transmission of a jamming signal. The optimality of the proposed scheme is established for the deterministic model for all possible parameter settings using the outer bounds derived by the authors in a previous work. Using the insights obtained from the deterministic model, a lower bound on the secrecy capacity region of the 2-user Gaussian Z-IC are obtained. The achievable scheme in this case uses stochastic encoding in addition to cooperative precoding and transmission of a jamming signal. The secure sum generalized degrees of freedom (GDOF) is characterized and shown to be optimal for the weak/moderate interference regime. It is also shown that the secure sum capacity lies within 2 bits/s/Hz of the outer bound for the weak/moderate interference regime for all values of the capacity of the cooperative link. Interestingly, in case of the deterministic model, it is found that there is no penalty on the capacity region of the Z-IC due to the secrecy constraints at the receivers in the weak/moderate interference regimes. Similarly, it is found that there is no loss in the secure sum GDOF for the Gaussian case due to the secrecy constraint at the receiver, in the weak/moderate interference regimes. The results highlight the importance of cooperation in facilitating secure communication over the Z-IC.

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arXiv2016

Outer Bounds on the Secrecy Capacity Region of the 2-user Z Interference Channel With Unidirectional Transmitter Cooperation

This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength of interference and signal. The obtained outer bounds are shown to be tight using the achievable scheme derived by the authors in a previous work. Using the insight obtained from the deterministic model, outer bounds on the secrecy capacity region of the 2-user Gaussian Z-IC are obtained. The equivalence between the outer bounds for both the models is also established. It is also shown that secrecy constraint at the receiver does not hurt the capacity region of the 2-user Z-IC for the deterministic model in the weak/moderate interference regime. On the other hand, the outer bounds developed for the Gaussian case shows that secrecy constraint at the receiver can reduce the capacity region for the weak/moderate interference regime. The study of the relative performance of these bounds reveals insight into the fundamental limits of the 2-user Z-IC with limited rate transmitter cooperation.

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arXiv2016

On Finding a Subset of Healthy Individuals from a Large Population

In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of "non defective" items from a large population containing a small number of "defective" items. We show that a reduction in the number of tests is achievable compared to the approach of first identifying all the defective items and then picking the required number of non-defective items from the complement set. In the asymptotic regime with the population size $N \rightarrow \infty$, to identify $L$ non-defective items out of a population containing $K$ defective items, when the tests are reliable, our results show that $\frac{C_s K}{1-o(1)} (Φ(α_0, β_0) + o(1))$ measurements are sufficient, where $C_s$ is a constant independent of $N, K$ and $L$, and $Φ(α_0, β_0)$ is a bounded function of $α_0 \triangleq \lim_{N\rightarrow \infty} \frac{L}{N-K}$ and $β_0 \triangleq \lim_{N\rightarrow \infty} \frac{K} {N-K}$. Further, in the nonadaptive group testing setup, we obtain rigorous upper and lower bounds on the number of tests under both dilution and additive noise models. Our results are derived using a general sparse signal model, by virtue of which, they are also applicable to other important sparse signal based applications such as compressive sensing.

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arXiv2016

Computationally Tractable Algorithms for Finding a Subset of Non-defective Items from a Large Population

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main goal of a "non-defective subset recovery" algorithm is to identify a "subset" of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with the information theoretic lower bounds, we show that the upper bounds on the number of tests are order-wise tight up to a $\log^2K$ factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and provide further insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.

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arXiv2015

Decentralized Joint-Sparse Signal Recovery: A Sparse Bayesian Learning Approach

This work proposes a decentralized, iterative, Bayesian algorithm called CB-DSBL for in-network estimation of multiple jointly sparse vectors by a network of nodes, using noisy and underdetermined linear measurements. The proposed algorithm exploits the network wide joint sparsity of the un- known sparse vectors to recover them from significantly fewer number of local measurements compared to standalone sparse signal recovery schemes. To reduce the amount of inter-node communication and the associated overheads, the nodes exchange messages with only a small subset of their single hop neighbors. Under this communication scheme, we separately analyze the convergence of the underlying Alternating Directions Method of Multipliers (ADMM) iterations used in our proposed algorithm and establish its linear convergence rate. The findings from the convergence analysis of decentralized ADMM are used to accelerate the convergence of the proposed CB-DSBL algorithm. Using Monte Carlo simulations, we demonstrate the superior signal reconstruction as well as support recovery performance of our proposed algorithm compared to existing decentralized algorithms: DRL-1, DCOMP and DCSP.

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arXiv2013

Secrecy in the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation

This work presents novel achievable schemes for the 2-user symmetric linear deterministic interference channel with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. The proposed achievable scheme consists of a combination of interference cancelation, relaying of the other user's data bits, time sharing, and transmission of random bits, depending on the rate of the cooperative link and the relative strengths of the signal and the interference. The results show, for example, that the proposed scheme achieves the same rate as the capacity without the secrecy constraints, in the initial part of the weak interference regime. Also, sharing random bits through the cooperative link can achieve a higher secrecy rate compared to sharing data bits, in the very high interference regime. The results highlight the importance of limited transmitter cooperation in facilitating secure communications over 2-user interference channels.

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arXiv2012

Throughput Analysis of Primary and Secondary Networks in a Shared IEEE 802.11 System

In this paper, we analyze the coexistence of a primary and a secondary (cognitive) network when both networks use the IEEE 802.11 based distributed coordination function for medium access control. Specifically, we consider the problem of channel capture by a secondary network that uses spectrum sensing to determine the availability of the channel, and its impact on the primary throughput. We integrate the notion of transmission slots in Bianchi's Markov model with the physical time slots, to derive the transmission probability of the secondary network as a function of its scan duration. This is used to obtain analytical expressions for the throughput achievable by the primary and secondary networks. Our analysis considers both saturated and unsaturated networks. By performing a numerical search, the secondary network parameters are selected to maximize its throughput for a given level of protection of the primary network throughput. The theoretical expressions are validated using extensive simulations carried out in the Network Simulator 2. Our results provide critical insights into the performance and robustness of different schemes for medium access by the secondary network. In particular, we find that the channel captures by the secondary network does not significantly impact the primary throughput, and that simply increasing the secondary contention window size is only marginally inferior to silent-period based methods in terms of its throughput performance.

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arXiv2012

On Whitespace Identification Using Randomly Deployed Sensors

This work considers the identification of the available whitespace, i.e., the regions that are not covered by any of the existing transmitters, within a given geographical area. To this end, $n$ sensors are deployed at random locations within the area. These sensors detect for the presence of a transmitter within their radio range $r_s$, and their individual decisions are combined to estimate the available whitespace. The limiting behavior of the recovered whitespace as a function of $n$ and $r_s$ is analyzed. It is shown that both the fraction of the available whitespace that the nodes fail to recover as well as their radio range both optimally scale as $\log(n)/n$ as $n$ gets large. The analysis is extended to the case of unreliable sensors, and it is shown that, surprisingly, the optimal scaling is still $\log(n)/n$ even in this case. A related problem of estimating the number of transmitters and their locations is also analyzed, with the sum absolute error in localization as performance metric. The optimal scaling of the radio range and the necessary minimum transmitter separation is determined, that ensure that the sum absolute error in transmitter localization is minimized, with high probability, as $n$ gets large. Finally, the optimal distribution of sensor deployment is determined, given the distribution of the transmitters, and the resulting performance benefit is characterized.

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arXiv2012

On the DMT of TDD-SIMO Systems with Channel-Dependent Reverse Channel Training

This paper investigates the Diversity-Multiplexing gain Trade-off (DMT) of a training based reciprocal Single Input Multiple Output (SIMO) system, with (i) perfect Channel State Information (CSI) at the Receiver (CSIR) and noisy CSI at the Transmitter (CSIT), and (ii) noisy CSIR and noisy CSIT. In both the cases, the CSIT is acquired through Reverse Channel Training (RCT), i.e., by sending a training sequence from the receiver to the transmitter. A channel-dependent fixed-power training scheme is proposed for acquiring CSIT, along with a forward-link data transmit power control scheme. With perfect CSIR, the proposed scheme is shown to achieve a diversity order that is quadratically increasing with the number of receive antennas. This is in contrast with conventional orthogonal RCT schemes, where the diversity order is known to saturate as the number of receive antennas is increased, for a given channel coherence time. Moreover, the proposed scheme can achieve a larger DMT compared to the orthogonal training scheme. With noisy CSIR and noisy CSIT, a three-way training scheme is proposed and its DMT performance is analyzed. It is shown that nearly the same diversity order is achievable as in the perfect CSIR case. The time-overhead in the training schemes is explicitly accounted for in this work, and the results show that the proposed channel-dependent RCT and data power control schemes offer a significant improvement in terms of the DMT, compared to channel-agnostic orthogonal RCT schemes. The outage performance of the proposed scheme is illustrated through Monte-Carlo simulations.

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arXiv2012

Cramer Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-t prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. It is found that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. Through simulations, we demonstrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.

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arXiv2012

On the Generalized Degrees of Freedom of the K-user Symmetric MIMO Gaussian Interference Channel

The K-user symmetric multiple input multiple output (MIMO) Gaussian interference channel (IC) where each transmitter has M antennas and each receiver has N antennas is studied from a generalized degrees of freedom (GDOF) perspective. An inner bound on the GDOF is derived using a combination of techniques such as treating interference as noise, zero forcing (ZF) at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, as a function of the number of antennas and the log (INR) / log (SNR) level. Three outer bounds are derived, under different assumptions of cooperation and providing side information to receivers. The novelty in the derivation lies in the careful selection of side information, which results in the cancellation of the negative differential entropy terms containing signal components, leading to a tractable outer bound. The overall outer bound is obtained by taking the minimum of the three outer bounds. The derived bounds are simplified for the MIMO Gaussian symmetric IC to obtain outer bounds on the generalized degrees of freedom (GDOF). Several interesting conclusions are drawn from the derived bounds. For example, when K > N/M + 1, a combination of the HK and IA schemes performs the best among the schemes considered. When N/M < K <= N/M + 1, the HK-scheme outperforms other schemes and is shown to be GDOF optimal. In addition, when the SNR and INR are at the same level, ZF-receiving and the HK-scheme have the same GDOF performance. It is also shown that many of the existing results on the GDOF of the Gaussian IC can be obtained as special cases of the bounds, e.g., by setting K=2 or the number of antennas at each user to 1.

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arXiv2012

Capacity Bounds for State-Dependent Broadcast Channels

In this paper, we derive information-theoretic performance limits for three classes of two-user state-dependent discrete memoryless broadcast channels, with noncausal side-information at the encoder. The first class of channels comprises a sender broadcasting two independent messages to two non-cooperating receivers; for channels of the second class, each receiver is given the message it need not decode; and the third class comprises channels where the sender is constrained to keep each message confidential from the unintended receiver. We derive inner bounds for all the three classes of channels. For the first and second class of channels, we discuss the rate penalty on the achievable region for having to deal with side-information. For channels of third class, we characterize the rate penalties for having to deal not only with side-information, but also to satisfy confidentiality constraints. We then derive outer bounds, where we present an explicit characterization of sum-rate bounds for the first and third class of channels. For channels of the second class, we show that our outer bounds are within a fixed gap away from the achievable rate region, where the gap is independent of the distribution characterizing this class of channels. The channel models presented in this paper are useful variants of the classical broadcast channel, and provide fundamental building blocks for cellular downlink communications with side-information, such as fading in the wireless medium, interference caused by neighboring nodes in the network, {\etc}. at the encoder; two-way relay communications; and secure wireless broadcasting.

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arXiv2011

Asymmetric Transmitter Cooperation in Multiuser Wireless Networks: Achievable Rate Regions

In this work, we derive achievable rate regions for the three-user interference channels with asymmetric transmitter cooperation and various decoding capabilities at the receivers. The three-user channel facilitates different ways of message sharing between the transmitters. We introduce two natural ways of extending the concept of unidirectional message sharing from two users to three users - (i) cumulative message sharing and (ii) primary-only message sharing. In addition, we define several cognitive interference channels based on the decoding capability of the receivers. We employ a coding technique, which is a combination of superposition and Gel'fand-Pinsker coding techniques, to derive an achievable rate region for each of the cognitive interference channels. Simulation results, by considering the Gaussian channel case, enables a visual comparison of the two message-sharing schemes considered in this paper. It also provides useful insights into the effect of message-splitting at the transmitters and the decoding capability of the receivers on the achievable rates.

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arXiv2011

Multiuser Cognitive Radio Networks: An Information Theoretic Perspective

Achievable rate regions and outer bounds are derived for three-user interference channels where the transmitters cooperate in a unidirectional manner via a noncausal message-sharing mechanism. The three-user channel facilitates different ways of message-sharing between the primary and secondary (or cognitive) transmitters. Three natural extensions of unidirectional message-sharing from two users to three users are introduced: (i) Cumulative message sharing; (ii) primary-only message sharing; and (iii) cognitive-only message sharing. To emphasize the notion of interference management, channels are classified based on different rate-splitting strategies at the transmitters. Standard techniques, superposition coding and Gel'fand-Pinsker's binning principle, are employed to derive an achievable rate region for each of the cognitive interference channels. Simulation results for the Gaussian channel case are presented; they enable visual comparison of the achievable rate regions for different message-sharing schemes along with the outer bounds. These results also provide useful insights into the effect of rate-splitting at the transmitters, which aids in better interference management at the receivers.

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arXiv2010

Cooperative Sequential Spectrum Sensing Algorithms for OFDM

This paper considers the problem of spectrum sensing in cognitive radio networks when the primary user employs Orthogonal Frequency Division Multiplexing (OFDM). We develop cooperative sequential detection algorithms based on energy detectors and the autocorrelation property of cyclic prefix (CP) used in OFDM systems and compare their performances. We show that sequential detection provides much better performance than the traditional fixed sample size (snapshot) based detectors. We also study the effect of model uncertainties such as timing and frequency offset, IQ-imbalance and uncertainty in noise and transmit power on the performance of the detectors. We modify the detectors to mitigate the effects of these impairments. The performance of the proposed algorithms are studied via simulations. It is shown that energy detector performs significantly better than the CP-based detector, except in case of a snapshot detector with noise power uncertainty. Also, unlike for the CP-based detector, most of the above mentioned impairments have no effect on the energy detector.

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