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In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, multi-access channel where $K$ active users (out of a total of $N$ users) seek to access. A solution to the partition problem places each of the $N$ users in one of $K$ groups (or blocks) such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative case of $K=2$ active users and study the number of steps $T$ used to solve the partition problem. By random coding and a suboptimal decoding scheme, we show that for any $T\geq (C_1 +\xi_1)\log N$, where $C_1$ and $\xi_1$ are positive constants (independent of $N$), and $\xi_1$ can be arbitrary small, the partition problem can be solved with error probability $P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from the other direction, establishing that, for any $T \leq (C_2 - \xi_2) \log N$, the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $\xi_2$ are constants and $\xi_2$ can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower-bound in terms of $T \geq (C_g +\xi)\log N $ for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing., Comment: This paper was submitted in June 2014 to IEEE Transactions on Information Theory, and is under review now

The rise of wireless rechargeable sensor networks calls for an analytical study of planned charging trips of wireless charging vehicles (WCVs). Often times, the WCV receives a number of charging requests and form a Hamiltonian cycle and visit these nodes one-by-one. Therefore, it is important to learn the statistics of such cycles. In this work, we use a heuristic algorithm, which we term HQuad, that takes O(N) to generate a Hamiltonian cycle in a 2-D network plane before we analyze its statistics. HQuad is based on a recursive approximation of dividing the region into four quadrants and the non-empty quadrants will be visited one-by-one. Our analysis is based on Poisson point distribution of nodes and models such Hamiltonian cycles surprisingly well in both expected values and the distribution functions of lengths as a function of different network parameters. Numerical results of our analysis model are compared with simulations and demonstrated to be accurate.

In this paper, we propose a novel formulation to understand the tradeoff between binning utility and meta information leakage when we face the problems of partitioning random items. As an example, such problems could emerge when online users attempt to protect their browsing behavior patterns to certain extent by resorting to multiple proxy websites. Under the framework, we formulate a constrained optimization problem where the goal is to maximize binning utility while restraining a certain level of information leakage by properly dividing a set of $M$ random items into $N$ bins. By doing so, we formulate a new multi-agent multivariate optimization problem which is NP-complicated. We then utilize the submodular nature of the problem to find sufficient conditions to (1) secure the existence of a solution to our problem; (2) lower the complexity of the problem at the cost of accuracy. To do so, we exploit the dual nature of set functions in multi-agent multi-variate problems, a novel addition to the field. After proving sufficient conditions to secure the existence of a solution in more general cases, we offer algorithms and complexity orders to solve a simplified version of the problem where $N=2$ which helps signify the use of submodular properties.

Radio Frequency IDentification (RFID) systems are prevalent in all sorts of daily life endeavors. Most previous tag estimation schemes worked with relatively smaller frame size and large number of rounds. Here we propose a new estimator named \textquotedblleft Gaussian Estimator of RFID Tags,\textquotedblright (GERT), that works with large enough frame size to be accurately approximated to Gaussian distribution within a frame. The selection of the frame size is done according to Triangular Array Central Limit Theorem which also enables us to quantify the approximation error. Larger frame size helps the statistical average to converge faster to the ensemble mean of the estimator and the quantification of the approximation error helps to determine the number of rounds to keep up with the accuracy requirements. The overall performance of GERT is better than the previously proposed schemes considering the number of slots required for estimation to achieve a given level of estimation accuracy.

We propose a mixture-Gaussian model for a cognitive radio channel to analyze the interplay between the interference in the system and the degrees-of-freedom (DOF), i.e., the average number of channel uses per transmission frame, used by the secondary user (SU) for communications in the long run. In contrast to the conventional studies, we assume that the SU receiver (SU-RX) does not precisely know whether the primary-user (PU) transmitter is on or off. Due to this assumption the resulting interference channel is mixture-Gaussian. Our objective is to find the optimal sensing threshold and sensing time for the signal detector used by the SU transmitter (SU-TX). Our formulation of the optimization problem reflects the trade-off between SU-TX’s DOF for communications and that for detection. Both the DOFs affect PU’s interference to SU, and SU’s interference to PU. The latter interference causes PU performance degradation, which is kept within tolerable range as a constraint. As a further contribution, we define interference regimes for SU performance on the basis of PU transmission power level. We also address the scenario when PU receiver uses the nearest neighbor decoding while wrongly anticipating that the channel is Gaussian. Finally, we demonstrate that even if SU-TX’s signal detector performs suboptimally, SU can still achieve the optimal detector’s performance in the high interference regime by adjusting the sensing parameters.

We study the optimal control of both admission and preemption in a two-class finite source loss system, and prove that the optimal low priority (LP) job admission policy is a state dependent threshold based policy. We also provide the sufficient cost conditions for which the LP job admission and preemption are always optimal. Finally, we demonstrate that the optimal LP job preemption policy is a threshold based policy, using numerical results.

In this paper, we propose a novel partition reservation system to study the partition information and its transmission over a noise-free Boolean multi-access channel. The objective of transmission is not message restoration, but to partition active users into distinct groups so that they can, subsequently, transmit their messages without collision. We first calculate (by mutual information) the amount of information needed for the partitioning without channel effects, and then propose two different coding schemes to obtain achievable transmission rates over the channel. The first one is the brute force method, where the codebook design is based on centralized source coding; the second method uses random coding where the codebook is generated randomly and optimal Bayesian decoding is employed to reconstruct the partition. Both methods shed light on the internal structure of the partition problem. A novel hypergraph formulation is proposed for the random coding scheme, which intuitively describes the information in terms of a strong coloring of a hypergraph induced by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple, but non-trivial, case with two active users. A comparison between these methods and group testing is conducted to demonstrate the uniqueness of our problem., Comment: Submitted to IEEE Transactions on Information Theory, major revision

Secret key establishment from common randomness has been traditionally investigated under cartain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated random variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In this paper, we derive a computationally-efficient asymptotic converse bound for the secret key capacity of the correlated-HMM scenario. The main obstacle, not only for our model, but also for other non-i.i.d cases, is the computational complexity. We address this by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent. The methods developed in the paper are easily extensible to derive a secret-key capacity lower bound.

In this paper, we want to find out the determining factors of Chernoff information in distinguishing a set of Gaussian graphs. We find that Chernoff information of two Gaussian graphs can be determined by the generalized eigenvalues of their covariance matrices. We find that the unit generalized eigenvalue doesn't affect Chernoff information and its corresponding dimension doesn't provide information for classification purpose. In addition, we can provide a partial ordering using Chernoff information between a series of Gaussian trees connected by independent grafting operations. With the relationship between generalized eigenvalues and Chernoff information, we can do optimal linear dimension reduction with least loss of information for classification., Comment: Submitted to Allerton2018, and this version contains proofs of the propositions in the paper

This paper focuses on the problem of sharing secret keys using Automatic Repeat reQuest (ARQ) protocol. We consider cases where forward and feedback channels are erasure channels for a legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, the wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmissions that is mapped into a destination set using a first-order digital filter with feedback. Then, we characterize Eve's information loss about this shared destination set, due to inevitable transmission errors. This set is then transformed into a highly secure key using privacy amplification in order to intensify and exploit Eve's lack of knowledge. We adopt two criteria for analysis and design of the system: secrecy outage probability as a measure of the secrecy quality, and secret key rate as a metric for efficiency. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than legitimate receivers, and her channel conditions are unknown to legitimate users.

awareness of their environment and internal state, fulfills the need of dynamic spectrum access for higher spectrum utilization. However, at the same time, the use of cognitive radios further complicates the security problems in wireless networks and introduces additional challenges for a counter measure. Due to the intelligence of the attackers, many of the attacks may be stealthy by nature, such as the anomalous spectrum usage attacks, which usually cannot be detected only using information from one layer of the protocol stack. In this paper, we propose a crosslayer model for anomalous spectrum usage attacks detection with stealthy jammer as a prime example. Quickest detection technique is adopted and embedded in the proposed framework since the attacks usually happen at unknown time and are unpredictable due to the lack of prior knowledge of the attackers. A case study is performed by combining physical layer spectrum sensing with multipath routing at the network layer. The results demonstrate the effectiveness of the proposed approach.

In this paper, our objective is to find out the determining factors of Chernoff information in distinguishing a set of Gaussian trees. In this set, each tree can be attained via an edge removal and grafting operation from another tree. This is equivalent to asking for the Chernoff information between the most-likely confused, i.e. "bottleneck", Gaussian trees, as shown to be the case in ML estimated Gaussian tree graphs lately. We prove that the Chernoff information between two Gaussian trees related through an edge removal and a grafting operation is the same as that between two three-node Gaussian trees, whose topologies and edge weights are subject to the underlying graph operation. In addition, such Chernoff information is shown to be determined only by the maximum generalized eigenvalue of the two Gaussian covariance matrices. The Chernoff information of scalar Gaussian variables as a result of linear transformation (LT) of the original Gaussian vectors is also uniquely determined by the same maximum generalized eigenvalue. What is even more interesting is that after incorporating the cost of measurements into a normalized Chernoff information, Gaussian variables from LT have larger normalized Chernoff information than the one based on the original Gaussian vectors, as shown in our proved bounds, Submitted to ISIT2016, and this version contains proofs of the propositions in the paper

In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: First, we quantify the amount of information loss due to unrecoverable sign information. Second, we show the importance of such information in determining the maximum achievable rate region, in which the observed output vector can be synthesized, given its probability density function. In particular, we model the graphical model as a communication channel and propose a new layered encoding framework to synthesize observed data using upper layer Gaussian inputs and independent Bernoulli correlation sign inputs from each layer. We find the achievable rate region for the rate tuples of multi-layer latent Gaussian messages to synthesize the desired observables., 14 pages, 9 figures, part of this work is submitted to Allerton 2016 conference, UIUC, IL, USA

In this paper, we study the problem of half-duplex active eavesdropping in fast-fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode)-the active eavesdropper cannot function in full duplex mode. We consider a conservative scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair's strategy, and thus, the transmitter and legitimate receiver have to plan for the worst. We show that conventional physical-layer secrecy approaches perform poorly (if at all), and we introduce a novel encoding scheme, based on very limited and unsecured feedback-the Block-Markov Wyner encoding scheme-which outperforms any schemes currently available.

Consider a parallel channel with M independent flat-fading subchannels. There exists a smart jammer which has possession of a copy of perfect channel state information (CSI) measured and sent back by a receiver to its transmitter. Under this model, a class of two-person zero-sum games is investigated where either achievable mutual information rate or Chernoff bound is taken as the underlying pay-off function with the strategy space of each player determined by respective power control and hopping functions. More specifically, we have tackled and answered the following three fundamental questions. The first one is about whether the transmitter and jammer should hop or fully use all degrees of freedom over the entire parallel channels given the full CSI available to both of them, i.e. to hop or not to hop. The second question is about the impact of sending back CSI on system performance considering that the smart jammer can exploit CSI to further enhance its interference effects, i.e. to feedback or not to feedback. The last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer, i.e. when to feedback and when not to.

We consider a constrained energy optimization called minimum energy scheduling problem (MESP) for a wireless network of N users transmitting over M time slots, where the constraints arise because of interference between wireless nodes that limits their transmission rates along with load and duty-cycle (on-off) restrictions. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the nonconvex constraints, we consider approximation schemes for finding the optimal (minimum energy) transmission schedule by discretizing power levels over the interference channel. First, we show the toughness of approximating MESP for an arbitrary number of users N even with a fixed M. For any r > 0, we demonstrate that there does not exist any (r, r)-bicriteria approximation for this MESP, unless P = NP . Conversely, we show that there exist good approximations for MESP with given N users transmitting over an arbitrary number of M time slots by developing fully polynomial (1,1+?) approximation schemes (FPAS). For any ? > 0, we develop an algorithm for computing the optimal number of discrete power levels per time slot (O(1/?)), and use this to design a (1, 1+?)-FPAS that consumes no more energy than the optimal while violating each rate constraint by at most a 1+?-factor. For wireless networks with low-cost transmitters, where nodes are restricted to transmitting at a fixed power over active time slots, we develop a two-factor approximation for finding the optimal fixed transmission power value P opt that results in the minimum energy schedule.

In this paper, we propose a novel model to study the efficiency of detecting latent connection relationships, represented by a given set of graphs, among N users. A subset of active nodes transmit following a common codebook over a multiple access Boolean channel. To maximize the error exponent of the structure detection, we formulate an optimization problem whose objective is to max-minimize the pairwise Chernoff information, and the constraint is a probability simplex due to the users' multiple dependency relationships, which are further shown to have close relationship to the internal connectivity of graphs. Case studies are provided to show certain inherent properties of the optimal solution. In addition, we present a particular case with two equally weighted complementary Paley graphs of prime square order, whose optimal solution for the codebook is proved and the resulting exponent is shown to be O(1/N). The case study demonstrates how the fundamental graph discrepancy property affects the solution to the problem.

We present a novel model for multiple access systems that jointly models the access-control and communication layers. This model helps us jointly quantify both the collision loss at the control layer and congestion loss at the communication layer. A joint quantification of both losses is necessary because the performance of one layer directly impacts that of the other one, and thus, both these layers are inseparable. However, the conventional theoretical models quantify the collision and congestion losses separately, thereby unable to capture the coupling issues in networks with finite sources' constraint. Under our proposed framework, we further optimize the number of control and communication channels in order to minimize the joint total loss rate given a constraint on the total number of available channels. The corresponding optimization results are further visualized using our proposed channel allocation map under all possible traffic parameters needed in the considered system model.

Extensive works have been undertaken to develop efficient statistical inference algorithms based on graphical models. However, there still lacks sufficient understanding about how topological properties affect certain information related metrics for certain graphs. In this paper, we are particularly interested in finding out how topological properties of rooted polytrees for Gaussian random variables determine its security robustness, which is measured by our proposed max-min information (MaMI) metric. MaMI is defined as the maximin value of the conditional mutual information between any two random variables (nodes) in a given DAG, conditioned on the value of a third random variable, which is at full disposal of an eavesdropper, under a constraint of a given fixed joint entropy. We show some general topological properties which the desired max-min solutions satisfy. Under such properties, we prove the superior max-min feature of the linear topology for a simple but non-trivial case. The results not only help us understand the security strength of different rooted polytree type DAGs, which is critical when we evaluate the information leakage issues for various jointly Gaussian distributed measurements in networks, but also provide us another algebraic and analysis perspective in grasping some fundamental properties of such DAGs.

Public safety communication systems are implemented as trunked mobile radio systems. The finite-source queueing model, i.e., the Engset model, has been suggested as the appropriate model in literature for these systems. In this paper, we present the analytical framework and characteristics of the optimal call admission and preemption control for such systems. We consider two classes of users, namely, of high and low priority. We show that the optimal low priority (LP) call admission policy is a state dependent threshold based policy. We also demonstrate that the optimal LP call preemption policy is a threshold based policy.

Cooperative diversity, which employs multiple nodes for the simultaneous relaying of a given packet in wireless ad hoc networks, has been shown to be an effective means of improving diversity, and, hence, mitigating the detrimental effects of multipath fading. However, in previously proposed cooperative diversity schemes, it has been assumed that coordination among the relays allows for accurate symbol-level timing synchronization at the destination and orthogonal channel allocation, which can be quite costly in terms of signaling overhead in mobile ad hoc networks, which are often defined by their lack of a fixed infrastructure and the difficulty of centralized control. In this paper, cooperative diversity schemes are considered that do not require symbol-level timing synchronization or orthogonal channelization between the relays employed. In the process, a novel minimum mean-squared error (MMSE) receiver is designed for combining disparate inputs in the multiple-relay channel. Outage probability calculations and simulation results demonstrate the not unexpected significant performance gains of the proposed schemes over single-hop transmission, and, more importantly, demonstrate performance comparable to schemes requiring accurate symbol-level synchronization and orthogonal channelization

Impulsive ultra-wideband (UWB) radio provides many promising features for wireless communications in a dense multipath environment. However, these features are largely the result of the enormous effective processing gain, which can make acquisition difficult at the receiver. In this paper, a recently developed theory of minimum complexity sequential detection is applied to the hybrid acquisition problem. As in previous hybrid schemes, a number of potential timing phases are checked as a group; however, a phase is disregarded as soon as it appears unlikely rather than waiting for a "winner" to be chosen from the group. Another phase then replaces the disregarded one. Analysis and simulation results indicate that the proposed scheme can improve average acquisition times for highly spread systems operating over either additive white Gaussian noise (AWGN) or multipath fading channels.

We present a novel formulation of the problem of energy misbehavior and develop an analytical framework for quantifying its impact on other nodes. Specifically, we formulate two versions of the power control problem for wireless sensor networks with latency constraints arising from duty cycle allocations. In the first version, strategic power optimization, nodes are modeled as rational agents in a power game, who strategically adjust their powers to minimize their own energy. In the other version, joint power optimization, sensor nodes adjust their transmission powers to minimize the aggregate energy expenditure. Our analysis of these models yields insight into the different energy outcomes of strategic versus joint power optimization. We show that while joint power optimization fits the accepted paradigm of cooperation among sensor nodes (for example large number of sensor nodes cooperating for a task such as target tracking), it comes with both advantages and disadvantages when energy misbehavior is taken into account. One advantage is that it can (sometimes) be energy-dominant, i.e., the optimal energy cost for each node under joint energy minimization is lower than its strategically optimal energy cost. We then develop a model for characterizing energy misbehavior and show that joint optimization is disadvantageous because it is impossible to prevent misbehavior under any channel quality and load constraints, whereas strategic optimization is more resilient. We prove that it is impossible for a node to unilaterally and undetectably follow a different energy optimization strategy than the other nodes and hence the only threat to the network is misbehavior through false advertisement. We then provide sufficient conditions under which misbehavior through false advertisement can be prevented under a strategic optimization regime. Our analytical results reveal optimal strategies for attacking nodes in an enemy network through energy depletion and help develop effective defense mechanisms for protecting our own wireless network against energy attacks by an intelligent adversary.

Due to the huge popularity of online social networks, many researchers focus on adding links, e.g., link prediction to help friend recommendation. So far, no research has been performed on link cuts. However, the spread of malware and misinformation can cause havoc and hence it is interesting to see how to cut links such that malware and misinformation will not run rampant. In fact, many online social networks can be modeled as undirected graphs. In this paper, we investigate different strategies to cut links among different users in undirected graphs so that the speed of virus and misinformation spread can be slowed down the most or even cut off. Two measures are chosen to evaluate the performance of these strategies: Average Inverse of Shortest Path Length (AIPL) and Rumor Saturation Rate (RSR). AIPL measures the communication efficiency of the whole graph while RSR checks the percentage of users receiving information within a certain time interval.

In this paper, our objective is to find out how topological and algebraic properties of unrooted Gaussian tree models determine their security robustness, which is measured by our proposed max-min information (MaMI) metric. Such metric quantifies the amount of common randomness extractable through public discussion between two legitimate nodes under an eavesdropper attack. We show some general topological properties that the desired max-min solutions shall satisfy. Under such properties, we develop conditions under which comparable trees are put together to form partially ordered sets (posets). Each poset contains the most favorable structure as the poset leader, and the least favorable structure. Then, we compute the Tutte-like polynomial for each tree in a poset in order to assign a polynomial to any tree in a poset. Moreover, we propose a novel method, based on restricted integer partitions, to effectively enumerate all poset leaders. The results not only help us understand the security strength of different Gaussian trees, which is critical when we evaluate the information leakage issues for various jointly Gaussian distributed measurements in networks, but also provide us both an algebraic and a topological perspective in grasping some fundamental properties of such models.

Previous authors have shown that the asymptotic capacity of a multiple-element-antenna (MEA) system with N transmit and N receive antennas [termed an (N,N) MEA] grows linearly with N if, for all l, the correlation of the fading for two antenna elements whose indices differ by l remains fixed as antennas are added to the array. However, in practice, the total size of the array is often fixed, and thus the correlation of the fading for two elements separated in index by some value l will change as the number of antenna elements is increased. In this paper, under the condition that the size of an array of antennas is fixed, and assuming that the transmitter does not have access to the channel state information (CSI) while the receiver has perfect CSI, the asymptotic properties of the instantaneous mutual information I/sub N,N/ of an (N,N) MEA wireless system employing uniform linear arrays in a quasi-static fading channel are derived analytically and tested for accuracy for finite N through simulations. For many channel correlation structures, it is demonstrated that the asymptotic performance converges almost surely, implying that such MEA systems have a certain strong robustness to the instantiation of the channel fading values.

In this paper, we propose a novel framework to study the transmission of partitioning information over a Boolean multi-access channel. The objective of transmission is not for message restoration purpose, but rather to make active users partitioned into distinct groups so that they can transmit their messages without collision subsequently. Random coding and MAP decoding are employed for achievability proof under a novel framework for strong coloring of a resulting hypergraph, which is created by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple but non-trivial case with K = 2 active users. The derived achievable bound is shown better than the converse bound of group testing, which is intended for identification of all active users, rather than the partition we are seeking, thereby further demonstrating the uniqueness of our problems.

In this paper without tailoring to any physical channel condition or any restriction on adversary's computational resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only advantage for legitimate users over eavesdropper is existence of a key source that is partially known by Eve. A key extractor based on a sampler and a Renyi extractor derives secret keys with the required entropy from this source. Encryption using this key with a general cipher maps Eve's uncertainty about the key to uncertainty about the plaintext that can also be interpreted as degradation in her channel. Using privacy amplification on top of this cipher based on inverse universal2 hashing results in information leakage with decreasing exponent that can be optimized to guarantee a higher level of secrecy.

We explore the degrees-of-freedom and interference tradeoff for a simple cognitive radio system under an assumption that the secondary-user (SU) receiver operates incoherently with the primary-user (PU) transmitter. This assumption makes our system model practically more rigorous, as compared to the conventional studies where a coherent operation is assumed. Due to the incoherent operation of SU receiver, the resulting interference channel is mixture-Gaussian. Our objective is to find the optimal sensing threshold and sensing time, for the signal detector that is used by the SU, such that the SU performance is maximized while the PU performance degradation, caused by the interference due to SU, remains within a tolerable range. Also, we define the interference regimes for SU performances on the basis of PU transmission power level.

In this paper we propose an encoding-encryption approach to take advantage of intentional noise introduced in ciphertexts for a block cipher working in CFB or CBC mode. First of all, we provide a rigorous analysis of the impacts of channel degradation on block ciphered systems. We show that the overall channel can be modeled as a Finite State Markov Chain (FSMC) with symmetric channels associated in each state, whose underlying non-coherent Shannon capacity is derived and computed. Despite Eve's efforts in modifying her linear crytanalysis given the intercepted noisy ciphertexts, there is still a non-negligible probability of having possible failures in her attack. We essentially create a wiretap channel in application layer that is a degraded version of the main channel and measure security of the system in terms of secrecy capacity and show that it depends on the deliberately introduced bit error rate. In addition, Alice can accordingly adjust cross over probability of the channel to maximize secrecy rate. This secrecy rate can be achieved by wiretap channel coding over multiple frames in application layer if the delay in system is bearable.

The introduction of cognitive radio enables systems awareness of their environment and internal state, fulfills the need of dynamic spectrum access for higher spectrum utilization. However, at the same time, the use of cognitive radios further complicates the security problems in wireless networks and introduces additional challenges for a counter measure. Due to the intelligence of the attackers, many of the attacks may be stealthy by nature. In this paper, we propose a cross-layer model for stealthy attacks detection with stealthy jammer as a prime example. Quickest detection technique is adopted and embedded in the proposed framework since the attacks usually happen at unknown time and are unpredictable due to the lack of prior knowledge of the attackers. A case study is performed by combining physical layer spectrum sensing with multipath routing at the network layer. The results demonstrate the effectiveness of the proposed approach.

In this paper, we study the effect of channel errors on the performance of linear cryptanalysis against block ciphered system. We study DES block cipher working in cipher feedback mode (CFB) as a special case. In our model, eavesdropper launches linear attack by querying an oracle which provides her with corrupted ciphertexts over a binary symmetric channel (BSC). A new verification strategy in linear attack has been designed and numerically optimized to allow Eve to mount a successful attack in noisy environments. However, we show that even by utilizing this optimized strategy, there is still possibility of misdetection in Eve's cryptanalysis, which directly depends on the channel degradation level. Numerical results show that the proposed attack strategy lets Eve maintain a high performance even for relatively high noise levels. On the other hand, they suggest that due to Eve's possible failures in her attack, tunable cross over probability of the channel can bring about the lowest performance for Eve as well as a higher security.

This paper focuses on the problem of sharing secret keys using the Automatic Repeat reQuest (ARQ) protocol. We first model the forward and feedback channels as erasure channels for both legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmission that will be mapped into a destination set using the first order digital filter with feedback. Then, we characterize Eve's information loss about this shared destination set, due to inevitable transmission errors that will be manipulated by privacy amplification to generate a series of secret keys about which Eve's knowledge remains negligible. We define two metrics to measure secrecy enhancement: outage probability and secret key rate. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than the legitimate receiver, and her channel condition is unknown.

In this paper, we provide a fundamental channel model to characterize the interference effect inherent in cognitive radio systems. Mutual information rates of our proposed probabilistic block interference channels for both primary and secondary users are derived without assuming that receivers have knowledge on channel interference states. Novel constrained optimization problems are then put forward with a constraint on the performance loss margin tolerated by the primary user. Furthermore, we investigate some special cases where conditions are provided to justify the optimality of adopting Neyman-Pearson rule. Also presented are some scenarios in which randomized decision without using sensing measurement is needed to balance the rateloss for PU and throughput gain for SD.

The main idea in this paper is to design and analyze a symmetric key generation algorithm whereby we can strengthen wireless network security. Our main goal is generating a sequence of highly secure secret keys based on an ARQ based transmission mechanism that relies on the statistical independence of channel errors between the attacker and legitimate users. This leads to some information loss for the adversary which allows us to constantly extract keys by using universal Hashing techniques from communication process, about which we can make sure that adversarys knowledge remains negligible. More specifically, the key generation algorithm is analyzed and designed in a way that targeted security as well as the required throughput and synchronization goals for the transmission are achieved. Simulation results show that the designed algorithm achieves the desired requirements for both system security and throughput.

The efficiency of a cognitive radio system depends critically on sensing reliability since post-sensing communication efficiency is subject to optimal resource allocation under this sensing uncertainty. In this paper, we develop online algorithms for maximizing throughput in a cognitive radio when the sensing outcome of the primary channel (available/unavailable) is not always reliable. We first develop a very efficient per-slot power allocation algorithm for a secondary user transmitting under total power constraints over a period of M time slots, assuming reliable sensing during each slot but with no look-ahead capability. Specifically, we show that it is always possible to achieve a transmission rate that is a constant fraction of the optimal transmission rate even with no apriori knowledge of the number of available slots. Our online power-allocation algorithm is 3.7-competitive, i.e the rate achieved by this algorithm is within a factor of 1 — 1/M) even with sensing errors under the worst-possible input sequence, provided the number of good time slots is reasonably large as a function of M. However, when the number of good time slots is small (M0(1), for example λ/Μ), we show that no online algorithm can achieve a constant-factor competitive ratio.

In this paper, we study the effects of channel errors on security and decoding error probability of three encryption systems where encrypted message is sent and eavesdropped over binary symmetric channels (BSC). The three systems are all based on Data Encryption Standard (DES) in cipher feedback (CFB) mode. They are DES only (DC), DES concatenated with Reed Solomon encoding (DCRS), and DES concatenated with RS coding and S-box diffusion (DCRSS). We adopt linear crypt-analysis to quantitatively measure the effects of channel errors on the security of these systems. We have found the required known cipher-plain text pairs in each system for linear attack launched by Eve, an eavesdropper. In addition, performance analysis in terms of decoded information bit error probability (IBER) for Bob, the legitimate receiver, has been conducted for each system, whose accuracy is later verified by simulation results. Our results suggest there exists tradeoff between communication reliability and security. More security level can be attained by sacrificing the accuracy at the legitimate receiver end, which can be captured by the relationship between IBER and our proposed novel metric, security improvement factor (SIF).

This paper studies the problem of active eavesdropping in fast fading channels. The active eavesdropper (Eve-A) is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping (Ex mode), and jamming (Jx mode) - Eve-A cannot function in full duplex mode. We consider the most conservative scenario, when the Eve-A can choose her strategy based on the legitimate transmitter-receiver pair's strategy - and thus the transmitter and legitimate receiver have to plan for the worst. We introduce a novel encoding scheme, based on very limited and unprotected feedback - the Block-Markov Wyner (BMW) encoding scheme - which outperforms any schemes currently available.

In this paper we study the problem of active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) - the active eavesdropper cannot function in full duplex mode. In this paper we only consider the best-case scenario, when the transmitter knows the eavesdropper's strategy in advance - and hence can adaptively choose an encoding strategy. We show that, even under these most optimistic assumptions, an active eavesdropper can induce moderate to severe degradation of the achievable secrecy rate.

We consider the problem of a transmitter transmitting to its receiver over a wireless link subject to jamming and develop two online power control algorithms for maximizing wireless link quality (transmission rate). We assume that the transmitter transmits and the jammer interferes over a period of M time slots. The impact of the jammer is to deteriorate the quality of the wireless channel during time slots in which it is present. We assume a powerful random jammer with the ability to arbitrarily decrease the channel quality and affect any (unknown) number of time slots. Since the presence of the jammer is arbitrary, the complete jamming pattern (channel quality) over the given time period is unknown apriori. The current channel quality is revealed to the transmitter at the start of the current time slot while future channel quality remains unknown. The transmitter must then allocate power optimally to maximize the total transmission rate over M slots given only its knowledge of the current channel quality, thus giving rise to an online power control problem. We develop two online power control algorithms for maximizing the wireless link quality (transmission rate). The first algorithm is based on constant power scaling and has O(1) competitive ratio when the average received power quality over M time slots (ĥh g P T /M) is either very small or very large. However when ĥh g P T = O(M), this algorithm has an upper bound on its competitive ratio of O(logM/log logM}. This upper bound is tight. The second online algorithm based on constant rate scaling has a worst case competitive ratio of given equation. By judiciously choosing which algorithm to use based on the offline available parameter of average received power, we can assure an almost constant competitive ratio for maximizing link quality under all cases.

It has been shown lately the optimality of uncoded transmission in estimating Gaussian sources over homogeneous/symmetric Gaussian multiple access channels (MAC) using multiple sensors. It remains, however, unclear whether it still holds for any arbitrary networks and/or with high channel signal-to-noise ratio (SNR) and high signal-to-measurement-noise ratio (SMNR). In this paper, we first provide a joint source and channel coding approach in estimating Gaussian sources over Gaussian MAC channels, as well as its sufficient and necessary condition in restoring Gaussian sources with a prescribed distortion value. An interesting relationship between our proposed joint approach with a more straightforward separate source and channel coding scheme is then established. We then formulate constrained power minimization problems and transform them to relaxed convex geometric programming problems, whose numerical results exhibit that either separate or uncoded scheme becomes dominant over a linear topology network. In addition, we prove that the optimal decoding order to minimize the total transmission powers for both source and channel coding parts is solely subject to the ranking of MAC channel qualities, and has nothing to do with the ranking of measurement qualities. Finally, asymptotic results for homogeneous networks are obtained which not only confirm the existing optimality of the uncoded approach, but also show that the asymptotic SNR exponents of these three approaches are all the same. Moreover, the proposed joint approach share the same asymptotic ratio with respect to high SNR and high SMNR as the uncoded scheme.

Consider a parallel Gaussian channel with M subchannels each of which experiences independent flat fading. There exists a smart jammer which is capable of intercepting the feedback channel message such that channel state information (CSI) measured and sent back by a receiver can be perfectly known to the jammer, as well. We formulate a novel two-layer two-person zero-sum game. Under this zero-sum game framework, the following three fundamental questions are addressed. The first one is about whether to hop or to spread power over M frequency bands given the full CSI at both transmitter and jammer sides. We prove that spreading versus spreading is the Nash equilibrium point. The second question is about the impact of sending back CSI on the overall throughput, to feedback or not to feedback, considering the presence of a smart jammer capable to exploit CSI for its malicious purpose. We show that possessing the full CSI enables a better means to defend against the jammerpsilas attacks. The last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer. We prove that the receiver should also get involved by adaptively sending CSI without compromising the sum rate at the equilibrium point.

In the existing works on distributed detection in sensor networks, local sensor nodes either quantize the observation or directly scale the analog observation and then transmit the processed information independently over wireless channels to a fusion center. In this paper, we exploit the advantages of both of these two approaches by constructing an equivalent Sigma-Delta ADC across space over wireless sensor networks. Sensors are arranged in a mixing of parallel and serial topologies, enabling each sensor to transmit binary information to the fusion center, while in the meantime preserving the analog information through collaborative processing. Comparison with existing approaches demonstrates the superiority of our proposed scheme in both AWGN and fading channels in terms of the resulting detection error probability.

We formulate an expression for the channel capacity of a soft-decision cognitive network in which cognitive radio transmitters can share spectrum usage with primary users depending on adaptive interference tolerance limits. We consider the problem of capacity maximization in this domain and provide an efficient polynomial time algorithm for cognitive radio power control. Results obtained using this algorithm will be useful in soft-decision spectrum allocation for cognitive radio (CR) transmitters as well as for developing the general analytic enabling waveform for soft-decision CR.

Relaying is often advocated for improving system performance by enhancing spatial diversity in wireless networks. In this paper, we address the issue of energy tradeoff made by relay nodes between transmitting their own data and forwarding other nodes' information in fading channels. First, assuming perfect channel state information (CSI), we propose a power control policy in a two-node relay network under which total energy consumption across both nodes is minimized while meeting both outage probability requirements. However perfect CSI at each node is not possible in general due to bandwidth limitations that prevent the full exchange of precise channel information. Thus in this paper, we develop power control algorithms for relaying under bandwidth constraints, via quantization. Specifically, we develop a quantization protocol that accounts for the asymmetric nature of uplink/downlink communication bandwidths and develop an optimal polynomial time algorithm for channel quantization using this protocol. The quantization algorithm minimizes the sum of expected transmission powers at the source and relay, required for collaborative relaying to satisfy the given outage probability.

We propose two-level superposition coding based relaying schemes in which optimal power and rate allocations are investigated. Instead of confining us with fixed decoding order, two-levels of signals are considered as virtual users in a two-user multiple access channel and we prove that in certain cases the optimal joint multiuser decoding is equivalent to an approach using successive interference cancellation in a fixed order. Numerical results are provided to show the improvements in power savings using our proposed strategies compared with fixed rate and single level coding approach. I. INTRODUCTION Channel quality plays an important role in determining the average throughput of wireless systems. If channel quality is too bad, transmitted signals will be corrupted and the receiver terminal will not be able to decode the data. Hence we need to have an adaptive transmitter which reduces the rate when the channel quality is bad. This cannot be accomplished in compound channels where channel state information is not available to transmitters. Shamai (1) and Liu (2) investigated employing superposition coding in compound channels to enhance average throughput. The message to be transmitted is encoded using multi-level superposition coding (3) and all layers of messages are transmitted over the channel simul- taneously. In this approach, they treated channel states as the virtual users of a broadcast channel, which means that the decoding order has been fixed for the destination, i.e. successive interference cancellation is assumed at the receiver end.

We develop algorithms for finding the minimum energy transmission schedule for duty-cycle and rate constrained wireless sensor nodes transmitting over an interference channel. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the non-convex constraints, we develop fully polynomial approximation schemes (FPAS) for finding optimal schedules by considering restricted versions of the problem using multiple discrete power levels. We first show a simple dynamic programming solution that optimally solves the restricted problem. For two fixed transmit power levels (0 and P), we then develop a 2-factor approximation for finding the optimal fixed transmission power level per time slot, Popt, that generates the optimal (minimum) energy schedule. This can then be used to develop a (2, 1+e)-FPAS that approximates the optimal power consumption and rate constraints to within factors of 2 and arbitrarily small e>0, respectively. Finally, we develop an algorithm for computing the optimal number of discrete power levels per time slot (O(1/e)), and use this to design a (1, 1+e)-FPAS that consumes less energy than the optimal while violating each rate constraint by at most a 1+e factor.

This paper studies the capacity, as well as the performance of dirty paper coding (DPC) for a point to point power constrained fading channel given two-sided mixed state information on additive and multiplicative interferences. We show the optimality of DPC when perfect channel state information about fading variable is available to both transmitter and receiver, and provide multiplexing/demultiplexing based strategies to achieve capacity. By employing an adaptation of Heegard's algorithm to this channel model, we also evaluate numerically both the achievable rate of the modified DPC strategy, as well as the actual channel capacity when transmitter has imperfect side information. Numerical results demonstrate significant improvements on channel capacity, as well as increased disparity between the achievable rate using DPC and channel capacity when only one-bit feedback on channel sate information of fading variable is available to encoder. The futility of knowing the additive interference at transmitter, when the multiplicative interference is only available to the receiver, is also shown numerically.