csi usage over parallel fading channels under jamming attacks a game theory study 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

mutual information games in multiuser channels with correlated jamming we investigate the behavior of two users and one jammer in an additive white gaussian noise awgn channel with and without fading when they participate in a noncooperative zero sum game with the channel s input output mutual information as the objective function we assume that the jammer can eavesdrop on the channel and can use the information obtained to perform correlated jamming we also differentiate between the availability of perfect and noisy information about the user signals at the jammer 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 nonexistence of a simultaneously optimal set of strategies for the users and the jammer and characterize those strategies whenever they exist

a regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its l norm the i th singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one we show that near a local maximum however the largest singular value has a lipschitz second derivative but need not have a third derivative using this regularity result we give a quadratically convergent algorithm for computing the l norm of a transfer matrix

information capacity of channels with partially unknown noise i finite dimensional channels information capacity is considered for a finite dimensional communication channel in which the noise is the sum of a known gaussian noise and an independent component with unknown statistical properties the problem is modeled as a zero sum two person game between the coder and a jammer with mutual information as the payoff function the jammer does not control the ambient gaussian noise the constraints employed are appropriate for extension to infinite dimensional channels and for consideration of coding capacity the original problem is reformulated to prove existence of both a saddle value and a saddle point the saddle value and a saddle point are determined along with the jammer s minimax strategy

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

classification by evolutionary ensembles this paper is about building an ensemble of classifiers each of which is trained based on a particular weighting over the training examples a weighting is a set of weights associated with the examples the task concerns search in a tremendous weighting space in this view we propose to incorporate a genetic algorithm ga it performs a wide yet efficient search for appropriate weightings chromosomes the difference from a traditional ga is that all the weightings throughout evolution will be exploited to form the final ensemble not just the best weighting our algorithm is tested on the uci benchmark data sets and used to design a face detection system robust and consistently accurate classification is experienced comparative results with two other algorithms i e adaboost and bagging are also given

optimum linear causal coding schemes for gaussian stochastic processes in the presence of correlated jamming the complete solution is obtained to the following problem a gaussian stochastic process theta sub t t in 0 t sub f satisfying a certain stochastic differential equation is to be transmitted through a stochastic channel to a receiver under minimum mean squared error distortion measure the channel is to be used for exactly t sub f seconds and in addition to white gaussian noise with a given energy level the channel is corrupted by another source whose output may be correlated with the input to the channel and which satisfied a given power constraint there is an input power constraint to the channel and noiseless feedback is allowed between the receiver decoder and the transmitter encoder the authors determine the linear causal encoder and decoder structures that function optimally under the worst admissible noise inputs to the channel the least favorable probability distribution for this unknown noise is found to be gaussian and is correlated with the transmitted signal also included is a comparative study of these results with earlier ones that addressed a similar problem without a causality restriction imposed on the transmitter

correlated jamming on mimo gaussian fading channels we consider a zero sum mutual information game on multiple input multiple output mimo gaussian rayleigh fading channels the players are an encoder decoder pair as the maximizer and a jammer as the minimizer of the mutual information between the input and the output of the channel there are total power constraints on both the jammer and the encoder also the jammer has access to the encoder output we find the unique saddle point of this game and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

the gaussian test channel with an intelligent jammer the problem of transmitting a sequence of identically distributed independent gaussian random variables through a gaussian memoryless channel with a given input power constraint in the presence of an intelligent jammer is considered the jammer taps the channel and feeds back a signal at a given energy level for the purpose of jamming the transmitting sequence under a square difference distortion measure which is to be maximized by the jammer and to be minimized by the transmitter and the receiver this correspondence obtains the complete set of optimal saddle point policies the solution is essentially unique and it is structurally different in three different regions in the parameter space which are determined by the signal to noise ratios and relative magnitudes of the noise variances the best maximin policy of the jammer is either to choose a linear function of the measurement he receives through channel tapping or to choose in addition and additively an independent gaussian noise sequence depending on the region where the parameters lie the optimal minimax policy of the transmitter is to amplify the input sequence to the given power level by a linear transformation and that of the receiver is to use a bayes estimator

a framework for evaluating the data hiding capacity of image sources an information theoretic model for image watermarking and data hiding is presented in this paper previous theoretical results are used to characterize the fundamental capacity limits of image watermarking and data hiding systems capacity is determined by the statistical model used for the host image by the distortion constraints on the data hider and the attacker and by the information available to the data hider to the attacker and to the decoder we consider autoregressive block dct and wavelet statistical models for images and compute data hiding capacity for compressed and uncompressed host image sources closed form expressions are obtained under sparse model approximations models for geometric attacks and distortion measures that are invariant to such attacks are considered

analysis of an on off jamming situation as a dynamic game the process of communication jamming can be modeled as a two person zero sum noncooperative dynamic game played between a communicator a transmitter receiver pair and a jammer we consider a one way time slotted packet radio communication link in the presence of a jammer where the data rate is fixed and 1 in each slot the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value 2 both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating the payoff function is the time average of the mean payoff per slot the game is solved for certain ranges of the players transmitter parameters structures of steady state solutions to the game are also investigated the general behavior of the players strategies and payoff increment is found to depend on a parameter related to the payoff matrix which me call the payoff parameter and the transmitters parameters when the payoff parameter is lower than a threshold the optimal steady state strategies are mixed and the payoff increment constant over time whereas when it is greater than the threshold the strategies are pure and the payoff increment exhibits oscillatory behavior

a generalized iterative water filling algorithm for distributed power control in the presence of a jammer consider a scenario in which k users and a jammer share a common spectrum of n orthogonal tones both the users and the jammer have limited power budgets the goal of each user is to allocate its power across the n tones in such a way that maximizes the total sum rate that he she can achieve while treating the interference of other users and the jammer s signal as additive gaussian noise the jammer on the other hand wishes to allocate its power in such a way that minimizes the utility of the whole system that being the total sum of the rates communicated over the network for this noncooperative game we propose a generalized version of the existing iterative water filling algorithm whereby the users and the jammer update their power allocations in a greedy manner we study the existence of a nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water filling algorithm converges to a nash equilibrium of the game the conditions that we derive in this paper depend only on the system parameters and hence can be checked a priori simulations show that when the convergence conditions are violated the presence of a jammer can cause the otherwise convergent iterative water filling algorithm to oscillate

capacity of second order cyclostationary complex gaussian noise channels in this paper we derive the capacity of a continuous time single input single output siso frequency selective band limited linear time invariant lti channel whose output is corrupted by a second order cyclostationary socs complex gaussian noise by using a pair of invertible linear conjugate linear time varying operators called a properizing frequency shift p fresh vectorizer and a p fresh scalarizer it is shown that whether the complex noise is proper or improper the siso channel can always be converted to an equivalent multiple input multiple output mimo lti channel whose output is now corrupted by a proper complex vector wide sense stationary noise a variational problem is then formulated in the frequency domain to find the optimal input distribution that maximizes the throughput of the equivalent mimo channel it turns out that the optimal input to the siso channel obtained through a procedure similar to the water filling is an socs complex gaussian random process with the same cycle period as the noise it is shown that this procedure named cyclic water filling significantly outperforms ordinary water filling by effectively utilizing the spectral correlation of the cyclostationary noise

generalized linear quadratic control we consider the problem of stochastic finite and infinite horizon linear quadratic control under power constraints the calculations of the optimal control law can be done off line as in the classical linear quadratic gaussian control theory using dynamic programming which turns out to be a special case of the new theory developed in this technical note a numerical example is solved using the new methods

some information theoretic saddlepoints in order to study communication in the presence of jamming or vice versa one can formulate a two person zero sum game with mutual information as the payoff function since mutual information is convex concave in just the right way one often finds saddlepoint strategies which are simultaneously optimal for both players in this paper we shall discuss these saddlepoints for four distinct cases additive noise average power constraints and any combination of hard soft input output quantization one of these cases soft soft has been previously studied shannon dobrushin blachman but the other three appear to be new

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

product multicommodity flow in wireless networks we provide a tight approximate characterization of the n dimensional product multicommodity flow pmf region for a wireless network of n nodes separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information theoretic sense and for a combinatorial interference model e g protocol model these provide an inner approximation to the n 2 dimensional capacity region our results hold for general node distributions traffic models and channel fading models we first establish that the random source destination model assumed in many previous results on capacity scaling laws is essentially a one dimensional approximation to the capacity region and a special case of pmf we then build on the results for a wireline network graph that relate pmf to its spectral or cut properties specifically for a combinatorial interference model given by a network graph and a conflict graph we relate the pmf to the spectral properties of the underlying graphs resulting in simple computational upper and lower bounds these results show that the 1 radicn scaling law obtained by gupta and kumar for a geometric random network can be explained in terms of the scaling law of the conductance of a geometric random graph for the more interesting random fading model with additive white gaussian noise awgn we show that the scaling laws for pmf can again be tightly characterized by the spectral properties of appropriately defined graphs such a characterization for general wireless networks has not been available before as an implication we obtain computationally efficient upper and lower bounds on the pmf for any wireless network with a guaranteed approximation factor

simple covariance approach to mathcal h _ infty analysis we revisit the classical mathcal h infty analysis problem of computing the ell 2 induced norm and the mathcal l 2 induced norm of a linear time invariant system for the discrete time case and the continuous time case respectively we follow an approach based on converting the problem of maximization over signals to that of maximization over a sort of deterministic covariance matrices the reformulation in terms of these covariance matrices greatly simplifies the dynamic analysis problem and converts the computation to a convex constrained matrix maximization problem furthermore the equivalence is for the actual mathcal h infty norm of the system rather than a bound and thus does not require the typical gamma iterations we argue that this approach is both attractive elementary and constructive in that the worst case disturbance is also easily obtained as a state feedback constructed from the solution of the matrix problem

a robust evolutionary algorithm for the recovery of rational gielis curves gielis curves gc can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons and even self intersecting curves such patterns appear in natural objects or phenomena such as flowers crystals pollen structures animals or even wave propagation gielis curves and surfaces are an extension of lame curves and surfaces superquadrics which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types such as range images 2d and 3d point clouds etc unfortunately the most efficient techniques for superquadrics recovery based on deterministic methods cannot directly be adapted to gielis curves indeed the different nature of their parameters forbids the use of a unified gradient descent approach which requires initial pre processings such as the symmetry detection and a reliable pose and scale estimation furthermore even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data we present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach the key ideas in this paper are the replacement of the potential fields used for the cost function closed form by the shortest euclidean distance sed iterative approach the construction of cost functions which minimize the shortest distance as well as the curve length using r functions and slight modifications of the evolutionary operators we show that the proposed cost function based on sed and r function offers the best compromise in terms of accuracy robustness to noise and missing data

arcing classifier with discussion and a rejoinder by the author recent work has shown that combining multiple versions of unstable classifiers such as trees or neural nets results in reduced test set error one of the more effective is bagging here modified training sets are formed by resampling from the original training set classifiers constructed using these training sets and then combined by voting freund and schapire propose an algorithm the basis of which is to adaptively resample and combine hence the acronym arcing so that the weights in the resampling are increased for those cases most often misclassified and the combining is done by weighted voting arcing is more successful than bagging in test set error reduction we explore two arcing algorithms compare them to each other and to bagging and try to understand how arcing works we introduce the definitions of bias and variance for a classifier as components of the test set error unstable classifiers can have low bias on a large range of data sets their problem is high variance combining multiple versions either through bagging or arcing reduces variance significantly

a complete characterization of minimax and maximin encoder decoder policies for communication channels with incomplete statistical description the problem is considered of transmitting a sequence of independent and identically distributed gaussian random variables over a channel whose statistical description is incomplete the channel is modeled as one that is conditionally gaussian with the unknown part being controlled by a so called jammer who may have access to the input to the encoder and operates under a given power constraint by adopting a game theoretic approach a complete set of solutions is obtained encoder and decoder mappings and least favorable distributions for the channel noise for this statistical decision problem under two different sets of conditions depending on whether the encoder mapping is deterministic or stochastic in the latter case existence of a mixed saddle point solution can be verified when a side channel of a specific nature is available between the transmitter and the receiver in the former case however only minimax and maximin solutions can be derived

comments on correlated jamming on mimo gaussian fading channels for original paper by kashyap et al see ieee trans inf theory vol 50 no 9 p 2119 23 2004 september in the subject paper a lemma concerning the convexity of a particular log det function is proposed and proved however it is shown here that while the lemma itself is correct the derivation of the proof is subject to a major defect in this correspondence the defect is discussed and amended and a full and correct derivation using the same approach is also given

information theoretic bounds for compound mimo gaussian channels in this paper achievable rates for compound gaussian multiple input multiple output mimo channels are derived two types of channels modeled in the frequency domain are considered when 1 the channel frequency response matrix h belongs to a subset of h infin normed linear space and 2 the power spectral density psd matrix of the gaussian noise belongs to a subset of l 1 space the achievable rates of these two compound channels are related to the maximin of the mutual information rate the minimum is with respect to the set of all possible h matrices or all possible psd matrices of the noise the maximum is with respect to all possible psd matrices of the transmitted signal with bounded power for the compound channel modeled by the set of h matrices it is shown under certain conditions that the code for the worst case channel can be used for the whole class of channels for the same model the water filling argument implies that the larger the set of matrices h the smaller the bandwidth of the transmitted signal will be for the second compound channel the explicit relation between the maximizing psd matrix of the transmitted signal and the minimizing psd matrix of the noise is found two psd matrices are related through a riccati equation which is always present in kalman filtering and liner quadratic gaussian control problems

coding capacity for a class of additive channels coding capacity is considered for a class of additive dimension limited channels the channels may be with or without memory stationary or nonstationary the constraint is partially given in terms of an increasing family of finite dimensional subspaces a general expression for the capacity is obtained which depends on the family of subspaces and the relation between the noise covariance and the covariance giving the energy frequency constraint on the transmitted signal this result holds for all classical discrete time gaussian channels and for continuous time gaussian channels with fixed time of transmission so long as a peak energy constraint is used on the codewords the expression also provides upper bounds for a class of non gaussian channels several results are obtained that aid in calculation of capacity for specific applications for this class of channels it is shown that coding capacity is equal to information capacity error bounds are given for gaussian channels

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

gaussian arbitrarily varying channels the em arbitrarily varying channel avc can be interpreted as a model of a channel jammed by an intelligent and unpredictable adversary we investigate the asymptotic reliability of optimal random block codes on gaussian arbitrarily varying channels gavc s a gavc is a discrete time memoryless gaussian channel with input power constraint p t and noise power n e which is further corrupted by an additive jamming signal the statistics of this signal are unknown and may be arbitrary except that they are subject to a power constraint p j we distinguish between two types of power constraints em peak and em average for peak constraints on the input power and the jamming power we show that the gavc has a random coding capacity for the remaining cases in which either the transmitter or the jammer or both are subject to average power constraints no capacities exist and only lambda capacities are found the asymptotic error probability suffered by optimal random codes in these cases is determined our results suggest that if the jammer is subject only to an average power constraint reliable communication is impossible at any positive code rate

the mimo radar and jammer games the interaction between a smart target and a smart mimo radar is investigated from a game theory perspective since the target and the radar form an adversarial system their interaction is modeled as a two person zero sum game the mutual information criterion is used in formulating the utility functions the unilateral hierarchical and symmetric games are studied and the equilibria solutions are derived

shannon meets von neumann a minimax theorem for channel coding in the presence of a jammer we study the setting of channel coding over a family of channels whose state is controlled by an adversarial jammer by viewing it as a zero sum game between a finite blocklength encoder decoder team and the jammer the encoder decoder team choose stochastic encoding and decoding strategies to minimize the average probability of error in transmission while the jammer chooses a distribution on the state space to maximize this probability the min max value of the game is equivalent to channel coding for a compound channel we call this the shannon solution of the problem the max min value corresponds to finding a mixed channel with the largest value of the minimum achievable probability of error when the min max and max min values are equal the problem is said to admit a saddle point or von neumann solution while a shannon solution always exists the communicating team s problem is nonconvex for finite blocklengths whereby a von neumann solution may not exist despite this we show that the min max and max min values become equal asymptotically in the large blocklength limit for all but finitely many rates we explicitly characterize this limiting value as a function of the rate and obtain tight finite blocklength bounds on the min max and max min value as a corollary we get an explicit expression for the epsilon capacity of a compound channel under stochastic codes the first such result to the best of our knowledge our results demonstrate a deeper relation between the compound channel and mixed channel than was previously known they also show that the conventional information theoretic viewpoint articulated via the shannon solution coincides asymptotically with the game theoretic one articulated via the von neumann solution key to our results is the derivation of new finite blocklength upper bounds on the min max value of the game via a novel achievability scheme and lower bounds on the max min value obtained via the linear programming relaxation based approach we introduced in 2

a fast algorithm to computer the h norm of a transfer function matrix abstract a fast algorithm is presented to compute the h norm of a transfer function matrix based on the relation between the singular values of the transfer function matrix and the eigenvalues of a related hamiltonian matrix the norm is computed with guaranteed accuracy a very simple method to compute a rather close lower bound on the h norm is given

optimal zero delay jamming over an additive noise channel this paper considers the problem of optimal zero delay jamming over an additive noise channel building on a sequence of recent results on conditions for linearity of optimal estimation and of optimal mappings in source channel coding the saddle point solution to the jamming problem is derived for general sources and channels without recourse to gaussianity assumptions the linearity conditions are shown to play a pivotal role in jamming in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings i e the jammer ensures whenever possible that the transmitter and the receiver cannot benefit from non linear strategies this result is shown to subsume the known result for gaussian source and channel the conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer are analyzed moreover a numerical procedure is provided to approximate the optimal jamming strategy in the remaining source channel cases where the jammer cannot impose linearity on the transmitter and the receiver next the analysis is extended to vector sources and channels this extension involves a new aspect of optimization the allocation of available transmit and jamming power over source and channel components similar to the scalar setting the saddle point solution is derived using the linearity conditions in vector spaces the optimal power allocation strategies for the jammer and the transmitter have an intuitive interpretation as the jammer allocates power according to water filling over the channel eigenvalues while the transmitter performs water pouring reverse water filling over the source eigenvalues