In this paper we extend the classical DP approach to decentralized discrete-time stochastic nonlinear dynamical optimal control problems, with multiple control strategies, each assigned an information pattern or structure, that consists of private and delayed sharing components, using the concept of Person-by-Person (PbP) optimality of static team theory. We characterize PbP optimality by value functions that satisfy generalized DP equations, with corresponding limited-pathwise information states which are sufficient statistics for the strategies. The value functions and information states satisfy the Fundamental Properties of classical partially observable Markov decision problems (POMDP): both are independent of the minimizing strategies. The generalized DP approach of this paper, builds on the concept that, each control strategy, estimates the unobservable state process and the private information components of all other strategies, from its own private and delayed sharing information components, using a limited-pathwise conditional probability distribution (which is an information state in the classical sense).

We characterize the feedback capacity$C_{FB}$of general nonlinear decision models (N-DM) through the$n$-finite trans-mission or block length feedback information$(n$- FTFI) capacity,$c_{FB,n}$. For an application we consider the multiple-input multiple-output (MIMO) Gaussian DM with memory on past outputs and inputs driven by nonstationary Gaussian noise, and finite-dimensional Gaussian noise in state space form, subject to an average cost constraint of quadratic form. The main theorems show that optimal randomized control strategies that achieve$c_{FB,n}$, consist of multiple parts, that include control, estimation, and information transmission/signalling strategies. These strategies are determined using decentralized optimization techniques, and involve filtering Riccati equations and a control Riccati equation.

This paper analyzes the joint Rate Distortion Function (RDF) of correlated multivariate Gaussian sources with individual square-error distortions. Leveraging Hotelling's canonical variable form, presented is a closed-form characterization of the joint RDF, that involves a system of nonlinear equations. Furthermore, for the special case of symmetric distortions (i.e., equal distortions), the joint RDF is explicitly expressed in terms of two water-filling variables. The results greatly improve our understanding and advance the development of closed-form solutions of the joint RDF for multivariate Gaussian sources with individual square-error distortions.

We show that the nonfeedback capacity of multiple-input multiple-output (MIMO) additive Gaussian noise (AGN) channels, when the noise is nonstationary and unstable, is characterized by an asymptotic optimization problem–the per unit time limit of the characterization of a finite block or transmission without feedback information (FTwFI) capacity, that involves two generalized matrix difference Riccati equations (DREs) of filtering theory, and a matrix difference Lyapunov equation of stability theory, of Gaussian systems. Further, we identify conditions and prove, that the characterization of nonfeedback capacity is the uniform asymptotic per unit time limit, over all initial distributions. The asymptotic characterization of capacity involves two generalized matrix algebraic Riccati equations (AREs) and a matrix algebraic Lyapunov equation. We also present an example to illustrate that our characterization of capacity produces a known closed-form expression of the water-filling solution of capacity (for power levels above a minimum power).

This paper derives the optimal test channel distribution and the complete characterization of the classical Gorbunov and Pinsker (1973), Gorbunov and Pinsker (1974) nonanticipatory epsilon entropy of multivariate Gaussian Markov sources with square-error fidelity, which remained an open problem since 1974. The paper also formulates a state dependent nonanticipatory epsilon entropy, in which past reproductions are available to the decoder and not to the encoder, the test channel is specified with respect to an auxiliary (state) random process, and the reproduction process is a causal function of past reproduction and the auxiliary random process. This variation is analogous to the Wyner and Ziv (1976) and Wyner (1978) rate distortion function (RDF), of memoryless sources. It is shown that the operational rate of zero-delay codes, with past reproductions available to the decoder but not to the encoder is bounded below by the state dependent nonanticipatory epsilon entropy rate. For the case of multivariate Gaussian Markov sources with square-error fidelity, the optimal test channel distribution and the complete characterization of the state dependent of nonanticipatory epsilon entropy are derived, and also shown that that the two nonanticipatory epsilon entropies coincide. The derivations are new; they are based on structural properties of the stochastic realizations of the reproduction process that induce the optimal test channel distributions. They are derived using, achievable lower bounds on information theoretic measures, properties of mean-square estimation theory, Hadamard’s inequality, and canonical correlation coefficients of a tuple of multivariate jointly Gaussian random processes. Applications of the nonanticipatory epsilon entropy and its state dependent variation are discussed to the areas of control of unstable Gaussian systems over limited memory channels, design of causal estimators for Gaussian Markov sources with a fidelity criterion, computation of the rate loss of causal and zero-delay codes of Gaussian Markov sources with respect to non-causal codes.

In this paper, we consider Wyner's [1] lossy distributed source coding problem of Fig. 1, for multivariate Gaussian distributed sources with square-error fidelity, when i) the side information, random variable (RV)$Y$, is available at the decoder only, and ii)$Y$is available at both the encoder and the decoder. We derive structural properties of optimal test channels that achieve the operational information rate distortion functions (RDFs) for i) and ii), i.e.,$\overline{R}(d)$and$R_{X\vert Y}(d)$, respectively. We also show there is no loss of compression if the side information$Y$is only available at the decoder, i.e.,$\overline{R}(d)=R_{X\vert Y}(d)$. This paper also points out that the two test channels of the RDF of the distributed remote source coding problem given in [2] and [3], do not generate Wyner's value of the RDF of scalar RVs, as one would expect; this observation implies that the results in [2, Theorem 4] and [3, Theorem 3A] should be read with caution.

In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs,$X_{1}:\Omega\rightarrow \mathbb{R}^{p_{1}}, X_{2}:\Omega\rightarrow \mathbb{R}^{p_{2}}$with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Gray's [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.

The multiple-input multiple-output (MIMO) generalization of Cover’s and Pombra’s Gaussian feedback capacity [1] is considered. A sequential characterization of the finite block or transmission feedback information (FTFI) capacity is derived, with the optimal channel input process expressed as functional of a sufficient statistic and a Gaussian orthogonal innovations process. From the new representations follows that the MIMO version of the Cover and Pombra characterization of the FTFI capacity is expressed as a functional of two generalized matrix difference Riccati equations (DRE) of filtering theory of Gaussian systems. Analogous expressions for nonfeedback capacity are also derived, which involve a Lyapunov equation. The derivations follow directly from [2]; application examples to autoregressive moving average noise are found in [3], and to autoregressive noise in [4], [5]. Asymptotic formulas of feedback, nonfeedback capacity, and achievable lower bound incurred by asymptotically stationary channel inputs follow from the analysis of [2, Section III].

Presented are closed-form feedback capacity formulas, and lower bounds on nonfeedback achievable rates, for additive Gaussian noise (AGN) channels, driven by unstable, i.e., nonstationary, and stable, autoregressive moving average noise, ARMA $(a,c),a\in(-\infty,\infty),c\in(-\infty,\infty)$ (with one pole at c and one zero at a), which are independent of the distributions of the initial random variables, i.e., the initial state of the noise. The feedback capacity exhibits multiple regimes of capacity; (i) for the regime that includes the stable noise, ARMA $(a,c),a\in(-{1},{1}), c\in$(−1, 1) and for all transmit powers $\kappa\in(0,\infty)$, feedback does not increase capacity, (ii) for the regime that includes the unstable noise, ARMA $(a,c), |c| \gt 1,a\in$(−1, 1), and for transmit power above a threshold $\kappa \gt \kappa_{{\min}}$, feedback increases capacity, and the higher the $|c|$ the higher the capacity. The unstable regime is verified by the semi-definite program of [1]. Although, our answer} feedback does not increase capacity for stable noise, ARMA $(a,c)$, $a\in$(−1, 1), $c\in$(−1, 1) contradicts the feedback capacity, $C_{FB}$, in [2, Theorem 6.1,] $C_{FB}]$, [1] and the maximal information rate, $I_{{\max}}$ in [3, Theorem 7,] $I_{{\max}}$, this is attributed to the fact that rates in [1] –[3], depend on the initial state of the noise, and these rates are not achievable, for asymptotically stationary noise. This paper uses results from [4].

The complete characterization of the Gorbunov and Pinsker [1], [2] nonanticipatory epsilon entropy of multivariate Gauss-Markov sources with square-error fidelity is derived, which remained an open problem since 1974. Specifically, it is shown that the optimal matrices of the stochastic realization of the optimal test channel or reproduction distribution, admit spectral representations with respect to the same unitary matrices, and that the optimal reproduction process is generated, subject to pre-processing and post-processing by memoryless parallel additive Gaussian noise channels. The derivations and analyses are new and bring out several properties of such optimization problems over the space of conditional distributions and their realizations.

The Gray and Wyner lossy source coding for a simple network for sources that generate a tuple of jointly Gaussian random variables (RVs) X1: Ω → Rp1and X2: Ω → Rp2, with respect to square-error distortion at the two decoders is reexamined using (1) Hotelling's geometric approach of Gaussian RVs-the canonical variable form, and (2) van Putten's and van Schuppen's parametrization of joint distributions PX1,X2,Wby Gaussian RVs W : Ω → Rnwhich make (X1,X2) conditionally independent, and the weak stochastic realization of (X1,X2). Item (2) is used to parametrize the lossy rate region of the Gray and Wyner source coding problem for joint decoding with mean-square error distortions E{||Xi- Xi||Rpi2} ≤ Δi∈ [0,∞],i = 1,2, by the covariance matrix of RV W. From this then follows Wyner's common information CW(X1,X2) (information definition) is achieved by W with identity covariance matrix, while a formula for Wyner's lossy common information (operational definition) is derived, given by CWL(X1,X2) =CW (X1,X2) = 1/2 Σj=1nIn (1+dj/1-dj), for the distortion region 0 ≤ Δ1≤ n(1-d1), 0 ≤ Δ2≤ n(1 - d1), and where 1 > d1≥ d2≥ ... ≥ dn> 0 in (0,1) are the canonical correlation coefficients computed from the canonical variable form of the tuple (X1,X2). The methods are of fundamental importance to other problems of multi-user communication, where conditional independence is imposed as a constraint.

In this paper we characterize the feedback capacity of Additive Gaussian Noise (AGN) channels driven by stable and unstable autoregressive noise, for time-invariant feedback codes (channel input distributions). For stable (resp. unstable) channel noise we identify necessary and sufficient conditions for the optimal input process to induce asymptotic stationarity and ergodicity of the channel output (resp. innovations) process. We call this the ergodic feedback capacity. From our characterization follows the surprising result: for a time-invariant unit memory Gaussian autoregressive noise AR(c), c ∈ (-∞, ∞), (i) feedback does not increase capacity for the region with c ∈ (-1, 1) and certain unstable c, and total transmit power κ ∈ [0,%), and (ii) feedback increases capacity for the compliment of the region of values of (c, κ), not covered in (i).

In this paper we employ the information structures of optimal channel inputs of feedback capacity of additive Gaussian noise (AGN) channels, driven by stable and unstable autoregressive noise, to derive achievable rates for nofeedback capacity, and the corresponding channel input processes. The expressions of rates are derived using time-domain methods, they hold for stable and unstable noise, for all values of transmit power. The method avoids power spectral techniques and their limitations. The lower bounds are evaluated against the classical nonfeedback capacity obtained via water-filling frequency-domain techniques.

Shannon's coding capacity of memoryless additive Gaussian noise (AGN) channels with noiseless feedback, is known to be achieved by the Elias [1] coding scheme of communicating the mean square-error (MSE) of a Gaussian RV X ~ N(0, σ'), from past channel outputs, and decoding it using a MSE decoder. Further, it is known that among all encoders, and decoders that minimize the MSE, then the Elias encoder and decoder are globally optimal. In this paper we derive analogous results, for communicating unstable Gaussian Markov processes over unstable multiple-input multiple-output (MIMO) Gaussian recursive models (GRM) with memory, often called infinite impulse response (IIR) models, subject to an average cost of quadratic form. However, unlike memoryless AGNs, certain conditions are required, for such generalizations. Further, to show global optimality, we need to invoke Gorbunov and Pinsker [2] nonanticipatory € entropy, instead of the classical rate distortion function of the source. Another important observation is that we need a two-parameter coding scheme, instead of the one-parameter coding scheme of memoryless AGN channels.

A method is developed to realize optimal channel input conditional distributions, which maximize the finite transmission feedback information (FTFI) capacity, often called $n$ -block length feedback capacity, by information lossless randomized strategies. The method is applied to compute closed form expressions for the FTFI capacity and feedback capacity, of nonstationary, nonergodic, unstable, multiple input multiple output Gaussian channels with memory on past channel outputs, subject to average transmission cost constraints of quadratic form in the channel inputs and outputs. It is shown that randomized strategies decompose into two orthogonal parts-an deterministic part, which controls the channel output process, and an innovation part, which transmits new information over the channel. Then a separation principle is shown between the computation of the optimal deterministic part and the random part of the optimal randomized strategies. Finally, the ergodic theory of linear-quadratic-Gaussian stochastic optimal control theory, is applied to identify sufficient conditions, expressed in terms of solutions to matrix difference and algebraic Riccati equations, so that the optimal control part of randomized strategies induces asymptotic stationarity and ergodicity, and feedback capacity is characterized by the per unit time limit of the FTFI capacity. The method reveals an interaction of the control and the information transmission parts of the optimal randomized strategies, and that whether feedback increases capacity, is directly related to the channel parameters and the transmission cost function, through the solutions of the matrix Riccati equations. For unstable channels, it is shown that feedback capacity exists and it is strictly positive, provided the power exceeds a critical threshold.

Stochastic optimal control theory and a variational equality of directed information are applied, to develop a methodology to identify the information structures of optimal channel input conditional distributions, which maximize directed information, for classes of channel conditional distributions and transmission cost functions that depend on previous channel output symbols. The subsets of the maximizing distributions are characterized by conditional independence. One of the main theorems of this paper states that, for any channel conditional distribution with finite memory on past channel outputs, subject to an average cost constraint, then the information structure of the optimal channel input conditional distribution, which maximizes directed information, is determined by the maximum of the memory of the channel distribution and the functional dependence of the transmission cost function on past channel outputs. This theorem provides, for the first time, a direct analogy, in terms of the conditional independence properties of maximizing distributions, between the characterization of feedback capacity of channels with memory, and Shannon's two-letter characterization of capacity of memoryless channels. Another main result of the paper is the identification of sufficient conditions for the validity of direct and converse coding theorems, for unstable Gaussian channel models with memory, that is based on the ergodic theory of Markov decision.

Feedback capacity is extended beyond classical communication channels, to stochastic dynamical systems, which may correspond to unstable control systems or unstable communication channels, subject to average cost constraints of total power κ ∈ [0, ∞). It is shown that optimal conditional distributions or randomized strategies, have a dual role, to simultaneously control the output process and to encode information. The dual role is due to the interaction of control and information transmission; it states that encoders in communication channels operate as encoders-controllers, while controllers in control systems operate as controllers-encoders. The concepts are illustrated through the analysis of Gaussian control systems with randomized strategies, which are equivalent to Additive Gaussian Noise channels, Stable or Unstable, with arbitrary memory on past outputs, with an average constraint of quadratic form. It is shown that such unstable dynamical systems have Control-Coding Capacity which is operational, precisely as in Shannon's operational definition. However, the control-coding capacity is zero, unless the power κ allocated to the system, exceeds a threshold Kmin, where Kminis the minimum cost of ensuring asymptotic stability and ergodicity. The excess power κ - Kminis turned into an achievable rate of information transmission over the dynamical system.

For a class of channels with unit memory on previous channels outputs, we identify necessary and sufficient conditions, to test whether the capacity achieving channel input distributions with feedback are time-invariant, and whether feedback capacity is characterized by a two-letter expression, similar to that of memoryless channels. The method is based on showing that a certain dynamic programming equation, which in general, is a nested optimization problem over the sequence of channel input distributions, reduces to a non-nested optimization problem. We then apply these conditions to derive a two-letter expression for the feedback capacity of the Binary State Symmetric Channel, which is evaluated explicitly. Further, we derive computationally efficient upper bounds on the probability of maximum likelihood decoding error in the finite-blocklength regime.

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal “test-channel” of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.

We derive sequential necessary and sufficient conditions for any channel input conditional distribution P0,n=Δ{PXt|Xt-1,Yt-1: t = 0, ..., n} to maximize the finite-time horizon directed information defined by CXn→YnFB =ΔsupP0,nI(Xn→ Yn), where I(Xn→ Yn) = Σt=0nI(Xt; Yt|Yt-1), for channel distributions {PYt|Yt-1,Xt: t = 0, ..., n} and {PYt|Yt-Mt-1,Xt: t = 0, ..., n}, where Yt =Δ{Y-1, Y0, ..., Yt} and Xt =Δ{X0, ..., Xt} are the channel input and output random processes, and M is a finite non-negative integer. We apply the necessary and sufficient conditions to application examples of time-varying channels with memory to derive recursive closed form expressions of the optimal distributions, which maximize the finite-time horizon directed information. Furthermore, we derive the feedback capacity from the asymptotic properties of the optimal distributions by investigating the limit CX∞→Y∞FB =Δlimn→∞(1/(n + 1))CXn→YnFBwithout any á priori assumptions, such as stationarity, ergodicity, or irreducibility of the channel distribution. The framework based on sequential necessary and sufficient conditions can be easily applied to a variety of channels with memory, beyond the ones considered in this paper.

The information structures of the optimal channel input distributions P[0,n]=Δ{PAi|Ai-1, Bi-1: i = 0,1,..., n}, which correspond to the extremum problem of feedback capacity CAn→BnFB=Δsup P[0,n]Σi=0nI(Ai;Bi|Bi-1) are identified, for any class of channel distributions {PBi|Bi-1,Ai: i = 0,1,...,n} and {PBi|Bi-Mi-1,Ai: i = 0,1,...,n}, where Bn=Δ{Bj: j = 0,1,...,n} are the channel output RVs, An=Δ{Aj: j = 0,1,...,n} are the channel inputs RVs, and M is a finite nonnegative integer. The methodology utilizes stochastic optimal control theory, to identify the control process, the controlled process, and a variational equality of directed information, to derive upper bounds on I(An→ Bn)=ΔΣi=0nI(Ai;Bi|Bi-1), which are achievable over specific subsets of P[0,n], which satisfy conditional independence. The main theorem states, that for any channel with memory M, the optimal channel input conditional distribution occur in the subset P[0,n]=Δ{PAi|Bi-Mi-1: i = 1,...,n} ⊂ P[0,n], and the corresponding extremum problem simplifies to the following characterization CAn→BnFB,M=Δsup P[0,n]Σi=0nI(Ai;Bi|Bi-Mi-1).

A discrete compound channel with memory is considered, where no stationarity, ergodicity or information stability is required, and where the uncertainty set can be arbitrary. When the discrete noise is additive but otherwise arbitrary and there is no cost constraint on the input, it is shown that the causal feedback does not increase the capacity. This extends the earlier result obtained for general channels with full transmitter (Tx) channel state information (CSI). It is further shown that, for this compound setting and under a mild technical condition on the additive noise, the addition of the full Tx CSI does not increase the capacity either, so that the worst-case and compound channel capacities are the same, thus revealing a saddle-point property.

We derive Sequential Necessary and Sufficient Conditions (SNSC) for any channel input distribution P0,n=̑{P((Xt)|Xt-1,Yt-1):t=0,1,...,n} to maximize directed information for channel distributions of the form {P(Yt|Yt-Mt-1,xt): t=0,1,...,n} where Xn=̑{X0...,Xn} , and Yn=̑{Y0,...,Yn} are the channel input and output random variables, and M is nonnegative and finite. The results are obtained using the information structures of the optimal channel input distributions and the corresponding Finite Transmission Feedback Information (FTFI) capacity, convexity properties of directed information, and dynamic programming recursions. The conditions are applied to a finite alphabet channel with M = 1 to derive recursive closed form expressions for the optimal (nonstationary) distributions, which achieve the FTFI capacity. Further, ergodic feedback capacity is obtained in closed form, using the asymptotic properties of the optimal distributions. A numerical example is presented to illustrate the convergence properties of the per unit time limiting version of the FTFI capacity.

Capacity-achieving signaling strategies for the Gaussian wiretap multiple-input multple-output (MIMO) channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance matrix are obtained. The case of a weak eavesdropper is considered in detail, and the optimal covariance is established in an explicit, closed form with no extra assumptions. This provides lower and upper bounds to the secrecy capacity in the general case with a bounded gap, which are tight for a weak eavesdropper or/and low SNR. Closed-form solutions are also obtained for isotropic and omnidirectional eavesdroppers, based on which lower and upper bounds to the secrecy capacity are established in the general case. Sufficient and necessary conditions for the optimality of three popular transmission techniques, namely, the zero-forcing (ZF), the standard water-filling over the channel eigenmodes, and the isotropic signaling (IS), are established for the MIMO wiretap channel. These solutions are appealing due to their lower complexity. In particular, no wiretap codes are needed for the ZF transmission, and no precoding or feedback is needed for the isotropic signaling.

Directed information or its variants are utilized extensively in the characterization of the capacity of channels with memory and feedback, nonanticipative lossy data compression, and their generalizations to networks. In this paper, we derive several functional and topological properties of directed information, defined on general abstract alphabets (complete separable metric spaces), using the topology of weak convergence of probability measures. These include the convexity of the set of consistent distributions, which uniquely define causally conditioned distributions, convexity, and concavity of directed information with respect to the sets of consistent distributions, weak compactness of such sets of distributions, their joint distributions, and their marginals. Furthermore, we show lower semicontinuity of directed information, and under certain conditions, we also establish continuity. Finally, we derive variational equalities for directed information, including sequential versions. These may be viewed as the analog of the variational equalities of mutual information (utilized in Blahut-Arimoto algorithms). In summary, we extend the basic functional and topological properties of mutual information to directed information. These properties are discussed throughout this paper, in the context of extremum problems of directed information.

Optimal signaling over the Gaussian multiple-input multiple-output wire-tap channel is studied under the total transmit power constraint. A closed-form solution for an optimal transmit covariance matrix is obtained when the channel is strictly degraded. In combination with the rank-1 solution, this provides the complete characterization of the optimal covariance for the case of two transmit antennas. The cases of weak eavesdropper and high SNR are considered. It is shown that the optimal covariance does not converge to a scaled identity in the high-SNR regime. Necessary optimality conditions and a tight upper bound on the rank of an optimal covariance matrix are established for the general case, along with a lower bound to the secrecy capacity, which is tight in a number of scenarios.

In this paper we analyze nonanticipative (delayless) transmission of source symbols with memory over channels with memory (with and without feedback). We employ duality of {source, channel} pairs with respect to {distortion function, transmission cost} pairs to show achievability of nonanticipative transmission in terms of excess distortion probability. We apply the method to the Binary Markov source with Hamming distortion function and the Binary Unit Memory channel with transmission cost, with the joint-design operating optimally and in real-time, with and without feedback encoding and decoding.

A general formula for the capacity of arbitrary compound channels, which are not necessarily ergodic, stationary or information-stable, is obtained using the information density approach. A direct (constructive) proof is given. To prove achievability, we generalize Feinstein Lemma to the compound channel setting, and to prove converse, we generalize Verdu-Han Lemma to the same compound setting. This extends the general formula for channel capacity in [8] to arbitrary compound channels (not necessarily finite-state or countable).

We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution for the BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC, with or without feedback, is achieved by a first order symmetric Markov process.

Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the optimality of Gaussian signalling, an optimal transmit covariance matrix is known for some special cases only and the general case remains an open problem. An iterative custom-made algorithm to find a globally-optimal transmit covariance matrix in the general case is developed in this paper, with guaranteed convergence to a global optimum. While the original optimization problem is not convex and hence difficult to solve, its minimax reformulation can be solved via the convex optimization tools, which is exploited here. The proposed algorithm is based on the barrier method extended to deal with a minimax problem at hand. Its convergence to a global optimum is proved for the general case (degraded or not) and a bound for the optimality gap is given for each step of the barrier method. The performance of the algorithm is demonstrated via numerical examples. In particular, 20 to 40 Newton steps are already sufficient to solve the sufficient optimality conditions with very high precision (up to the machine precision level), even for large systems. Even fewer steps are required if the secrecy capacity is the only quantity of interest. The algorithm can be significantly simplified for the degraded channel case and can also be adopted to include the per-antenna power constraints (instead or in addition to the total power constraint). It also solves the dual problem of minimizing the total power subject to the secrecy rate constraint.

Novel matrix singular value inequalities are established for a sum/product of three matrices. Their application to the uncertain (compound) multiple-input multiple-output (MIMO) channel subject to normed additive uncertainty establishes the saddle-point property for a wide range of performance metrics monotonic in the channel singular values, including, among others, the mutual information, MMSE, error exponent, and pairwise error probability. This, in turn, implies that the transmission on the eigenmodes of the nominal (or worst case) channel is also optimal for the whole set of channels under a general power constraint and hence achieves the compound channel capacity. The worst case channel turns out to be antiparallel of the nominal one for all these performance metrics. An application of these results to beamforming over compound MIMO channels is discussed. An optimal robust precoder for the uncertain MIMO channel is obtained in a closed-form under the sum-MSE criterion and the total power constraint. The saddle-point property is shown to hold and the optimal strategy is to diagonalize the nominal (or worst case) channel.

Capacity-achieving signaling strategies for the Gaussian wiretap MIMO channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance matrix are obtained. The case of weak eavesdropper is considered in details and the optimal covariance is established in an explicit, closed-form with no extra assumptions. The conditions for optimality of zero-forcing signaling are established, and the standard water-filling is shown to be optimal under those conditions. No wiretap codes are needed in this case. The case of identical right singular vectors for the required and eavesdropper channels is studied and the optimal covariance is established in an explicit closed form. As a by-product of this analysis, we establish a generalization of celebrated Hadamard determinantal inequality using information-theoretic tools.

The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter p (BSMS(p)) with Hamming distance distortion, and the multidimensional partially observed Gaussian-Markov source. For the BSMS(p), we give the solution to the NRDF, and we use it to compute the Rate Loss (RL) of causal codes with respect to noncausal codes. For the multidimensional Gaussian-Markov source, we give the solution to the NRDF, we show its operational meaning via joint source-channel matching over a vector of parallel Gaussian channels, and we compute the RL of causal and zero-delay codes with respect to noncausal codes.

This paper presents lossless prefix codes optimized with respect to a payoff criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new coding algorithm, which transforms the initial source probability vector into a new probability vector according to a merging rule. The coding algorithm is equivalent to a partition of the source alphabet into disjoint sets on which a new transformed probability vector is defined as a function of the initial source probability vector and scalar parameter. The payoff criterion considered encompasses a tradeoff between maximum and average codeword length; it is related to a payoff criterion consisting of a convex combination of average codeword length and average of an exponential function of the codeword length, and to an average codeword length payoff criterion subject to a limited length constraint. A special case of the first related payoff is connected to coding problems involving source probability uncertainty and codeword overflow probability, whereas the second related payoff compliments limited length Huffman coding algorithms.

Optimal signalling over the wire-tap MIMO Gaussian channel is studied under the total transmit power constraint. The recent results are extended in several directions, including a rank-deficient solution for the optimal covariance, lower and upper capacity bounds for the general case, and characterization of optimality of the isotropic signaling. An isotropic eavesdropper model is studied, which provides (tight) upper and lower capacity bounds for the non-isotropic case and also serves as the worst-case scenario. The optimal signaling for this model is obtained in an explicit form and its properties are studied, including the high and low-SNR behavior, the conditions for the eavesdropper to be negligible and the capacity saturation effect.

In this paper we introduce two variational equalities of directed information, which are analogous to those of mutual information employed in the Blahut-Arimoto Algorithm (BAA). Subsequently, we introduce nonanticipative Rate Distortion Function (RDF) Ro, nna(D) defined via directed information introduced in, and we establish its equivalence to Gorbunov-Pinsker's nonanticipatory ε-entropy Ro, nε(D). By invoking certain results we first establish existence of the infimizing reproduction distribution for Ro, nna(D), and then we give its implicit form for the stationary case. Finally, we utilize one of the variational equalities and the closed form expression of the optimal reproduction distribution to provide an algorithm for the computation of Ro, nna(D).

This paper describes a framework in which directed information is defined on abstract spaces. The framework is employed to derive properties of directed information such as convexity, concavity, lower semicontinuity, by using the topology of weak convergence of probability measures on Polish spaces. Two extremum problems of directed information related to capacity of channels with memory and feedback, and non-anticipative and sequential rate distortion are analyzed showing existence of maximizing and minimizing distributions, respectively.

Optimal signalling over the wire-tap MIMO Gaussian channel is studied under the total transmit power constraint. A direct proof of the necessary condition of optimality (signaling on the positive directions of the difference channel) is given using the necessary KKT conditions. Based on it, an explicit, closed-form solution for the optimal transmit covariance matrix is given when the latter is of the full rank. The cases of weak eavesdropper and high SNR are considered. It is shown that the optimal covariance does not converge to a scaled identity in the latter regime. A refined estimate of the rank of an optimal covariance matrix is given for the general case.

Outage probability and capacity of a class of block fading MIMO channels are considered under partial channel distribution information. Specifically, the channel or its distribution is not known but the latter is known to belong to a class of distributions where each member is within a certain distance (uncertainty) from a nominal distribution. Relative entropy is used as a measure of distance between distributions. Compound outage probability defined as min (over the transmitted signal distribution) -max (over the channel distribution class) outage probability is introduced and investigated. This generalizes the standard outage probability to the case of partial channel distribution information. Compound outage probability characterization (via 1-D convex optimization and in a closed form), its properties, and approximations are given. It is shown to have two-regime behavior: when the nominal outage probability decreases (e.g., by increasing the SNR), the compound outage first decreases linearly down to a certain threshold (related to the relative entropy distance; this is the nominal outage-dominated regime) and then only logarithmically (i.e., very slowly; this is the uncertainty-dominated regime) so that no significant further decrease is possible. This suggests the following design guideline: the outage probability is decreased by increasing the SNR or optimizing the transmitted signal distribution (both decrease nominal outage) in the first regime and by reducing the channel distribution uncertainty (e.g., via better estimation) in the second one. The compound outage depends on the relative entropy distance and the nominal outage only, all other details (nominal fading and noise distributions) being irrelevant. The transmit signal distribution optimized for the nominal channel distribution is shown to be also optimal for the whole class of distributions. The effect of swapping the distributions in relative entropy is investigated and an error floor effect is established. The compound outage probability under Lpdistance constraint is also investigated. The obtained results hold in full generality, i.e., for the general channel model with arbitrary nominal fading and noise distributions.

The compound capacity of uncertain multiple-input multiple-output channels is considered, when the channel is modeled by a class described by a (known) nominal channel and a constrained-norm (unknown) uncertainty. Within this framework, two types of classes are investigated with additive and multiplicative uncertainties subject to a spectral norm constraint, using the singular value decomposition and related singular value inequalities as the main tools. The compound capacity is a maxmin mutual information, representing the capacity of the class, in which the minimization is done over the class of channels while the maximization is done over the transmit covariance. Closed-form solutions for the compound capacity of the classes are obtained and several properties related to transmit and receive eigenvectors are presented. It is shown that, under certain conditions, the compound capacity of the class is equal to the worst-case channel capacity, thus establishing a saddle-point property. Explicit closed-form solutions are given for the worst-case channel uncertainty and the capacity-achieving transmit covariance matrix: the best transmission strategy achieving the compound capacity is a multiple beamforming on the nominal (known) channel eigenmodes with the beam power distribution via the water filling at a degraded SNR. As the uncertainty increases, fewer eigenmodes are used until only the strongest one remains active so that transmit beamforming is an optimal robust transmission strategy in this large-uncertainty regime, for which explicit conditions are given. Using these results, upper and lower bounds of the compound capacity are constructed for other bounded uncertainties and some generic properties are pointed out. The results are extended to compound multiple-access and broadcast channels. In all considered cases, the price to pay for channel uncertainty is an SNR loss (or, equivalently, the nominal channel degradation) commensurate with the uncertainty set radius measured by the spectral norm and the optimal signaling strategy is the transmission on the degraded nominal channel.

This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length, or, a convex combination of the average of an exponential function of the codeword length and the average codeword length. This framework encompasses as a special case several criteria previously investigated in the literature, while relations to universal coding is discussed. The coding algorithm derived is parametric resulting in re-adjusting the initial source probabilities via a weighted probability vector according to a merging rule. An algorithm is presented to compute the weighting vector.

Outage probability of a class of block-fading (MIMO) channels is considered under channel distribution uncertainty, when the channel or its distribution are not known but the latter is known to belong to a class of distributions where each member is within a certain distance from a nominal distribution. Relative entropy is used as a measure of distance between distributions. Compound outage probability defined as min (over the input distribution) -max (over the channel distribution class) outage probability is introduced and investigated, which generalizes the standard outage probability to the case of partial channel distribution information. Compound outage probability characterization via one-dimensional convex optimization, its properties and approximations are given. It is shown to have a two-regime behavior: when the nominal outage probability decreases, the compound outage first decreases linearly down to a certain threshold and then only logarithmically (i.e. very slowly), so that no significant further decrease is possible. The input distribution optimized for the nominal channel distribution is shown to be also optimal for the whole class of distributions. The effect of swapping the distributions in relative entropy is investigated and an error floor effect is established. The obtained results hold for a generic channel model (arbitrary nominal fading and noise distributions).

In this letter, filtering over wireless communication channels subject to packet losses is considered. The packet losses are assumed to follow a Bernoulli distribution. The latter is interpreted as a special case of a Markov process for which hybrid filtering theory is shown to provide an exact solution. Unlike existing works where only the linear optimal state estimate is derived as a linear function of measurements, this paper shows that the optimal state estimate is in fact a nonlinear function of measurements. In addition, the optimal estimator is derived explicitly. Illustrative examples compare the performance of the linear optimal estimator and the optimal estimator, and show that the latter offer superior performance, in particular for unstable systems.

As the CMOS semiconductor technology enters nanometer regime, interconnect processes must be compatible with device roadmaps and meet manufacturing targets at the specified wafer size. The resulting ubiquitous process variations cause errors in data delivering through interconnects. This paper proposes an Information Theory based design method to accommodate process variations. Different from the traditional delay based design metric, the current approach uses achievable rate to relate interconnect designs directly to communication applications. More specifically, the data communication over a typical interconnect, a bus, subject to process variations (“uncertain” bus), is defined as a communication problem under uncertainty. A data rate, called the achievable rate, is computed for such a bus, which represents the lower bound on the maximal data rate attainable over the bus. When a data rate applied over the bus is smaller than the achievable data rate, a reliable communication can be guaranteed regardless of process variations, i.e., a bit error rate arbitrarily close to zero is achievable. A single communication strategy to combat the process variations is proposed whose code rate is equal to the computed achievable rate. The simulations show that the variations in the interconnect resistivity could have the most harmful effect regarding the achievable rate reduction. Also, the simulations illustrate the importance of taking into account bus parasitic parameters correlations when measuring the influence of the process variations on the achievable rates.

This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropyD(middot||middot) such thatD(p||pnom) lesd,dges 0, wheredis the distance from the so-called nominal channel matrix distribution pnom(H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution pnom(H) and parameterd. A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect todis shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.

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$H^{\infty}$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.

This paper considers nonlinear estimation problems for classes of models, and employs relative entropy to describe the uncertainty classes. Two optimization problems are formulated on general Banach spaces, and their solutions are sought: 1) when the transition probability between the signal to be estimated X and the measurement Y or stochastic kernel is unknown, and 2) when the joint probability induced by the random variables (RVs) X, Y is unknown. For both problems, the uncertainty is described by a relative entropy constraint between the unknown distribution and a fixed nominal distribution. The results include existence of the optimal measures using weak convergence techniques, and properties associated with the estimate of the true distribution. Classical examples are chosen to illustrate the applicability of the results.

Mobile-to-mobile networks are characterized by node mobility that makes the propagation environment time varying and subject to fading. As a consequence, the statistical characteristics of the received signal vary continuously, giving rise to a Doppler power spectral density (DPSD) which varies from one observation instant to the next. The current models do not capture and track the time varying characteristics. This paper is concerned with dynamical modeling of time varying mobile-to-mobile channels, parameter estimation and identification from received signal measurements. The evolution of the propagation environment is described by stochastic differential equations, whose parameters can be determined by approximating the band-limited DPSD using the Gauss-Newton method. However, since the DPSD is not available online, we propose to use a filter-based expectation maximization algorithm and Kalman filter to estimate the channel parameters and states, respectively. The scheme results in a finite dimensional filter which only uses the first and second order statistics. The algorithm is recursive allowing the inphase and quadrature components and parameters to be estimated online from received signal measurements. The algorithms are tested using experimental data collected from moving sensor nodes in indoor and outdoor environments demonstrating the method's viability.

The compound capacity of uncertain MIMO channels is considered, when the channel is modeled by a class described by an induced norm constraint. Within this framework, two types of classes are investigated, namely, additive and multiplicative uncertainties subject to a spectral norm constraint, using partial channel state information at the transmitter side. The compound capacity is defined as a maxmin of the mutual information, corresponding to the capacity of the class, in which the minimization is done over the class of channels while the maximization is done over the transmit covariance. Closed form solutions for the compound capacity of the classes are obtained while several properties related to transmit and received eigenvectors are presented. It is also shown that capacity of the class of channels is equal to the worst-case channel capacity, while establishing a saddle-point property. Additionally, explicit closed-from solutions are given for the capacity-achieving Tx covariance matrix and the worst-case channel uncertainty. The effect of uncertainty is shown to be equivalent to an SNR loss which is proportional to the size of the uncertainty of the channel matrix measured by the spectral norm.

This paper derives robust minimax estimators for a class of uncertain models. The uncertainty is described by a relative entropy constraint between the unknown joint distribution and a fixed nominal joint distribution. The maximization is addressed using variational methods, while the minimization is addressed using the concept of a sufficient statistic, which is an unnormalized version of the a posteriori density. The theory developed is applied to multipath fading wireless channels, to derive minimax envelope and phase estimates. Related results are also derived when the uncertainty shrinks to zero.

This paper is concerned with modeling and identification of wireless channels using noisy measurements. The models employed are governed by stochastic differential equations (SDEs) in state space form, while the identification method is based on the expectation-maximization (EM) algorithm and Kalman filtering. The algorithm is tested against real channel measurements. The results presented include state space models for the channels, estimates of inphase and quadrature components, and estimates of the corresponding Doppler power spectral densities (DPSDs), from sample noisy measurements. Based on the available measurements, it is concluded that state space models of order two are sufficient for wireless flat fading channel characterization.

The control of partially observed jump linear systems over jump communication channels is investigated when the Plant State Information (PSI) and the Channel State Information (CSI) are present at the transmitter and the receiver side of the communication channel. The PSI refers to the state of a Markov chain driving the plant dynamics, while the CSI is the state of a Markov chain driving the communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean are derived by using information transmission theorem and Shannon's lower bound on the rate distortion. Based on the source-channel matching principle, a transmission technique is designed that achieves observability and stabilizability of the controlled jump system in mean-square sense.

This paper addresses the issue of multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix is modelled by using a relative entropy D(pparq). All possible channel matrix distributions p(H) satisfy D(pparpnom) les d, d ges 0, i.e., they lie within d distance from the so-called nominal channel matrix distribution pnom(H). The information channel capacity is defined as a maximin optimization problem, where the mutual information is a pay-off function. The minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. Based on the derived characteristics of the pay-off function, the formula for the channel matrix distribution, which minimizes the mutual information, is derived. In the case of the Rayleigh fading, the formula for the information capacity and the optimal transmit covariance matrix are obtained. In addition, the existence of the saddle point of the maximin optimization problem is established for this particular case

This paper considers nonlinear estimation problems for a class of models, and employs relative entropy to describe the uncertainty classes. Two problems are formulated and their solutions are sought. 1) When the transition probability between the signal to be estimated X and the measurement Y or stochastic kernel is unknown, and 2) when the joint probability induced by the R.V.'s X, Y is unknown. For both problems, the uncertainty is described by a relative entropy constraint between the unknown distribution and a fixed nominal distribution. The solutions provided bring forward some properties associated with the estimate of the true distribution. Classical examples are chosen to illustrate the applicability of the results

Due to node mobility and environmental changes in mobile ad-hoc networks, the ad-hoc channel is time varying and subject to fading. As a consequence of these variations, the statistical characteristics of the received signal vary continuously, giving rise to a Doppler power spectral density (DPSD) which varies from one observation instant to the next. As a result, the traditional models can no longer capture and track complex time variations in the propagation environment. These time variations compel us to introduce more advanced dynamical models in order to capture higher order dynamics of the ad-hoc channel. A stochastic ad-hoc short term fading channel model, in which the evolution of the dynamical channel is described by a stochastic state space representation, is derived. The parameters of the stochastic state space model are determined by approximating the band limited DPSD. Inphase and quadrature components of the ad-hoc channel are derived. Numerical results show that link performance for ad-hoc case is worse than cellular case, but the performance gap shrinks with increased mobility

This paper is concerned with designing minimum average length uniquely decodable codes, for a family of source distributions for which the relative entropy with respect to a given nominal distribution is bounded above by some fixed number. This formulation leads to a minimax source coding problem, in which the minimizing players are the codeword lengths, while the maximizing players are the uncertain source distributions. It is further shown, via a large deviations duality relation, that the minimax source coding problem is equivalent to a coding problem which minimizes the average of an exponential pay-off instead of the conventional average length pay-off. Both Shannon coding and Huffman coding methods are generalized to this new criterion of performance, leading to robust codes which perform well with respect to an uncountable family of source distributions. However, the code lengths are designed with respect to a known nominal distribution, which is obtained either through modeling assumptions or via empirical techniques. Simulations are also presented comparing the Shannon/Huffman codes with the robust codes, when the source distribution is uncertain, while a sensitivity analysis shows that the new codes are much less sensitive to the uncertainty description. In addition, a fixed length source coding theorem is derived in which the encoding error tends to zero as the length of the codes tends to infinity, uniformly over the set of uncertain distributions which satisfy the relative entropy bound. Finally, generalizations to uncertainty described by the total variation norm is discussed.

The paper presents a new two-step cellular location determination (CLD) method based on signal strength and wave scattering models. The received signal level (RSL) method is first used in combination with maximum likelihood estimation (MLE) and triangulation to obtain an estimate of the location of the mobile. Due to non line of sight (NLOS) conditions and multipath propagation, this estimate lacks acceptable accuracy and consistency for demanding services, as numerical simulations reveal. Thus, the wave scattering 3D multipath channel model of Aulin is employed together with extended Kalman filtering (EKF) to obtain improved location estimates with high accuracy. The EKF is initialized at the MLE obtained from the RSL method, which is proved to be highly appropriate. Numerical simulations under urban, suburban and rural environments were utilized to evaluate the accuracy and consistency of the proposed two-step enhanced RSL method; the results of the worst-case rural environment are presented.

The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations (SDEs). The latter capture the spatio-temporal variations of the communication link, as well as the randomness. This class of models is more realistic than the static models usually encountered in the literature. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy by using Chernoff bounds. Moreover, the Chernoff bound is computed explicitly, while the solution of the stochastic optimal power control is obtained through pathwise optimization. The pathwise optimization can be solved using linear programming if predictable control strategies are introduced. Finally, if predictable control strategies do not hold, it is shown that the proposed power control problem reduces to particular convex optimizations.

The user retrial phenomenon and its significant impact on network performance in unicast wireless systems are known and relatively well studied in the literature. However, there have been no previous studies on the impact of the user retrial phenomenon on other types of wireless networks. The objective of this paper is to extend the analysis of the user retrial phenomenon to wireless systems which, in addition to unicast service, also support a data broadcast service. This objective is realized by defining several performance measures appropriate for the analysis of hybrid unicast-broadcast systems in the presence of users' retrials. Subsequently, we derive the exact mathematical expression for each of the measures. Based on these expressions, we prove the existence of a single broadcast scheduling scheme, which ensures optimal system performance, with respect to the given set of proposed measures, the system's throughput, and the grade and quality of service. We also take a closer look at the class of hybrid unicast-broadcast systems with autonomous estimation of data item popularities, and we elaborate on the major challenges associated with such systems. Finally, we evaluate our theoretical expressions through simulation, and we discuss their robustness with respect to moderate deviations in the underlying model.

In recent years, both wireless data broadcast (WDB) and hierarchical cell structure (HCS) have attracted the attention of the scientific community, yet they have been treated as entirely separate research topics. This paper presents one of the first attempts to bring the two subjects together. In particular, the paper deals with the issue of optimized data broadcast in systems of hierarchical cellular organization. We see the following as the main contributions of the paper: 1) considerably superior performance of HCS-over single-layer- WDB system is proven; 2) an algorithm for fast identification of the optimal broadcast schedule in HCS-WDM systems is proposed. As we are moving in the era of pervasive computing, where millions of devices - many of them of mobile and nomadic nature - will be requesting network support for retrieval of information, development of efficient wireless based transfer systems become immensely important.

This paper is a continuation of a companion paper, in which multipath fading channels (MFC) are formulated as generalizations of the shot-noise analysis in investigating the statistical properties of wireless channels and their responses to different signals. These include second-order statistics, generalizations of Campbell's theorem and central-limit theorems. An application of the results to wide-sense-stationary-uncorrelated-scattering (WSSUS) channels reveals the effects of the rate of the counting process in shaping the power delay profile and Doppler spread of the channel.

The analysis, modeling and simulation of time-varying multipath wireless fading channels is usually done through input-output descriptions of the channel. In this paper, we introduce the concept of the state of the channel which is the solution of stochastic differential equations driven by white-noise (Brownian motion). In particular, we show that the dynamics of the instantaneous power associated with each path can be modeled using mean-reverting Ornstein-Uhlenbeck processes, and higher order models. These models are easy to analyze, implement and simulate, and therefore are important in the design and operation of wireless communication systems. The densities of these state processes are given by generalizations of the standard Rayleigh, Ricean, Nakagami-m densities.

We introduce, the use of the shot-noise analysis, brought forward by Rice (1944), as a natural tool in computing the various statistical properties of the multipath fading channels, in wireless communications. By adapting and generalizing this theory we derive the various statistical properties of the channel, including the second-order statistics, generalizations of Campbell's theorem and central-limit theorems.