In cognitive radio networks, secondary users (SUs) can access the spectrum licensed by primary users (PUs) in an opportunistic fashion provided they cause no harmful interference to primary transmissions. Assuming that selfish and malicious but rational types of SUs are present in the network, we consider a setting where the PUs can also benefit from the cooperation with the SUs. The SUs are autonomous agents, have disparate interests and aim at maximizing their own type-dependent interests. Since misbehaving users can impede the PUs' communications by malicious or selfish actions, we develop a trust management scheme employed by the PUs that rewards cooperative SUs and punishes non-cooperative ones. We study the impact of trust on both types of misbehaving SUs' optimal decision-making process, by utilizing the Markov Decision Process framework, and we derive conditions that provably thwart malicious and selfish behavior for certain model parameters.

Constructions of secure channel encoders, based on secret pruning, are considered in this paper. The key defines how pruning is applied on a mother convolutional code. This results in a secret subspace that legitimate users are using to perform decoding, in contrast to an eavesdropper that employs the mother code. Both reliability and security aspects of the joint scheme are treated. We derive the expected weight enumerating function of the secret subcode and show that the legitimate users achieve a better performance (that depends on the pruning rate) in terms of word and bit error rate compared with the eavesdroppers. The security relies on the notion of indistinguishability against chosen plaintext attacks. The security proofs are given in the random oracle model, and it is shown that a randomized version of the proposed joint scheme is semantically secure by relying on the hardness of the learning parities with noise problem. The above-mentioned results are achieved by introducing a new model for physical encryption to consider the contribution of the channel noise to the system's security.

A cooperative jamming protocol is studied in this paper and its ability to protect the communications of a pair of users in the presence of an eavesdropper. Communication of users is assisted by many helping interferers, assuming knowledge of channel state information. Closed form expressions are given for the optimal weights and power allocation maximizing the difference in the SNR between destination and eavesdropper; these are determined under transmit, reliability, and security constraints. Simulations show that noticeable improvements, of more than 30dB, may be attained in the SNR difference compared to the non-cooperative case.

Secure encoders are schemes aiming at providing both reliability and security in a lightweight fashion. In this paper, a secure channel encoder based on turbo codes is constructed by using the techniques of puncturing and trellis pruning. Puncturing is employed to downgrade the performance of the code and thus increase the error probability experienced by an eavesdropper at a given SNR. This has the advantage that various cryptanalytic attacks, whose complexity depends on the error probability, will become infeasible. On the other hand, trellis pruning is implemented in a secret fashion to enable legitimate users communicate reliably. An algorithm that, based on EXIT analysis, computes the corresponding puncturing and pruning rates is proposed.

This paper investigates the security offered by PHY schemes that are well oriented towards jointly providing security and protection form channel errors. In particular, we focus on constructions that were recently proposed in the literature, whose security relies on the secrecy of parameters defining the encoding/decoding process of convolutional codes. Such schemes were shown to be quite promising in terms of error correcting capabilities, but no security analysis was provided to justify their use for wireless communications. To this end, we evaluate the strength of the PHY security scheme against chosen plaintext attacks, as well as known plaintext attacks that are built upon an extension of the known algorithm of Blum, Kalai, and Wasserman. The security analysis derives the parameters to be used for achieving a high security level against such type of attacks with low encoding and decoding complexity.

In this paper, a distributed adaptive algorithm for sparsity-aware learning in diffusion networks is developed. The algorithm follows the greedy roadmap for sparsity along with the adapt-combine co-operation strategy, based on the LMS rationale for adaptivity. A bound on the error norm between the obtained estimates and the target vector is computed, and the algorithm is shown to converge in the mean under some general assumptions. Finally, comparative experiments with a recently developed sparsity-promoting diffusion LMS demonstrate the enhanced performance of the proposed algorithm.

Constructions of secure channel encoders based on trellis pruning are considered in this paper. The key defines how pruning is applied on the trellis of a mother convolutional code; this results into a secret pruned trellis that legitimate users are using to perform decoding, in contrast to the eavesdroppers that employ the full mother trellis diagram. We focus on two special forms of the pruning function, and in each case we compute the expected weight enumerating function of the secret pruned code. The theoretical analysis ensures that the legitimate users achieve superior performance, in terms of word and bit error rate, than the eavesdroppers, which depends on the pruning rate. We also derive design guidelines on properties that mother encoders must have to fully exploit the proposed scheme. Simulation results also show the potential of catastrophic encoders for PHY security and yet the ability of the legitimate users to communicate reliably.

This paper establishes new achievable rates for nonlinear Volterra communication channels using refined versions of the Azuma-Hoeffding inequality. The characteristics of these rates are illuminated in special cases of interest that include time invariant linear channels with memory, memoryless non-linear channels, and Volterra channel models.

In this study, a method is presented for constructing convolutional codes of variable rate and decoding complexity. Starting with an (n,1,m) mother code, the techniques of puncturing and path pruning are utilized in order to construct large families of convolutional codes of various code rates and complexity. Decoding is performed using the trellis of the mother code.

Greedy algorithms are proposed for fast decoding of linear block codes over a binary symmetric channel. They are motivated by matching pursuit schemes developed in compressive sensing. Theoretical guarantees are provided for regular LDPC codes. The algorithms are highly efficient, as they only require vector-matrix multiplications and mostly use binary arithmetic. Their complexity is completely determined and depends on the code's block length and a sparsity parameter. The experimental results validate the performance of the proposed algorithms.

The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. We prove that minor modifications of functions achieving maximum algebraic immunity yield functions which are bound to have maximum or almost maximum algebraic immunity. Based on this, a new efficient algorithm to produce functions of guaranteed maximum algebraic immunity is developed. Moreover, it is shown that known constructions of functions with maximum algebraic immunity may also be generalized by using the same concepts.

It is known that an (n,n-1) non catastrophic antipodal punctured convolutional encoder of memory m is minimal. That is, the corresponding code cannot be produced by an encoder of smaller memory size. In this letter it is shown that the trellis module of a code produced by an (n,n-1) non catastrophic punctured convolutional encoder is optimum, if and only if the encoder is antipodal.

Random coding theorems and achievable rates for nonlinear additive noise channels are presented. Modeling the channel's nonlinear behavior as a causal, stationary Volterra system, upper bounds on the average error probability are obtained for maximum likelihood and weakly typical set decoding. The proposed bounds are deduced by treating correct decoding regions as subspaces of high concentration measure and deploying exponential martingale inequalities. Due to the union bound effect and the i.i.d. assumption imposed on the codewords components, the deduced exponents constitute only lower bounds on the true random coding exponents of nonlinear channels. Cubic and fourth-order nonlinearities are used as examples to illustrate the relation of the random coding exponents and achievable rates with respect to the channel's parameters.

Random coding performance bounds for$L$-list permutation invariant binary linear block codes transmitted over output symmetric channels are presented. Under list decoding, double and single exponential bounds are deduced by considering permutation ensembles of the above codes and exploiting the concavity of the double exponential function over the region of erroneous received vectors. The proposed technique specifies fixed list sizes$L$for specific codes under which the corresponding list decoding error probability approaches zero in a double exponential manner. The single exponential bound constitutes a generalization of Shulman-Feder bound and allows the treatment of codes with rates below the cutoff limit. Numerical examples of the new bounds for the specific category of codes are presented.

In this paper, new constructions of low trellis complexity convolutional codes are presented. New codes are found by searching into a specific class of time varying convolutional codes, which is shaped by some basic properties and search restrictions. An efficient technique for obtaining minimal trellis modules for the proposed codes is provided. Finally, new low complexity convolutional codes of various code rates and memory sizes are tabulated.

In this paper new constructions of low trellis complexity convolutional codes are presented. New codes are found by searching into a specific class of time varying convolutional codes, which is shaped by some basic properties and search restrictions. An efficient technique for obtaining minimal trellis modules for the proposed codes is provided. Finally, new low complexity convolutional codes of various code rates and memory sizes are tabulated.

A random coding theorem for nonlinear additive Gaussian channels is presented. Modeling the channel's nonlinear behavior as a causal, stationary Volterra system and under maximum likelihood decoding, an upper bound on the average error probability is obtained. The proposed bound is deduced by deploying exponential martingale inequalities. Cubic nonlinearities are used as example to illustrate the validity of the random coding exponent and the usefulness of the proposed technique in the treatment of nonlinear channels.

This paper is concerned with the blind identification of passband and baseband Hammerstein channels using cumulants of the received sequence. The channel is excited by common communication signals such as QAM, PSK and OFDM; sparseness of the higher order cumulant lags is exploited. Exact expressions and algorithms involving the output cumulants are developed. Performance is assessed by simulations.

This paper studies the error linear complexity spectrum of binary sequences with period2n. A precise categorization of those sequences having two distinct critical points in their spectra, as well as an enumeration of these sequences, is given. An upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved, and a construction which yields a lower bound on this number is given. In the process simpler proofs of some known results on the linear complexity andk-error linear complexity of sequences with period2nare provided.

In this paper, we consider the problem of computing best low-order approximations of Boolean functions; we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation. Our methodology is developed upon properties of the best affine approximations of quadratic functions, for which formulas for their direct computation (not by means of the Walsh-Hadamard transform) are given. We determine the cubic functions in the above subclass that achieve the maximum second-order nonlinearity, thus yielding a lower bound for the covering radius of the second order Reed-Muller code\ssr RM(2,n) in\ssr RM(3,n). Simple extensions of these results to some special cases of higher degree functions, are seen to hold. Furthermore, a preliminary analysis of well-known constructions for bent functions, in terms of their second-order nonlinearity, is performed that indicates potential weaknesses if construction parameters are not properly chosen.

A new tight upper bound on the maximum-likelihood (ML) word and bit-error decoding probabilities for specific codes over discrete channels is presented. It constitutes an enhanced version of the Gallager upper bound and its variations resulting from the Duman-Salehi second bounding technique. An efficient technique is developed that, in the case of symmetric channels, overcomes the difficulties associated with the direct computation of the proposed bound. Surprisingly, apart from the distance and input-output weight enumerating functions (IOWEFs), the bound depends also on the coset weight distribution of the code.

Nonparametric identification of baseband and passband complex Volterra systems excited by communication inputs (PSK, QAM and OFDM) is considered. Closed form expressions are established using multidimensional orthogonal polynomials and higher order statistics. First multidimensional orthogonal polynomials are used for baseband and passband Volterra models driven by PSK and QAM inputs and closed form expressions are derived. Baseband Volterra models excited by IID circular Gaussian signals (OFDM) are identified using cross-cumulants. Performance is assessed by simulations.

This paper studies the error linear complexity profiles of binary sequences with period 2n. We give a precise categorization of those sequences having 2 distinct critical points in their profiles, as well as an enumeration of these sequences. We also give an upper bound on the maximum number of distinct critical points that the profile of a sequence can have, along with several constructions for sequences having many distinct critical points.

Binary sequences generated from finite state automata are studied in this correspondence by utilizing system theoretic concepts. We develop a new unified approach for analyzing the linear complexity of such sequences, via controllability and observability conditions. A vectorial trace representation of sequences with arbitrary period is provided, which leads to a new generalized discrete Fourier transform allowing the generation of sequences with prescribed linear complexity. Furthermore, we introduce new classes of nonlinear filters, using the proposed approach, which generalize currently known classes and guarantee the same lower bound on the linear complexity.

Low order approximations of Boolean functions are studied in this paper. In particular, best affine approximations of quadratic functions are analyzed using Dickson theorem, leading to an explicit formula for their direct computation, without using the Walsh transform. Expressions to determine all the best affine approximations of linear combinations of quadratic functions are proved. The tools developed are suitable to determining low order approximations; they are applied to certain low degree functions with arbitrary number of variables and allow to efficiently derive all of their best quadratic approximations.

The nonlinear complexity of binary sequences and its connections with Lempel-Ziv complexity is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given binary sequence. Moreover, it is shown that the eigenvalue profile of a sequence uniquely determines its nonlinear complexity profile, thus establishing a connection between Lempel-Ziv complexity and nonlinear complexity. Furthermore, a lower bound for the Lempel-Ziv compression ratio of a given sequence is proved that depends on its nonlinear complexity.

This paper is concerned with symbolic computations in Volterra system identification using higher order cumulants. An efficient method that implements the Leonov-Shiryaev theorem is introduced. The proposed method relies on the exploitation of recursive relations between cumulants. The method is applied on the problem of blind identification of Volterra-Hammerstein systems excited by stationary higher order white noise. It solves previously intractable instances

The complexity of binary sequences generated by state-space systems is studied in this paper via utilization of system theoretic concepts. Application of controllability and observability conditions lead to a new block-trace representation of binary sequences enabling the efficient generation of sequences with maximum period and linear complexity. These arguments are also used to study nonlinearly filtered m-sequences, resulting in a new type of filters that achieve the same lower bound for the linear complexity as Rueppel's equidistant filters

The problem of finding the length of a shortest feedback shift register that generates a given finite-length sequence is considered. An efficient algorithm for the determination of the span is proposed, that takes advantage of the special block structure of the associated system of linear equations. The span distribution of finite-length binary sequences is also studied.

The problem of finding the shortest feedback shift register, with quadratic feedback function that generates a given finite-length sequence is considered. An algorithm for the determination of the quadratic span and the feedback function, which takes advantage of the special block structure of the associated system of linear equations, is proposed.

The problem of finding the length of shortest feedback shift register that generates a given finite-length sequence is considered. An algorithm for the determination of the span is proposed, that takes advantage of the special block structure of the associated system of linear equations. The span distribution of finite-length binary sequences is also studied.

Binary sequences of period 2/sup n/-1 generated by a linear feedback shift register (LFSR) whose stages are filtered by a nonlinear function, f, are studied. New iterative formulas are derived for the calculation of the linear complexity of the output sequences. It is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal-length sequences.

The determination of the minimum linear span sequence that differs from a given binary sequence, of period N=2/sup n/-1, by at most one digit is discussed and three methods are presented: the sequential divisions method, the congruential equations method, and the phase synchronization method. High-level algorithm organizations are provided. Finally, guidelines on sequence characterization and design via the notion of robustness are given.

This paper is concerned with the blind identification of bilinear systems excited by higher-order white noise. Unlike prior work that restricted the bilinear system model to simple forms and required the excitation to be Gaussian distributed, the results of this paper are applicable to a more general class of bilinear systems and for the case when the excitation is non-Gaussian. We describe an estimation procedure for the computation of the system parameters using output cumulants of order less than four.

This paper is concerned with third order Volterra system identification. It is shown that crosscumulant information can be converted into a Fredholm integral equation. Closed form expressions for the Volterra kernels are derived using the determinant theory. Finally, special emphasis is focused on i.i.d. inputs.

In this paper convergence analysis of the parallel and deterministic asynchronous modes of operation for the Hamming network is carried out. Conditions ensuring convergence to a stable state in a finite number of steps are derived. An upper bound of the maximum number of steps that is required to reach a stable state is obtained. Finally, a geometrical interpretation of our results is obtained.

Efficient algorithms for multivariable system identification and multichannel FIR (finite impulse response) filtering are developed under the assumption that the predictor depends linearly on the unknown parameter. The proposed methods have a block adaptive format because they derive from efficient linear system solvers.>

Two efficient algorithmic families are developed for multichannel combiners characterized by unequal memory lengths for each of two input channels. The difference between the proposed methods lies in the way the Kalman gain vector is order-updated in each case. The first algorithm operates on both inputs simultaneously, utilizing block multichannel structured order recursions. The resulting scheme is called the diagonal update algorithm. The second approach updates the Kalman gain in a two-step procedure by reducing first the size of one input and then the size of the other input. The resulting method is called the stairwise update algorithm. Both algorithms are applicable to adaptive ARMA (autoregressive moving average) system identification, adaptive control, and the design of decision-feedback equalizers. Simulation results are included.>

The effects of a narrowband interference present in a pseudonoise (PN) spread-spectrum system can be minimized by using digital whitening techniques. A new efficient block LS algorithm for the design of an FIR filter with linear phase is derived and used as a whitening filter. Simulations are carried out to demonstrate the effectiveness of the LS optimum linear-phase filter in suppressing a narrowband interference in a PN spread-spectrum system. Comparisons to previously used methods are made. The simulations showed an improvement in the output SNR on the order of 4-5 dB over already existing schemes.>

Highly parallel algorithms are derived for multichannel FIR (finite-impulse response) smoothing and MEM (minimum-energy method) spectral analysis. The derived algorithms require O(p) computing time and can be performed on a linear array of O(p) processors, p being the order of the filter of AR (autoregressive) model. Thus, a computational saving of one order of magnitude is achieved, compared to Levinson-type algorithms.>

The effects of a narrowband interference in a PN spread spectrum system can be minimized by employing a whitening filter. The performance of this filter can be improved if its impulse response is symmetrical. In this paper an optimum LS FIR smoother is adopted to perform the whitening process and a new efficient algorithm is presented to compute the smoothers coefficients. To demonstrate the effectiveness of the LS FIR smoother in suppressing a narrowband interference, simulations are carried out and the results are compared with those obtained by previously employed techniques.

The purpose of this paper is to provide a brief overview of the algorithms and structures which can be used in connection with ℓ - lag FIR filtering. A number of existing efficient algorithms from the zero - lag problem are generalized here, to be applied to the ℓ - lag case. Both direct and lattice - ladder structures are considered. Four different families of techniques are discussed: time recursive, order recursive, lattice - ladder and "recursive in lag". The unified approach used in this paper for the derivation of the algorithms permits the underlining of the relationships among the variables appearing in the four families of recursive schemes discussed. The "prewindowing" assumption is used throughout.

Sequential Least-Squares (LS) methods play a prominent role in many digital signal processing applications. The conventional implementation of these schemes requires an amount of operations proportional to the square of the number of estimated parameters. In contrast a variety of existing fast algorithms offer a computational complexity proportional to the number of estimated parameters. Such schemes exist for both direct form and lattice-ladder filter structures. This paper offers a unified overview of fast sequential algorithms for LS FIR filters, implemented using a direct form realization, in the case of prewindowed multichannel signals. Although all these algorithms are theoretically equivalent, in practice they exhibit different performance due to round-off noise, incorrect initialization etc. The performance evaluation of all these shemes is still an area to be explored.

The present paper deals with a new, computationally efficient, algorithm for Sequential Least Squares (LS) estimation. This scheme requires only O(5p) MAD (Multiplications And Divisions) per recursion to update a Kalman type gain vector; p is the number of estimated parameters. In contrast the well-known fast Kalman algorithm requires O(8p) MAD. The introduced method is the fastest known algorithm featured by the rapid convergence characteristics of exact Least Squares estimation schemes. Another interesting feature of the new algorithm is the balanced role, the forward and backward prediction play.

In various signal processing applications we are confronted with the problem of finding the optimum in the least squares sense linear filter that matches the input signal with a certain lag of the desired response. The system of equations yielding all filters coefficients turns out to have a near-to-Toeplitz or near-to-Hankel structure with displacement rank 1 or 2 generically depending on whether windowing is used. Motivated by these questions the general linear system is considered and recursive procedures are derived for the determination of the solution which when the parameters have low displacement rank are proved very efficient. In particular if the parameters are Toeplitz the resulting algorithm coincides with a scheme introduced recently by the authors which in turn performs better than the well-known Simpson's sideways recursions.

In various signal processing applications one is often confronted with aspects such as linear system solution, triangularization or inversion of matrices with special block structure as well as entries of particular form. Toeplitz, Banded Toeplitz, circular and Hankel matrices provide typical examples often encountered in such diverse fields as image processing, computerized tomography and other array processing applications. The purpose of this paper is to algorithmically examine the issues of triangularization, inversion and linear system solution when the above particular structures are imposed at either the block level or the entry level. It is shown that the various resulting combinations of block and entry structure considerably reduce the computational complexity of the above problems.