design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

a relaxed condition for perfect cancellation of broadband noise in 3d enclosures this paper presents a relaxed condition for perfect cancellation of broadband noise in 3d enclosures on the basis of a truncated modal model it can be shown that the primary and secondary paths belong to a same subspace if a certain condition is satisfied there exists a finite impulse response fir filter transfer function vector for perfect cancellation of the primary paths the analytical result is verified numerically with an active noise control anc system in a 3d rectangular enclosure the proposed anc scheme is shown to fit well into the framework of an existing multichannel least mean squares lms algorithm for adaptive implementation

polarized endomorphisms of complex normal varieties it is shown that a complex normal projective variety has non positive kodaira dimension if it admits a non isomorphic quasi polarized endomorphism the geometric structure of the variety is described by methods of equivariant lifting and fibrations

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

exceptional points of an endomorphism of the projective plane let f an endomorphism of of degree 1 we show how to obtain a bound depending only on n on the number of codimension two subspaces in which are completely invariant for f where l is completely invariant for f means that f 1 l l set theoretically

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

l sub 1 optimality of feedback control systems the siso discrete time case controllers that optimally reject a class of disturbances are considered the problem of determining when a stabilizing control is l sub 1 optimal for a given plant is studied for some stable weighting function this problem belongs to the class of inverse problems in optimal control introduced by kalman it is shown that for a given plant the set of all the h sub infinity optimal controllers obtained by considering all stable weighting functions with no zeros on the unit circle is actually contained in the corresponding set of l sub 1 optimal controllers it is also demonstrated that an l sub 1 optimal controller unlike an h sub infinity optimal controller can remain l sub 1 optimal for the same plant for a wide range of nontrivially different weighting functions

synthesis of a robust broadband duct anc system using convex programming approach a robust active controller using spatially feedforward structure is proposed for broadband attenuation of noise in ducts to meet the requirements of performance and robust stability in the presence of plant uncertainties an h2 cost function and an h constrain are employed in the synthesis of the controller the design is then converted into a convex programming problem using q parametrization and frequency discretization an optimal controller that satisfies the quadratic cost functions and linear inequality constraints can be found by sequential quadratic programming the optimal controller was implemented via a digital signal processor dsp and verified by experiments experiment results showed that the system attained 16 5 db maximal attenuation and 5 9 db total attenuation in the frequency band 200 600 hz

robust disturbance rejection in e 1 optimal control systems abstract given a class of plants formed by perturbing a nominal discrete time linear shift invariant plant with norm bounded unstructured perturbation the problem of finding a single compensator that will stabilize all plants in this class and at the same time minimize the worst case norm of a certain performance measure is addressed assuming the performance measure of interest is the sensitivity function first an expression for the supremum over all plants in this class of such a measure is derived for a system with a robustly stabilizing compensator this is achieved by first showing that the proposed expression is an upper bound for the worst case sensitivity norm and then by constructing a plant in the allowable class that will achieve this upper bound combined with already known necessary and sufficient conditions for robust stability the derived expression provides an effective way of combining both robust stability and performance in one easy to compute measure secondly a scheme for finding a controller that minimizes the worst case norm of the sensitivity function while achieving robust stability is provided this makes possible the incorporation of stability and performance robustness requirements in one design procedure

development of the filtered u algorithm for active noise control the filtered x algorithm developed by widrow and burgess is an alternate form of the least mean square lms algorithm for use when there are transfer functions in the auxiliary path following the adaptive filter to ensure convergence of the algorithm the input to the error correlators is filtered by a copy of these auxiliary path transfer functions more recently the author has presented a new approach to active noise control in the presence of acoustic feedback that uses an infinite impulse response iir filter structure with an alternate form of the recursive least mean square rlms algorithm this algorithm may be described as a filtered u algorithm since it uses a copy of the auxiliary path transfer functions to filter the generalized input vector u to the error correlators of both the direct and recursive elements of the filter to ensure convergence the relationship of the filtered u to the filtered x algorithm and other earlier concepts is discussed

best achievable decentralized performance in this paper a novel parameterization of all decentralized stabilizing controllers is employed in mathematically formulating the best achievable decentralized performance problem as an infinite dimensional optimization problem finite dimensional optimization problems are then constructed that have values arbitrarily close to this infinite dimensional problem an algorithm which identifies the best achievable performance over all linear time invariant decentralized controllers is then presented it employs a global optimization approach to the solution of these finite dimensional approximating problems

integral points and relative sizes of coordinates of orbits in mathbb p n we give a generalization to higher dimensions of silverman s result on finiteness of integer points in orbits assuming vojta s conjecture we prove a sufficient condition for morphisms on mathbb p n so that s d integral points in each orbit are zariski non dense this condition is geometric and for dimension 1 it corresponds precisely to silverman s hypothesis that the second iterate of the map is not a polynomial in fact we will prove a more precise formulation comparing local heights outside s to the global height for hyperplanes this amounts to comparing logarithmic sizes of the coordinates generalizing silverman s precise version in dimension 1 we also discuss a variant where we can conclude that integral points in orbits are finite rather than just zariski non dense further we show unconditional results and examples using schmidt s subspace theorem and known cases of lang vojta conjecture we end with some extensions to the case of rational maps and to the case when the arithmetic of the orbit under one map is controlled by the geometric properties of another we include many explicit examples to illustrate different behaviors of integral points in orbits in higher dimensions

dual periodicity in l 1 norm minimisation problems the topic of this paper is the discrete time l1 norm minimisation problem with convolution constraints we find primal initial conditions for which the dual optimal solution is periodic periodicity of the dual optimal solution implies satisfaction of a simple linear recurrence relation by the primal optimal solution

study of the acoustic feedback problem of active noise control by using the l1 and l2 vector space optimization approaches this study attempts to explore the acoustic feedback problem that is frequently encountered in feedforward active noise control anc structure from the standpoint of control theories the analysis is carried out on the basis of the youla s parametrization and the l1 norm and l2 norm vector space optimization the anc problem is formulated as a model matching procedure and is solved via linear programming in the dual vector space these methods alleviate the problems caused by the nonminimum phase nmp zeros of the cancellation path the anc algorithms are implemented by using a digital signal processor various types of noises were chosen for validating the developed algorithms the proposed methods are also compared with the well known filtered u least mean square fulms method the experimental results show that the acoustic feedback problem significantly degrades the performance and stability of the anc system regardless which method is used insights into the difficulties due to acoustic feedback a

on nonlinear state feedback controllers for persistent disturbance rejection abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant in the state feedback case there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance in the case of d 12 square and invertible we show that it is enough to have the nonlinearity on a particular substate which can be used to significantly simplify the design problem

linearity of the exceptional set for maps of p k c let f be a holomorphic self map of p k c with degree larger than 2 we show that its exceptional set is a finite union of linear subspaces

optimal and robust controllers for periodic and multirate systems the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete time periodic systems the solution consists of solving an equivalent time invariant standard l sup 1 optimization problem subject to an additional constraint this constraint assures the causality of the resulting periodic controller by the duality theory the problem is shown to be equivalent to a linear programming problem which is no harder than the standard l sup 1 problem also it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems finally the results are applied to the problem of robust stabilization of periodic and multirate systems

a construction of rational wavelets and frames in hardy sobolev spaces with applications to system modeling using the daubechies wavelet theory we establish rational wavelet decompositions of the hardy sobolev classes on the half plane the decay of wavelet coefficients is analyzed and error bounds for approximation are given we give applications to the modeling of linear systems and to the model reduction of infinite dimensional systems

minimization of the worst case peak to peak gain via dynamic programming state feedback case considers the problem of designing a controller that minimizes the worst case peak to peak gain of a closed loop system in particular we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude we apply the principle of optimality and derive a dynamic programming formulation of the optimization problem under mild assumptions we show that at each step of the dynamic program the cost to go has the form of a gauge function and can be recursively determined through simple transformations we study both the finite horizon and the infinite horizon case under different information structures the proposed approach allows us to encompass and improve earlier results based on viability theory in particular we present a computational scheme alternative to the standard bisection algorithm or gamma iteration that allows us to compute the exact value of the worst case peak to peak gain for any finite horizon we show that the sequence of finite horizon optimal costs converges as the length of the horizon goes to infinity to the infinite horizon optimal cost the sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem we also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems

reduced complexity iterative decoding of low density parity check codes based on belief propagation two simplified versions of the belief propagation algorithm for fast iterative decoding of low density parity check codes on the additive white gaussian noise channel are proposed both versions are implemented with real additions only which greatly simplifies the decoding complexity of belief propagation in which products of probabilities have to be computed also these two algorithms do not require any knowledge about the channel characteristics both algorithms yield a good performance complexity trade off and can be efficiently implemented in software as well as in hardware with possibly quantized received values

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

potts models on hierarchical lattices and renormalization group dynamics we prove that the generator of the renormalization group of potts models on hierarchical lattices can be represented by a rational map acting on a finite dimensional product of complex projective spaces in this framework we can also consider models with an applied external magnetic field and multiple spin interactions we use recent results regarding iteration of rational maps in several complex variables to show that for some class of hierarchical lattices lee yang and fisher zeros belong to the unstable set of the renormalization map

new insights into weighted bit flipping decoding a natural relationship between weighted bit flipping wbf decoding and belief propagation like bp like decoding is explored this understanding can help us develop wbf algorithms from bp like algorithms for min sum decoding one can find that its wbf algorithm is the algorithm proposed by jiang et al for bp decoding we propose a new wbf algorithm and show its performance advantage the proposed wbf algorithms are parallelized to achieve rapid convergence two efficient simulation based procedures are proposed for the optimization of the associated thresholds

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

approximation and identification of continuous time systems an approximation approach to the identification of stable continuous time possibly infinite dimensional systems is studied for this purpose concrete exponential leg endre series methods are proposed and analysed here for the l1 and l2 approximations of continuous time systems rate of approximation results are given for the proposed methods for an important class of delay systems the proposed exponential legendre series method for the l2 approximation has a certain optimal rate of approximation property for this class of delay systems these results show that exponential legendre series techniques have promising properties in connection with the l1 and l2 identifications of stable continuous time systems the proposed l1 identification method has a direct application to the robust design of control systems

i 1 optimal control of multivariable systems with output norm constraints in this paper we consider the l1 optimal control problem for general rational plants it is shown that for plants with no poles or zeros on the unit circle an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs exactly or approximately optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed loop transfer function no assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators it is shown that constrained problems in which a set of outputs is regulated subject to l norm constraints on another set of outputs can be solved using a slight modification of the same algorithm

near optimum universal belief propagation based decoding of low density parity check codes in this paper we propose a belief propagation bp based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified bp based algorithm the normalization factors can be obtained not only by simulation but also importantly theoretically this new bp based algorithm is much simpler to implement than bp decoding as it requires only additions of the normalized received values and is universal i e the decoding is independent of the channel characteristics some simulation results are given which show this new decoding approach can achieve an error performance very close to that of bp on the additive white gaussian noise channel especially for low density parity check ldpc codes whose check sums have large weights the principle of normalization can also be used to improve the performance of the max log map algorithm in turbo decoding and some coding gain can be achieved if the code length is long enough

a differential binary message passing ldpc decoder in this paper we propose a binary message passing algorithm for decoding low density parity check ldpc codes the algorithm substantially improves the performance of purely hard decision iterative algorithms with a small increase in the memory requirements and the computational complexity we associate a reliability value to each nonzero element of the code s parity check matrix and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes for the tested random and finite geometry ldpc codes the proposed algorithm can perform as close as about 1 db and 0 5 db to belief propagation bp at the error rates of interest respectively this is while unlike bp the algorithm does not require the estimation of channel signal to noise ratio low memory and computational requirements and binary message passing make the proposed algorithm attractive for high speed low power applications

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

invariant curves for birational surface maps we classify invariant curves for birational surface maps that are expanding on cohomology when the expansion is exponential the arithmetic genus of an invariant curve is at most one this implies severe constraints on both the type and number of irreducible components of the curve in the case of an invariant curve with genus equal to one we show that there is an associated invariant meromorphic two form

two bit flipping decoding algorithms for low density parity check codes in this letter a low complexity decoding algorithm for binary linear block codes is applied to low density paritycheck ldpc codes and improvements are described namely an extension to soft decision decoding and a loop detection mechanism for soft decoding only one real valued addition per code symbol is needed while the remaining operations are only binary as in the hard decision case the decoding performance is considerably increased by the loop detection simulation results are used to compare the performance with other known decoding strategies for ldpc codes with the result that the presented algorithms offer excellent performances at smaller complexity

model reference adaptive control for nonminimum phase systems in this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty instead of the usual goal of asymptotic error regulation here we require that the limit superior of the magnitude of the error be less than a predefined constant times the limit superior of the magnitude of the external reference input this provides a natural way to incorporate uncertainty which includes nonminimum phase systems

a decoding algorithm for finite geometry ldpc codes in this paper we develop a new low complexity algorithm to decode low density parity check ldpc codes the developments are oriented specifically toward low cost yet effective decoding of high rate finite geometry fg ldpc codes the decoding procedure updates iteratively the hard decision received vector in search of a valid codeword in the vector space only one bit is changed in each iteration and the bit selection criterion combines the number of failed checks and the reliability of the received bits prior knowledge of the signal amplitude and noise power is not required an optional mechanism to avoid infinite loops in the search is also proposed our studies show that the algorithm achieves an appealing tradeoff between performance and complexity for fg ldpc codes

on optimal e to e filtering abstract in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l of the estimation error in the case of linear time invariant systems subjected to unknown but magnitude bounded l inputs these inputs consist of process and observation noise as well as initial conditions also the optimization problem is considered over an infinite time horizon taking a model matching approach suboptimal solutions are presented that stem from the resulting l induced norm minimization problem

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

an improved decoding algorithm for finite geometry ldpc codes in this letter an improved bit flipping decoding algorithm for high rate finite geometry low density parity check fg ldpc codes is proposed both improvement in performance and reduction in decoding delay are observed by flipping multiple bits in each iteration our studies show that the proposed algorithm achieves an appealing tradeoff between performance and complexity for fg ldpc codes

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem

two reliability based iterative majority logic decoding algorithms for ldpc codes this paper presents two novel reliability based iterative majority logic decoding algorithms for ldpc codes both algorithms are binary message passing algorithms and require only logical operations and integer additions consequently they can be implemented with simple combinational logic circuits they either outperform or perform just as well as the existing weighted bit flipping or other reliability based iterative decoding algorithms for ldpc codes in error performance with a faster rate of decoding convergence and less decoding complexity compared to the sum product algorithm for ldpc codes they offer effective trade offs between performance and decoding complexity