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

on a family of circulant matrices for quasi cyclic low density generator matrix codes we present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices their study is useful in the design of quasi cyclic low density generator matrix codes that are able to join the inner structure of quasi cyclic codes with sparse generator matrices so limiting the number of elementary operations needed for encoding circulant matrices of the proposed class permit to hit both targets without resorting to identity or permutation matrices that may penalize the code minimum distance and often cause significant error floors

on the algebraic structure of quasi cyclic codes i finite fields a new algebraic approach to quasi cyclic codes is introduced the key idea is to regard a quasi cyclic code over a field as a linear code over an auxiliary ring by the use of the chinese remainder theorem crt or of the discrete fourier transform dft that ring can be decomposed into a direct product of fields that ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the u spl upsi u spl upsi and vandermonde constructions all binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction quinting and septing constructions are introduced other results made possible by the ring decomposition are a characterization of self dual quasi cyclic codes and a trace representation that generalizes that of cyclic codes

pilot symbol assisted and code aided phase error estimation for high order qam transmission in this paper we present a novel phase error estimation scheme for low density parity check ldpc coded high order quadrature amplitude modulation qam transmission systems and we provide a theoretical analysis of its performance the scheme uses known pilot symbols which are assumed to be placed at equally spaced positions and phase errors occurred at these pilot symbol positions are first estimated they are then interpolated over the other positions by using a wiener filter wf and estimation accuracy is next refined by using an ldpc code aided phase locked loop pll we present an efficient implementation of this two stage pilot symbol assisted and code aided psa ca scheme and evaluate its performance by means of power spectrum analysis we determine the mean square error at each step of the psa ca scheme and we find an optimal value of the noise equivalent loop bandwidth of the pll under the assumption that local oscillator phase noise can be modeled as a single pole single zero model we show through simulations that the psa ca scheme has a very high phase noise tolerance comparable to that of state of the art phase estimation schemes and provides a computationally efficient alternative

an exact penalty function for semi infinite programming this paper introduces a global approach to the semi infinite programming problem that is based upon a generalisation of the l1 exact penalty function the advantages are that the ensuing penalty function is exact and the penalties include all violations the merit function requires integrals for the penalties which provides a consistent model for the algorithm the discretization is a result of the approximate quadrature rather than an a priori aspect of the model

a new construction of structured binary regular ldpc codes based on steiner systems with parameter t 2 this paper presents a novel method for constructing structured regular low density parity check ldpc codes based on a special type of combinatorial designs known as steiner systems this code design approach can be considered as a generalization of the well known method which uses the point block incidence matrix of a steiner 2 design for the code construction though the given method can be applied on any steiner system s t k v in this paper we focus only on steiner systems with t 3 furthermore we show that not only a steiner system x b itself but also its residual design with respect to an arbitrary point x x can be employed for code construction we also present a technique for constructing binary and non binary qc ldpc codes from steiner systems the tanner graph of the constructed codes is free of 4 cycles and hence the codes have girth at least six simulation results show that the so constructed codes perform well over the awgn channel with iterative message passing decoding

spillover stabilization in finite dimensional control and observer design for dissipative evolution equations we consider the problem of global stabilization of a semilinear dissipative evolution equation by finite dimensional control with finite dimensional outputs coupling between the system modes occurs directly through the nonlinearity and also through the control influence functions similar modal coupling occurs in the infinite dimensional error dynamics through the nonlinearity and measurements for both the control and observer designs rather than decompose the original system into fourier modes we consider lyapunov functions based on the infinite dimensional dynamics of the state and error systems respectively the inner product terms of the lyapunov derivative are decomposed into fourier modes upper bounds on the terms representing control and observation spillover are obtained linear quadratic regulator lqr designs are used to stabilize the state and error systems with these upper bounds relations between system and lqr design parameters are given to ensure global stability of the state and error dynamics with robustness with respect to control and observation spillover respectively it is shown that the control and observer designs can be combined to yield a globally stabilizing compensator the control and observer designs are numerically demonstrated on the problem of controlling stall in a model of axial compressors

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

on the mathematical model for linear elastic systems with analytic damping in the present paper we investigate linear elastic systems with damping ddot y b dot y ay 0 in hilbert spaces where a is a positive definite unbounded linear operator and b is a closed linear operator related in various ways to a alpha frac 1 2 leqq alpha leqq 1 we discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems

on the design of stabilizing compensators via semi infinite optimization the authors derive a modified nyquist stability test which makes possible the use of semi infinite optimization for the design of stabilizing compensators the test provide a simple necessary and sufficient condition of exponential stability and is computationally well conditioned computational aspects of the derived stability test are discussed and a design example is given

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

combined lp and quasi newton methods for minimax optimization we present an algorithm for minimax optimization that combines lp methods and quasi newton methods the quasi newton algorithm is used only if an irregular solution is detected in which case second order derivative information is needed in order to obtain a fast final rate of convergence we prove that the algorithm can converge only to a stationary point and that normally the final rate of convergence will be either quadratic or superlinear the performance is illustrated through some numerical examples

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

moving horizon control of linear systems with input saturation and plant uncertainty part 1 robustness we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem this is a two part paper in this part we show that the proposed moving horizon control system is robustly stable whether the state of the plant is measurable or not in the second part we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws

high rate quasi cyclic low density parity check codes derived from finite affine planes this paper shows that several attractive classes of quasi cyclic qc low density parity check ldpc codes can be obtained from affine planes over finite fields one class of these consists of duals of one generator qc codes presented here for codes contained in this class are the exact minimum distance and a lower bound on the multiplicity of the minimum weight codewords further it is shown that the minimum hamming distance of a code in this class is equal to its minimum additive white gaussian noise awgn pseudoweight also discussed is a class consisting of codes from circulant permutation matrices and an explicit formula for the rank of the parity check matrix is presented for these codes additionally it is shown that each of these codes can be identified with a code constructed from a constacyclic maximum distance separable code of dimension 2 the construction is similar to the derivation of reed solomon rs based ldpc codes presented by chen and djurdjevic experimental results show that a number of high rate qc ldpc codes with excellent error performance are contained in these classes

a barrier function method for minimax problems this paper presents an algorithm based on barrier functions for solving semi infinite minimax problems which arise in an engineering design setting the algorithm bears a resemblance to some of the current interior penalty function methods used to solve constrained minimization problems global convergence is proven and numerical results are reported which show that the algorithm is exceptionally robust and that its performance is comparable while its structure is simpler than that of current first order minimax algorithms

a matrix theoretic approach for analyzing quasi cyclic low density parity check codes a matrix theoretic approach for studying quasi cyclic codes based on matrix transformations via fourier transforms and row and column permutations is developed these transformations put a parity check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field the approach is amicable to the analysis and construction of quasi cyclic low density parity check codes since it takes into account the specific parity check matrix used for decoding with iterative message passing algorithms based on this approach the dimension of the codes and parity check matrices for the dual codes can be determined several algebraic and geometric constructions of quasi cyclic codes are presented as applications along with simulation results showing their performance over additive white gaussian noise channels decoded with iterative message passing algorithms

adaptive control of arma plants using worst case design by semi infinite optimization this paper presents a new approach to on line control system tuning based on worst case design using semi infinite optimlzation together with a plant uncertainty identification scheme which this approach requires

a smoothing iterative method for the finite minimax problem abstract in this paper we proposed a smoothing iterative method to solve the finite minimax problems based on the exponential penalty function of kort and bertsekas 1972 this approach can be viewed as the extension of one conjugate gradient method under suitable conditions the proposed method is globally convergent preliminary numerical results and comparisons show that the proposed method is effective and promising

cyclic and quasi cyclic ldpc codes on constrained parity check matrices and their trapping sets this paper is concerned with construction and structural analysis of both cyclic and quasi cyclic codes particularly low density parity check ldpc codes it consists of three parts the first part shows that a cyclic code given by a parity check matrix in circulant form can be decomposed into descendant cyclic and quasi cyclic codes of various lengths and rates some fundamental structural properties of these descendant codes are developed including the characterization of the roots of the generator polynomial of a cyclic descendant code the second part of the paper shows that cyclic and quasi cyclic descendant ldpc codes can be derived from cyclic finite geometry ldpc codes using the results developed in the first part of the paper this enlarges the repertoire of cyclic ldpc codes the third part of the paper analyzes the trapping set structure of regular ldpc codes whose parity check matrices satisfy a certain constraint on their rows and columns several classes of finite geometry and finite field cyclic and quasi cyclic ldpc codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances consequently their error floor performances are dominated by their minimum distances

ldpc codes on partial geometries construction trapping set structure and puncturing many known constructions of ldpc codes can be placed in a general framework using the notion of partial geometries based on this notion the structure of such ldpc codes can be analyzed using a geometric approach that illuminates important properties of their parity check matrices in this approach trapping sets are represented by subgeometries of the geometry used to construct the code based on the incidence relations between lines and points in this geometry the structure of trapping sets is investigated on the other hand it is shown that removing a subgeometry corresponding to a trapping set gives a punctured matrix which can be used as a parity check matrix of an ldpc code this relates trapping sets represented by subgeometries and punctured matrices represented by the residual geometries the null spaces of these punctured matrices are ldpc codes which inherit many of the good structural properties of the original code hence new ldpc codes with various lengths and rates can be obtained by puncturing an ldpc code constructed based on a partial geometry furthermore these punctured matrices and codes can be used in a two phase decoding scheme to correct combinations of errors and erasures

new classes of partial geometries and their associated ldpc codes the use of partial geometries to construct parity check matrices for binary low density parity check ldpc codes has resulted in the design of successful codes with a probability of error on the awgn channel close to the shannon capacity at bit error rate down to 10 15 such considerations have motivated this further investigation a new and simple construction of a type of partial geometries with a quasi cyclic qc structure is given and their properties are investigated two new classes of this type of partial geometries one based on prime fields and the other based on cyclic subgroups of prime orders of finite fields are constructed qc ldpc codes with good error performances are constructed based on these two new classes of partial geometries the trapping sets of the partial geometry codes were previously considered using the geometric aspects of the underlying structure to derive information on the size of allowable trapping sets this topic is further considered here finally there is a natural relationship between partial geometries and strongly regular graphs the eigenvalues of the adjacency matrices of such graphs are well known and it is of interest to determine if any of the tanner graphs derived from the partial geometries are good expanders for certain parameter sets since it can be argued that codes with good geometric and expansion properties might perform well on the awgn channel under message passing decoding

enhancing iterative decoding of cyclic ldpc codes using their automorphism groups for cyclic ldpc codes we propose to use their automorphism groups to improve the iterative decoding performance the basic idea is to construct nonequivalent parity check matrices via column permutations three types of iterative decoders are devised to take advantage of the code s automorphism group in this paper we focus on cyclic ldpc codes defined by a circulant parity check matrix and consider two known subgroups of the automorphism group of a cyclic code for the large class of idempotent based cyclic ldpc codes in the literature we show that the two subgroups only provide equivalent parity check matrices and thus cannot be harnessed for iterative decoding towards exploiting the automorphism group of a code we propose a new class of cyclic ldpc codes based on pseudo cyclic mds codes with two information symbols for which nonequivalent parity check matrices are obtained simulation results show that for our constructed codes of short lengths the automorphism group can significantly enhance the iterative decoding performance

proportional plus multiintegral stabilizing compensators for a class of mimo feedback systems with infinite dimensional plants a method is presented for designing proportional plus multiintegral stabilizing compensators for a class of feedback systems with exponentially stable infinite dimensional plants these compensators enable the feedback system to asymptotically track polynomial inputs and suppress polynomial disturbances of corresponding order when used in design the effectiveness of the construction procedure presented can be increased considerably by combining it with the computational stability criterion and semiinfinite optimization in this manner the coefficient matrices of a compensator designed by the method can be further modified to ensure better feedback system performance with respect to various performance requirements without destroying stability tracking and disturbance rejection properties

a revolving iterative algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes cyclic and quasi cyclic algebraic ldpc codes constructed based on finite fields finite geometries and combinatorial designs can achieve excellent performance in terms of error rate error floor and rate of decoding convergence with iterative decoding however the relatively high density of the parity check matrix of an algebraic cyclic or quasi cyclic ldpc code makes the hardware implementation complexity of the decoder quite large which may be a critical issue in practical applications this paper presents an effective reduced complexity algorithm for decoding algebraic cyclic and quasi cyclic ldpc codes based on the block cyclic structure and cyclic grouping of the rows of their parity check matrices the decoding of a code is carried out based on a single small submatrix of the parity check matrix of the code in a revolving manner the proposed decoding algorithm significantly reduces the hardware implementation complexity and the size of memory required to store information

construction of high rate regular quasi cyclic ldpc codes based on cyclic difference families for a high rate case it is difficult to randomly construct good low density parity check ldpc codes of short and moderate lengths because their tanner graphs are prone to have short cycles also the existing high rate quasi cyclic qc ldpc codes can be constructed only for very restricted code parameters in this paper based on special classes of cyclic difference families we propose a new construction method of high rate regular qc ldpc codes having parity check matrices consisting of a single row of circulants with column weight 3 or 4 the proposed qc ldpc codes can be constructed for various code rates and lengths including the minimum achievable length for given column weight and design rate under girth 6 it is observed that the parity check matrices of the proposed qc ldpc codes have full rank for column weight 3 and just one redundant row for column weight 4 it is shown that the error correcting performance of the proposed qc ldpc codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis

mutation selection stationary distribution in structured populations in this paper we address the evolution of finite and structured populations including two types of species the evolutionary dynamics of the system is governed by the moran process with constant fitnesses in the presence of mutation we obtain the stationary distribution in a number of topologies we also approximate the mixing time i e the time that the system needs to reach its stationary distribution it is observed that the mean frequency of a species in the stationary distribution is approximately independent of the population structure and the mixing time has a power law behavior with respect to the population size whose exponent is closely related to the population structure the obtained results indicate that more heterogeneity leads to longer mixing times

a modified nyquist stability test for use in computer aided design this note shows that the nyquist stability criterion is not a convenient tool for use in computer aided design of feedback systems a substitute graphical test is proposed which is more suitable for use in cad

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

effective diagonalization strategies for the solution of a class of optimal design problems it is shown that it is possible to obtain optimal diagonalization strategies for the discretization of semiinfinite minimax optimal design problems both exact and approximate methods for the computation of these optimal diagonalization strategies are proposed the algorithms for computing approximate diagonalization strategies yield very good approximations in much less computing time than needed to compute an optimal diagonalization strategy exactly the proposed diagonalization strategies can be implemented by using estimation schemes to obtain approximations to the various quantities which determine an optimal strategy experimental results involving the solution of optimal loop shaping problems for multivariable linear feedback systems show that the use of these implementable strategies leads to considerable savings in computer time over alternative approaches

relaxed variants of karmarkar s algorithm for linear programs with unknown optimal objective value variants of karmarkar s algorithm are given for solving linear programs with unknown optimal objective valuez these new methods combine the approach of goldfarb and mehrotra for relaxing the requirement that certain projections be computed exactly with the approach of todd and burrell for generating an improving sequence of lower bounds forz using dual feasible solutions these methods retain the polynomial time complexity of karmarkar s algorithm

on the design of finite dimensional stabilizing compensators for infinite dimensional feedback systems via semiinfinite optimization the computational stability criterion presented by e polak and t l wuu see ibid vol 34 p 196 200 feb 1989 is extended to a form that can be used in the design of finite dimensional stabilizing compensators for a class of feedback systems with infinite dimensional plants since in this case the characteristic function is not a polynomial there is no simple way to define a normalizing polynomial hence approximation theory has to be used the new stability test guarantees not only input output stability but also internal stability of the feedback system furthermore since the numerical implementation of the test does not depend on the use of a reduced plant model the test does not lead to spillover effects because the compensator is parametrized in the state space form the order of the compensator can be assigned by the designer

walds martingale and the conditional distributions of absorption time in the moran process many models of evolution are stochastic processes where some quantity of interest fluctuates randomly in time one classic example is the moranbirthdeath process where that quantity is the number

a projected lagrangian algorithm for semi infinite programming a globally convergent algorithm is presented for the solution of a wide class of semi infinite programming problems the method is based on the solution of a sequence of equality constrained quadratic programming problems and usually has a second order convergence rate numerical results illustrating the method are given

4 cycle free ldpc codes based on difference sets difference sets are used to give a novel method for constructing structured regular quasi cyclic low density parity check codes let fq be a field with q elements and assume that d d1 dk is a v k 1 difference set for zv with d1 d2 dk depending on v q 1 v 2dk or v 2dk 1 three code construction methods are given that produce regular 4 cycle free codes that is codes with girth at least 6 simulation results show that the constructed codes perform well over the awgn channel with an iterative sum product message passing decoding algorithm

evolutionary games on cycles with strong selection evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success quantified by the probability that a single mutant takes over a population graph structures compared to the well mixed case can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant properties of the associated mean fixation times can be more intricate especially when selection is strong the intuition is that fixation of a beneficial mutant happens fast in a dominance game that fixation takes very long in a coexistence game and that strong selection eliminates demographic noise here we show that these intuitions can be misleading in structured populations we analyze mean fixation times on the cycle graph under strong frequency dependent selection for two different microscopic evolutionary update rules death birth and birth death we establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size depending on the underlying game we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring death birth update in contrast if selection for an offspring occurs before random removal birth death update then strong selection can remove demographic noise almost entirely

an analysis of the fixation probability of a mutant on special classes of non directed graphs there is a growing interest in the study of evolutionary dynamics on populations with some non homogeneous structure in this paper we follow the model of lieberman et al lieberman et al 2005 na

pilot symbol assisted phase noise compensation with forward backward wiener smoothing filters we present a novel wiener smoothing filter procedure for pilot symbol assisted estimation of oscillator phase noise the procedure consists of forward and backward first order infinite impulse response filtering the pilot symbols and combining the filter outputs to generate an estimate of the phase noise we analyze the mean square error performance of this pilot symbol assisted forward backward wiener smoothing filter fbwsf procedure and show its optimality under the assumption that the phase noise is modeled as a first order autoregressive moving average process we then apply the fbwsf as a code aided phase noise compensation technique in an iterative receiver framework the iterative receiver presented here first estimates phase noise roughly by using the pilot symbol assisted fbwsf then it refines the estimates with the code aided version of fbwsf the resulting receiver achieves excellent error performance at a feasible level of computational complexity

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

explicit construction of families of ldpc codes with no 4 cycles low density parity check ldpc codes are serious contenders to turbo codes in terms of decoding performance one of the main problems is to give an explicit construction of such codes whose tanner graphs have known girth for a prime power q and m spl ges 2 lazebnik and ustimenko construct a q regular bipartite graph d m q on 2q sup m vertices which has girth at least 2 spl lceil m 2 spl rceil 4 we regard these graphs as tanner graphs of binary codes lu m q we can determine the dimension and minimum weight of lu 2 q and show that the weight of its minimum stopping set is at least q 2 for q odd and exactly q 2 for q even we know that d 2 q has girth 6 and diameter 4 whereas d 3 q has girth 8 and diameter 6 we prove that for an odd prime p lu 3 p is a p sup 3 k code with k spl ges p sup 3 2p sup 2 3p 2 2 we show that the minimum weight and the weight of the minimum stopping set of lu 3 q are at least 2q and they are exactly 2q for many lu 3 q codes we find some interesting ldpc codes by our partial row construction we also give simulation results for some of our codes

fixation time in evolutionary graphs a mean field approach using an analytical method we calculate average conditional fixation time of mutants in a general graph structured population of two types of species the method is based on markov chains and uses a mean field approximation to calculate the corresponding transition matrix analytical results are compared with the results of simulation of the moran process on a number of network structures

a class of 1 generator quasi cyclic codes if r f sub q x spl rceil x sup m 1 s f sub qn x x sup m 1 we define the mapping a x spl rarr a x spl sigma sub 0 sup n 1 a sub i x spl alpha sub i from r sup n onto s where spl alpha sub 0 spl alpha sub i spl alpha sub n 1 is a basis for f sub qn over f sub q this carries the q ray 1 generator quasicyclic qc code r a x onto the code ra x in s whose parity check polynomial p c p is defined as the monic polynomial h x over f sub q of least degree such that h x a x 0 in the special case where gcd q m 1 and where the prime factorizations of x sub m 1 over f sub q and f sub qn are the same we show that there exists a one to one correspondence between the q ary 1 generator quasis cyclic codes with p c p h x and the elements of the factor group j i where j is the ideal in s with p c p h x and i the corresponding quantity in r we then describe an algorithm for generating the elements of j i next we show that if we choose a normal basis for f sub qn over f sub q then we can modify the aforementioned algorithm to eliminate a certain number of equivalent codes thereby rending the algorithm more attractive from a computational point of view finally in section iv we show how to modify the above algorithm in order to generate all the binary self dual 1 generator qc codes

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

analytical calculation of average fixation time in evolutionary graphs the ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics fixation probability and average fixation time aft are two important parameters to quantify this ability in this paper we introduce an analytical approach for exact calculation of aft using this method we obtain aft for two types of evolutionary graphs cycle graph as a highly homogeneous graph and star graph as a highly heterogeneous graph we use symmetries of these graphs to calculate aft analytical results are confirmed with simulation we also examine the effect of adding some random edges to each of these structures

fitness dependence of the fixation time distribution for evolutionary dynamics on graphs evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and nonmutant individuals recent studies have found that fixation times in such systems often have right skewed distributions little is known however about how these distributions and their skew depend on mutant fitness here we calculate the fitness dependence of the fixation time distribution for the moran birth death process in populations modeled by two extreme networks the complete graph and the one dimensional ring lattice obtaining exact solutions in the limit of large network size we find that with non neutral fitness the moran process on the ring has normally distributed fixation times independent of the relative fitness of mutants and nonmutants in contrast on the complete graph the fixation time distribution is a fitness weighted convolution of two gumbel distributions when fitness is neutral the fixation time distribution jumps discontinuously and becomes highly skewed on both the complete graph and the ring even on these simple networks the fixation time distribution exhibits a rich fitness dependence with discontinuities and regions of universality extensions of our results to two fitness moran models times to partial fixation and evolution on random networks are discussed

an analysis of optimal modal regulation convergence and stability this paper treats the linear quadratic regulator problem for infinite dimensional second order in time linear oscillators we solve the problem approximately by modeling a finite number of mode

quasicyclic low density parity check codes from circulant permutation matrices in this correspondence the construction of low density parity check ldpc codes from circulant permutation matrices is investigated it is shown that such codes cannot have a tanner graph representation with girth larger than 12 and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived these results suggest that families of ldpc codes with such girth values are relatively easy to obtain and consequently additional parameters such as the minimum distance or the number of redundant check sums should be considered to this end a necessary condition for the codes investigated to reach their maximum possible minimum hamming distance is proposed

optimal low order controller design via lqg like parametrization abstract a new lqg like parametrization scheme is introduced for low order controller design descent based design methodologies are developed for optimizing an h 2 cost with respect to the controller design parameters in this case the reduced order regulator and estimator gain matrices in a modified version the reduced order model of the plant is also updated numerical experiments using large space structure models show the efficacy of this approach

construction of structured regular ldpc codes a design theoretic approach a new combinatorial technique for constructing girth 6 structured binary regular low density parity check ldpc codes based on special types of t designs is given a very large number of well known t designs can be used by this method for code construction based on this method a t v k design d x b can be exploited for code construction if it satisfies the following three conditions 1 b1 b2 t for any two blocks b1 b2 b and b1 b2 2 1 and 3 k t though the technique works for any t design satisfying these conditions we focus only on the utilization of simple triple systems super simple bibds steiner systems and large sets lss of t designs we also construct binary and non binary girth 6 qc ldpc codes from the t designs satisfying these conditions by using matrix dispersion method experimental results show that the constructed non binary qc ldpc codes can provide good practical performance under iterative decoding using the fast fourier transform based q ary sum product algorithm fft qspa and they can achieve acceptable coding gains over random like codes of comparable parameters decoded with sum product algorithm spa

incidence structures from the blown up plane and ldpc codes in this paper new regular incidence structures are presented they arise from sets of conics in the affine plane blown up at its rational points the ldpc codes given by these incidence matrices are studied these sparse incidence matrices turn out to be redundant which means that their number of rows exceeds their rank such a feature is absent from random ldpc codes and is in general interesting for the efficiency of iterative decoding the performance of some codes under iterative decoding is tested some of them turn out to perform better than regular gallager codes having similar rate and row weight

a comparative study of several semi infinite nonlinear programming algorithms abstract a computational comparison of several recent semi infinite nonlinear programming algorithms is presented because of the importance of this area there have recently been proposed a number of algorithms having a global convergence property the algorithms used in this study include a feasible direction method and some variants of successive quadratic programming methods robustness and relative efficiency of the algorithms are examined on the basis of the results for some standard test examples chosen from earlier literature

a smoothing trust region newton cg method for minimax problem abstract this paper presents a smooth approximate method with a new smoothing technique and a standard unconstrained minimization algorithm in the solution to the finite minimax problems the new smooth approximations only replace the original problem in some neighborhoods of the kink points with a twice continuously differentiable function its gradient and hessian matrix are the combination of the first and the second order derivative of the original functions respectively compared to the other smooth functions such as the exponential penalty function the remarkable advantage of the new smooth function is that the combination coefficients of its gradient and the hessian matrix have sparse properties furthermore the maximal possible difference value between the optimal values of the smooth approximate problem and the original one is determined by a fixed parameter selected previous an algorithm to solve the equivalent unconstrained problem by using the trust region newton conjugate gradient method is proposed in the solution process finally some numerical examples are reported to compare the proposed algorithm with sqp algorithm that implements in matlab toolbox and the algorithm in e polak j o royset r s womersley algorithms with adaptive smoothing for finite minimax problems journal of optimization theory and applications 119 3 2003 459 484 based on the exponential penalty function the numerical results prove that the proved algorithm is efficient

majorization a computational complexity reduction technique in control system design a methodology is presented for transcribing worst case control system design specifications into semi infinite inequalities of low computational complexity which are tractable by semi infinite programming algorithms these algorithms can be used to find a design which satisfies specifications or to find a design which satisfies specifications and minimizes a cost a computational example is given

on the design of linear multivariable feedback systems via constrained nondifferentiable optimization in h sup infinity spaces the design discussed is of linear lumped time invariant multivariable feedback systems subject to various frequency and time domain performance specifications the approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex nondifferentiable optimization problems these problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular uniformly locally lipschitz continuous functions in r sup n

pseudocyclic maximum distance separable codes the n k pseudocyclic maximum distance separable mds codes modulo x sup n a over gf q are considered suppose that n is a divisor of q 1 if n is odd pseudocyclic mds codes exist for all k however if n is even nontrivial pseudocyclic mds codes exist for odd k but not for even k if a is a quadratic residue in gf q and they exist for even k but not for odd k if a is not a quadratic residue in gf q also considered is the case when n is a divisor of q 1 and it is shown that pseudocyclic mds codes exist if and only if the multiplicative order of a divides q 1 n and that when this condition is satisfied such codes exist for all k if the condition is not satisfied every pseudocyclic code of length n is the result of interleaving a shorter pseudocyclic code

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

finite dimensional compensators for infinite dimensional systems with unbounded input operators this paper contains a design procedure for constructing finite dimensional compensators for a class of infinite dimensional systems with unbounded input operators applications to retarded functional differential systems with delays in the input or the output variable and to partial differential equations with boundary input operators are discussed

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance

linear state space systems in infinite dimensional space the role and characterization of joint stabilizability detectability several fundamental results from the theory of linear state space systems in finite dimensional space are extended to encompass a class of linear state space systems in infinite dimensional space the results treated are those pertaining to the relationship between input output and internal stability the problem of dynamic output feedback stabilization and the concept of joint stabilizability detectability a complete structural characterization of jointly stabilizable detectable systems is obtained the generalized theory applies to a large class of linear state space systems assuming only that i the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators ii the state space is hilbert space iii the input and output spaces are finite dimensional and iv the sensing and control operators are bounded general conclusions regarding the fundamental structure of control theoretic problems in infinite dimensional space can be drawn from these results