global smooth solutions and exponential stability for a nonlinear beam in this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi linear beam where the nonlinearity comes from hooke s law first we derive an existence result for short time solutions of the system of equations then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense in particular we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time the input being zero can be understood as a boundary feedback

a new upper bound on the ml decoding error probability of linear binary block codes in awgn interference performance evaluation of maximum likelihood ml soft decision decoded binary block codes is usually carried out using bounding techniques many tight upper bounds on the error probability of binary codes are based on the so called gallager s first bounding technique gfbt the tangential sphere bound tsb of poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example within the framework of the tsb and gfbt we apply a new method referred to as the added hyper plane ahp technique to the decomposition of the error probability this results in a bound developed upon the application of two stages of the gfbt with two different gallager regions culminating in a tightened upper bound beyond the tsb the proposed bound is simple and only requires the spectrum of the binary code

on improved bounds on the decoding error probability of block codes over interleaved fading channels with applications to turbo like codes we derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved rician fading channels coherently detected and maximum likelihood ml decoded we assume that the fading coefficients during each symbol are statistically independent due to a perfect channel interleaver and that perfect estimates of these fading coefficients are provided to the receiver the improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity and are found by generalizing some previously introduced upper bounds for the binary input additive white gaussian nose awgn channel the advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low density parity check ldpc codes and it is especially pronounced in a portion of the rate region exceeding the cutoff rate our generalization of the duman and salehi bound duman and salehi 1998 duman 1998 which is based on certain variations of gallager s 1965 bounding technique is demonstrated to be the tightest reported upper bound we therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo like codes referring to the optimal ml decoding for certain ensembles of uniformly interleaved turbo codes the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms

on the error exponents of improved tangential sphere bounds the performance of maximum likelihood ml decoded binary linear block codes over the additive white gaussian noise awgn channel is addressed via the tangential sphere bound tsb and two of its recent improved versions the correspondence is focused on the derivation of the error exponents of these bounds although it was shown that some recent improvements of the tsb tighten this bound for finite length codes it is demonstrated in this correspondence that their error exponents coincide for an arbitrary ensemble of binary linear block codes the common value of these error exponents is explicitly expressed in terms of the asymptotic growth rate of the average distance spectrum

on interleaved differentially encoded convolutional codes we study a serially interleaved concatenated code construction where the outer code is a standard convolutional code and the inner code is a recursive convolutional code of rate 1 we focus on the ubiquitous inner differential encoder used in particular to resolve phase ambiguities double differential encoder used to resolve both phase and frequency ambiguities and another rate 1 recursive convolutional code of memory 2 we substantiate analytically the rather surprising result that the error probabilities corresponding to a maximum likelihood ml coherently detected antipodal modulation over the additive white gaussian noise awgn channel for this construction are advantageous as compared to the stand alone outer convolutional code this is in spite of the fact that the inner code is of rate 1 the analysis is based on the tangential sphere upper bound of an ml decoder incorporating the ensemble weight distribution wd of the concatenated code where the ensemble is generated by all random and uniform interleavers this surprising result is attributed to the wd thinning observed for the concatenated scheme which shapes the wd of the outer convolutional code to resemble more closely the binomial distribution typical of a fully random code of the same length and rate this gain is maintained regardless of a rather dramatic decrease as demonstrated here in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand alone convolutional code the advantage of the examined serially interleaved concatenated code given in terms of bit and or block error probability which is decoded by a practical suboptimal decoder over the optimally decoded standard convolutional code is demonstrated by simulations and some insights into the performance of the iterative decoding algorithm are also discussed though we have investigated only specific constructions of constituent inner rate 1 and outer codes we trust hinging on the rational of the arguments here that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes

model reference adaptive control of 2 times 2 coupled linear hyperbolic pdes we solve a model reference adaptive control problem for a class of linear 2 times 2 hyperbolic partial differential equations pdes with uncertain system parameters subject to harmonic disturbances from a single boundary measurement anticollocated with the actuation this is done by transforming the system into a canonical form from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters a representation facilitating for the design of adaptive laws a stabilizing controller is then combined with the adaptive laws to make the measured signal asymptotically track the output of a reference model the reference model is taken as a simple transport pde moreover pointwise boundedness of all variables in the closed loop is proved provided the reference signal is bounded the theory is demonstrated in a simulation

a new ber upper bound for multiuser downlink systems we consider improvement of bit error rate ber upper bounds based on the notion of decomposable error vectors devs introduced by s verdu for downlink multiuser space time systems over rayleigh fading channels although omission of devs and limiting before averaging lba technique are known to improve the standard union bound ub considerably it is mathematically intractable to obtain a bound in a closed form in this paper assuming maximum likelihood ml detection for downlink multiuser space time spreading sts systems we introduce a new modification of the decomposability of error vectors and propose a new ber upper bound we prove that the proposed bound is tighter than the standard union bound and the bound based on the overall decomposability the numerical results show that the proposed bound is also tighter than the bound based on positive sum decomposability psd in the scenario of downlink multiuser transmission

brief paper boundary control of linearized saint venant equations oscillating modes the paper investigates the control of oscillating modes occurring in open channels due to the reflection of propagating waves on the boundaries these modes are well represented by linearized saint venant equations a set of hyperbolic partial differential equations which describe the dynamics of one dimensional open channel flow around a given stationary regime we use a distributed transfer function approach to compute a dynamic boundary controller that cancels the oscillating modes over all the canal pool this result is recovered with a riemann invariants approach in the case of a frictionless horizontal canal pool the effect of a proportional boundary control on the poles of the transfer matrix is then characterized by a root locus and we derive an asymptotic result for high frequencies closed loop poles

global solutions and blow up solutions for a nonlinear string with boundary input and output abstract in this paper we investigate the global solutions and blow up solutions for a nonlinear string with boundary input and output and prove that under some conditions the system has global solutions and blow up solutions respectively

performance bounds for erasure list and decision feedback schemes with linear block codes a message independence property and some new performance upper bounds are derived in this work for erasure list and decision feedback schemes with linear block codes transmitted over memoryless symmetric channels similar to the classical work of forney this work is focused on the derivation of some gallager type bounds on the achievable tradeoffs for these coding schemes where the main novelty is the suitability of the bounds for both random and structured linear block codes or code ensembles the bounds are applicable to finite length codes and to the asymptotic case of infinite block length and they are applied to low density parity check code ensembles

gallager bounds for noncoherent decoders in fading channels recently gallager s bounding techniques have been used to derive tight performance bounds for coded systems in fading channels most works in this field have thus far dealt with coherent decoding this paper develops gallager bounds for noncoherent systems in fading channels unlike coherent decoding the exact error probability of a noncoherent decoder detector conditioned on the fading coefficients does not admit a closed form expression this difficulty is overcome in this paper by employing the chernoff technique although it weakens the bounds to some extent the chernoff technique enables the derivations of the limit before average lba bound and gallager bounds in closed form for noncoherent fading channels numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound

an adaptive observer design for n 1 coupled linear hyperbolic pdes based on swapping in this paper we use swapping design filters to bring systems of n 1 partial differential equations of the hyperbolic type to static form standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions proof of boundedness of the adaptive laws are offered and the results are demonstrated in simulations

the mixed initial boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics in this paper we prove that the c0 boundedness of solution implies the global existence and uniqueness of c1 solution to the mixed initial boundary value problem for linearly degenerate reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the c0 norm of solution may blow up in a finite time this gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves the same result is still valid for the quasilinear hyperbolic system of rich type

bounds on maximum likelihood decoding performance for linear codes at low rates for a given linear code ensemble upper bounds on the error probability under maximum likelihood decoding are investigated at low rates a class of symmetric memoryless channels suitable for bhattacharyya type bounds which are particularly of importance at low rates is introduced over a symmetric channel a lower bound on the error exponent is derived for a given linear code a sufficient condition for achieving the expurgated exponent which is the best among known error exponents at low rates within a fixed discrepancy is given over a general discrete memoryless channel the same analysis provides a lower bound on the average error exponent for an ensemble of coset codes generated by a given linear code the bounding technique is extended to the case of generalized maximum likelihood decoding with erasure and list decoding options

the mixed initial boundary value problem for diagonalizable quasilinear hyperbolic systems in the first quadrant abstract in this paper we investigate the mixed initial boundary value problem for diagonalizable quasilinear hyperbolic systems with nonlinear boundary conditions on a half unbounded domain t x t 0 x 0 under the assumptions that system is strictly hyperbolic and linearly degenerate we obtain the global existence and uniqueness of c 1 solutions with the bounded l 1 l norm of the initial data as well as their derivatives and appropriate boundary condition based on the existence results of global classical solutions we also prove that when t tends to infinity the solutions approach a combination of c 1 travelling wave solutions under the appropriate assumptions of initial and boundary data the results can be applied to the equation of time like extremal surface in minkowski space r 1 1 n

decay rate for a class of viscoelasticity equation with nonlinear damping on the boundary abstract in this paper we study the equation of viscoelasticity u t t u x x t f u x x f x t with the nonlinear damping term on the boundary making use of the so called energy perturbation method and a comparison inequality we prove the relationship between decay rate of solutions and f x t that is they have the same exponential decay or algebraic decay for the case f s s s 2 2 and for the case f s s 2 2 they have the same algebraic decay

tightened upper bounds on the ml decoding error probability of binary linear block codes the performance of maximum likelihood ml decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability the upper bounds on the block and bit error probabilities are valid for any memoryless binary input and output symmetric communication channel and their effectiveness is exemplified for various ensembles of turbo like codes over the additive white gaussian noise awgn channel an expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds

new performance bounds for turbo codes we derive a new upper bound on the word and bit error probabilities of turbo codes with maximum likelihood decoding by using the gallager bound since the derivation of the bound for a given interleaver is intractable we assume uniform interleaving as in the derivation of the standard union bound for turbo codes the result is a generalization of the transfer function bound and remains useful for a wider range of signal to noise ratios particularly for some range below the channel cutoff rate the new bound is also applicable to other linear codes

an energy preserving nonlinear system modeling a string with input and output on the boundary abstract we study an energy conserving distributed parameter system described by a nonlinear string equation with the input and output at the boundary we prove the existence of global smooth solutions to this quasilinear hyperbolic system if the initial data and the boundary input are small if moreover the input function becomes zero after some finite time then the state trajectories decay exponentially

on some nonlinear hyperbolic systems with damping boundary conditions in recent years the effect of boundary damping on the solutions to interior initial boundary value problems for hyperbolic equations has been extensively studied in 111 quinn and russell considered the wave equation with damping boundary condition on a part of the boundary it was proved by control theoretic method that if the boundary where the boundary condition was posed was star shaped then the solution of the wave equation had polynomial decay rate later on chen in l got the exponential decay of solutions to the wave equation under the more restrictive assumptions on the boundary and also lagnese in 6 got the exponential decay of solutions to the three dimensional elastic wave equations with damping boundary condition on a part of the boundary provided the geometry of the boundary is suitably restricted as for the nonlinear problem greenberg and li in 131 considered the nonlinear conservation system in one space dimension with damping boundary condition and proved the global existence of smooth solution when the initial data are small shen and zheng 14 and nagasawa 9 proved the global existence of classical solutions to the system of one dimensional thermoelasticity and to the system of one dimensional nonlinear problem in higher space dimension respectively for the nonlinear problem in higher space dimension to our knowledge the works were done by qin lo and zajaczkowski 26 only for the nonlinear wave equation with damping boundary conditions based on chen s results in l in this paper our aim is to derive the decay rate of solutions to the linear hyperbolic system of second order with damping boundary condition without any assumptions on the geometry of the boundary by using the spectral analysis method cf section 2 below and then to prove the global existence of smooth solutions to the corresponding nonlinear system with applications to nonlinear elastodynamics and to nonlinear acoustic wave equations our approach to obtaining the rate of decay of solutions to linear problem is completely different from l 6 and lo

generalized union bound for space time codes gallager s second bounding technique also known as the generalized union bound is employed to derive a new upper bound on the error probability of space time codes stcs with maximum likelihood ml decoding on quasi static rayleigh fading channels the new bound is distinguished by two characteristics unlike the classical union bound the new bound is rapidly convergent and is only a few decibels away from simulation results and compared with gallager s first bound it has better computational efficiency and numerical stability hence the new bound is a useful tool for performance analysis and computer search of good stcs moreover the correlation between fading coefficients is easily accommodated by the new bound the application of the new bound to convolutional coding on block fading channels is also demonstrated and an improved version is derived for the bit error probability of maximum a posteriori probability decoding

on the asymptotic input output weight distributions and thresholds of convolutional and turbo like encoders we present a general method for computing the asymptotic input output weight distribution of convolutional encoders in some instances one can derive explicit analytic expressions in general though to determine the growth rate of the input output weight distribution for a particular normalized input weight spl kappa and output weight spl omega a system of polynomial equations has to be solved this method is then used to determine the asymptotic weight distribution of various concatenated code ensembles and to derive lower bounds on the thresholds of these ensembles under maximum likelihood ml decoding

new techniques for upper bounding the ml decoding performance of binary linear codes in this paper new techniques are presented to either simplify or improve most existing upper bounds on the maximum likelihood ml decoding performance of the binary linear codes over additive white gaussian noise awgn channels firstly the recently proposed union bound using truncated weight spectrum by ma et al is re derived in a detailed way based on gallager s first bounding technique gfbt where the good region is specified by a sub optimal list decoding algorithm the error probability caused by the bad region can be upper bounded by the tail probability of a binomial distribution while the error probability caused by the good region can be upper bounded by most existing techniques secondly we propose two techniques to tighten the union bound on the error probability caused by the good region the first technique is based on pair wise error probabilities the second technique is based on triplet wise error probabilities which can be upper bounded by the fact that any three bipolar vectors form a non obtuse triangle the proposed bounds improve the conventional union bounds but have a similar complexity since they involve only the q function the proposed bounds can also be adapted to bit error probabilities

stability properties of one parameter flows this thesis is in two parts the first part consists of chapters 1 4 and the second part is chapter 5 in the first part we consider the idea of approximating pieces of orbits by a single orbit there are many examples of such properties approximation property a p see chapter one definitions 1 2 1 4 specification property s p 24 pseudo orbit tracing property p o t p 25 and definition 4 1 in chapter one we show that a p for a homeomorphism flow is equivalent to topological transitivity and density of periodic points and how this property a p is invariant under topological conjugacy in theorem 1 we prove that an expansive homeomorphism which is topologically mixing and has p o t p also has the s p in chapter two theorem 2 we prove that the p o t p for flows is invariant under topological conjugacy with preserved orientation velocity changes also we prove in theorem 3 that the suspension flow 2 for a homeomorphism t x x has p o t p if and only if t has the p o t p in chapter three we prove that an expansive flow which has the p o t p is topologically stable theorem 4 in chapter four the last theorem in this part is that every flow without fixed points on a compact manifold m which is topologically stable has the p o t p then some important corollaries are deduced in the second part of this thesis please see full thesis for rest of abstract

finite time stabilization of 2 times2 hyperbolic systems on tree shaped networks we investigate the finite time boundary stabilization of a one dimensional first order quasilinear hyperbolic system of diagonal form on 0 1 the dynamics of both boundary controls are governed by a finite time stable ode the solutions of the closed loop system issuing from small initial data in lip 0 1 are shown to exist for all times and to reach the null equilibrium state in finite time when only one boundary feedback law is available a finite time stabilization is shown to occur roughly in a twice longer time the above feedback strategy is then applied to the saint venant system for the regulation of water flows in a network of canals

brief paper lyapunov exponential stability of 1 d linear hyperbolic systems of balance laws explicit boundary dissipative conditions are given for the exponential stability in l 2 norm of one dimensional linear hyperbolic systems of balance laws email protected email protected email protected x 0 over a finite interval when the matrix m is marginally diagonally stable the result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised saint venant exner equations

topological entropy of fixed point free flows topological entropy was introduced as an invariant of topological conjugacy and also as an analogue of measure theoretic entropy topological entropy for one parameter flows on a compact metric spaces is defined by bowen general statements are proved about this entropy but it is not easy to calculate the topological entropy and to show it is invariant under conjugacy for all this i would like to try to pose a new direction and study a definition for the topological entropy that involves handling the technical difficulties that arise from allowing reparametrizations of orbits some well known results are proved as well using this definition these results enable us to prove some results which seem difficult to prove using bowen s definition also we show here that this definition is equivalent to bowen s definition for any flow without fixed points on a compact metric space finally it is shown that the topological entropy of an expansive flow can be defined globally on a local cross sections

estimation of boundary parameters in general heterodirectional linear hyperbolic systems abstract in this paper we extend recent results on state and boundary parameter estimation in coupled systems of linear partial differential equations pdes of the hyperbolic type consisting of n rightward and one leftward convecting equations to the general case which involves an arbitrary number of pdes convecting in both directions two adaptive observers are derived based on swapping design where one introduces a set of filters that can be used to express the system states as linear static combinations of the filter states and the unknown parameters standard parameter identification laws can then be applied to estimate the unknown parameters one observer which requires sensing at both boundaries generates estimates of the boundary parameters and system states while the second observer estimates the parameters from sensing limited to the boundary anti collocated with the uncertain parameters proof of boundedness of the adaptive laws is offered and sufficient conditions ensuring exponential convergence are derived the theory is verified in simulations

improvement of gallager upper bound and its variations for discrete channels 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

adaptive stabilization of 2 times 2 linear hyperbolic systems with an unknown boundary parameter from collocated sensing and control in this paper we solve an adaptive control problem for a class of 2 times 2 linear hyperbolic partial differential equations where sensing and actuation are restricted to the boundary anticollocated with an uncertain parameter this is done by combining a recently derived adaptive observer for the system states and the uncertain parameter with an adaptive control law proof of l 2 boundedness for all signals in the closed loop is given and the system states are proved to converge to zero pointwise in space the theory is demonstrated in a simulation

canonical coordinates and the pseudo orbit tracing property s smale 131 defines a hyperbolic closed invariant set 4 for a flow 4 on a compact manifold m smale s axiom a flows are those where the nonwandering set q is hyperbolic and 0 is the closure of the set of periodic points one of the most important properties of a hyperbolic set of a diffeomorphism or flow is the pseudo orbit tracing property also known as the shadowing property see section 1 for the definition the pseudo orbit tracing property potp is the key of the analysis of such maps or flows i 5 6 14 163 bowen and reddy l 2 121 and others have tried to generalize these ideas to homeomorphisms and flows on compact metric spaces in lo ombach shows that an expansive homeomorphism has canonical coordinates if and only if it has the pseudo orbit tracing property in this paper we investigate the same question for expansive oneparameter flows with canonical coordinates only but free of any hyperbolic assumption let 4 be a continuous flow on a compact manifold a4 and x a closedinvariant subset of m for xex and e o let

improved upper bounds on the ml decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum the ensemble performance of parallel and serial concatenated turbo codes is considered where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time varying recursive systematic convolutional codes following the derivation of the input output weight enumeration functions of the ensembles of random parallel and serial concatenated turbo codes the tangential sphere upper bound is employed to provide improved upper bounds on the block and bit error probabilities of these ensembles of codes for the binary input additive white gaussian noise awgn channel based on coherent detection of equi energy antipodal signals and maximum likelihood decoding the influence of the interleaver length and the memory length of the component codes is investigated the improved bounding technique proposed here is compared to the conventional union bound and to a alternative bounding technique by duman and salehi 1998 which incorporates modified gallager bounds the advantage of the derived bounds is demonstrated for a variety of parallel and serial concatenated coding schemes with either fixed or random recursive systematic convolutional component codes and it is especially pronounced in the region exceeding the cutoff rate where the performance of turbo codes is most appealing these upper bounds are also compared to simulation results of the iterative decoding algorithm

an analytical method for approximate performance evaluation of binary linear block codes an analytical method for approximate performance evaluation of binary linear block codes using an additive white gaussian noise channel model with binary phase shift keying modulation is presented we focus on the probability density function of the bit log likelihood ratio llr which is expressed in terms of the gram charlier series expansion this expansion requires knowledge of the statistical moments of the bit llr we introduce an analytical method for calculating these moments this is based on some recursive calculations involving certain weight enumerating functions of the code it is proved that the approximation can be as accurate as desired if we use enough terms in the gram charlier series expansion numerical results are provided for some examples which demonstrate close agreement with simulation results

topological pressure of continuous flows without fixed points in this paper we give the equivalent definitions of topological pressure for flows by using spanning sets weakly spanning sets strongly separated sets and tracing sets respectively we get an inequality between the topological pressures of lipschitz conjugate flows and prove that the topological pressure of expansive flows with tracing property can be described by its periodic orbits

performance analysis on ldpc coded systems over quasi static mimo fading channels in this paper we derive closed form upper bounds on the error probability of low density parity check ldpc coded modulation schemes operating on quasi static fading channels the bounds are obtained from the so called fano gallager s tight bounding techniques and can be readily calculated when the distance spectrum of the code is available in deriving the bounds for multiple input multiple output mimo systems we assume the ldpc code is concatenated with the orthogonal space time block code as an inner code we obtain an equivalent single input single output siso channel model for this concatenated coded modulation system the upper bounds derived here indicate good matches with simulation results of a complete transceiver system over rayleigh and rician mimo fading channels in which the iterative detection and decoding algorithm is employed at the receiver

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

upper bounds to error probabilities of coded systems beyond the cutoff rate a family of upper bounds to error probabilities of coded systems was recently proposed by d divsalar see ieee communication theory workshop 1999 jpl tmo prog rep 42 139 1999 these bounds are valid for transmission over the additive white gaussian noise channel and require only the knowledge of the weight spectrum of the code words after illustrating these bounds we extend them to fading channels contrary to the union bound our bounds maintain their effectiveness below the signal to noise ratio snr at which the cutoff rate of the channel equals the rate of the code some applications are shown first we derive upper bounds to the minimum snr necessary to achieve zero error probability as the code block length increases to infinity next we use our bounds to predict the performance of turbo codes and low density parity check codes

disturbance rejection in general heterodirectional 1 d linear hyperbolic systems using collocated sensing and control abstract we solve a disturbance rejection problem for a general class of heterodirectional 1 d linear hyperbolic partial differential equations pdes the disturbance enters at one boundary while sensing and actuation is limited to the opposite boundary we do this by combining a separately designed controller and observer into an output feedback controller and proving stability of the overall closed loop system and exponential regulation of the control objective to zero the theory is demonstrated in a simulation

design of integral controllers for nonlinear systems governed by scalar hyperbolic partial differential equations the paper deals with the control and regulation by integral controllers for the nonlinear systems governed by scalar quasi linear hyperbolic partial differential equations both the control input and the measured output are located on the boundary the closed loop stabilization of the linearized model with the designed integral controller is proved first by using the method of spectral analysis and then by the lyapunov direct method based on the elaborated lyapunov function we prove local exponential stability of the nonlinear closed loop system with the same controller the output regulation to the set point with zero static error by the integral controller is shown upon the nonlinear system numerical simulations by the preissmann scheme are carried out to validate the robustness performance of the designed controller to face to unknown constant disturbances

coding for parallel channels gallager bounds and applications to turbo like codes the transmission of coded communication systems is widely modeled to take place over a set of parallel channels this model is used for transmission over block fading channels rate compatible puncturing of turbo like codes multicarrier signaling multilevel coding etc new upper bounds on the maximum likelihood ml decoding error probability are derived in the parallel channel setting we focus on the generalization of the gallager type bounds and discuss the connections between some versions of these bounds the tightness of these bounds for parallel channels is exemplified for structured ensembles of turbo codes repeat accumulate ra codes and some of their recent variations e g punctured accumulate repeat accumulate codes the bounds on the decoding error probability of an ml decoder are compared to computer simulations of iterative decoding the new bounds show a remarkable improvement over the union bound and some other previously reported bounds for independent parallel channels this improvement is exemplified for relatively short block lengths and it is pronounced when the block length is increased in the asymptotic case where we let the block length tend to infinity inner bounds on the attainable channel regions of modern coding techniques under ml decoding are obtained based solely on the asymptotic growth rates of the average distance spectra of these code ensembles

feedback stabilization for the mass balance equations of an extrusion process in this article we study the stabilization problem for an extrusion process in the isothermal case the model expresses the mass conservation in the extruder chamber and consists of a hyperbolic partial differential equation pde and a nonlinear ordinary differential equation ode whose dynamics describes the evolution of a moving interface by using a lyapunov approach we obtain the exponential stabilization for the closed loop system under natural feedback controls through indirect measurements numerical simulations are also provided with a comparison between the proposed approach and linear pi feedback controller

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

variations on the gallager bounds with some applications by generalizing the framework of the second version of the duman salehi bound encompassing also deterministic and random codes we demonstrate its rather broad features and show that this variation provides the natural bridge between the 1961 and 1965 gallager bounds this approach entails a natural geometric interpretation encompassing also a large class of e0cient recent bounds or their cherno2 versions which are demonstrated to be special cases of the generalized second version of the duman salehi bound implications and applications of these observations are pointed out referring to known bounds as well as a novel extended version of the shulman feder bound c 2001 elsevier science b v all rights reserved

new gallager bounds in block fading channels in this paper we propose a new upper bound on the error performance of binary linear codes over block fading channels by employing gallager s first and second bounding techniques as the proposed bound is numerically intensive in its general form we consider two special cases namely the spherical bound and the ds2 exponential bound which are found to be tight in nonergodic and near ergodic block fading channels respectively the tightness of the proposed bounds is demonstrated for turbo codes many existing bounds for quasistatic or fully interleaved fading channels can be viewed as special cases of the proposed gallager bound

a quadratic lyapunov function for saint venant equations with arbitrary friction and space varying slope the exponential stability problem of the nonlinear saint venant equations is addressed in this paper we consider the general case where an arbitrary friction and space varying slope are both included in the system which lead to non uniform steady states an explicit quadratic lyapunov function as a weighted function of a small perturbation of the steady states is constructed then we show that by a suitable choice of boundary feedback controls that we give explicitly the local exponential stability of the nonlinear saint venant equations for the h 2 norm is guaranteed

boundary feedback stabilization of a class of coupled hyperbolic equations with nonlocal terms this paper solves the problem of boundary feedback stabilization of a class of coupled ordinary differential equations hyperbolic equations with boundary trace and integral nonlocal terms using the backstepping approach the controller is designed by formulating an integral operator whose kernel is required to satisfy a coupled hyperbolic partial integral differential equation by applying the method of successive approximations the kernel s well posedness is given we prove the exponential stability of the origin of the system in a suitable hilbert space moreover a wave system with nonlocal terms is stabilized by applying the above result

performance bounds for nonbinary linear block codes over memoryless symmetric channels the performance of nonbinary linear block codes is studied in this paper via the derivation of new upper bounds on the block error probability under maximum likelihood ml decoding the transmission of these codes is assumed to take place over a memoryless and symmetric channel the new bounds which are based on the gallager bounds and their variations are applied to the gallager ensembles of nonbinary and regular low density parity check ldpc codes these upper bounds are also compared with sphere packing lower bounds this study indicates that the new upper bounds are useful for the performance evaluation of coded communication systems which incorporate nonbinary coding techniques

distance spectrum and performance of channel coded physical layer network coding for binary input gaussian two way relay channels we investigate a channel coded physical layer network coding cpnc scheme for binary input gaussian two way relay channels in this scheme the codewords of the two users are transmitted simultaneously the relay computes and forwards a network coded nc codeword without complete decoding of the two users individual messages we propose a new punctured codebook method to explicitly find the distance spectrum of the cpnc scheme based on that we derive an asymptotically tight performance bound for the error probability our analysis shows that compared to the single user scenario the cpnc scheme exhibits the same minimum euclidean distance but an increased multiplicity of error events with minimum distance at a high snr this leads to an snr penalty of at most ln2 in linear scale for long channel codes of various rates our analytical results match well with the simulated performance

c 1 stably expansive flows abstract in this paper the c 1 interior of the set of vector fields whose integrated flows are expansive is characterized as the set of vector fields without singularities satisfying both axiom a and the quasi transversality condition and it is proved that the above vector fields possessing the shadowing property must be structurally stable as a corollary there exists a non empty c 1 open set of vector fields whose integrated flows do not have the shadowing property

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

on the modelling and stabilization of flows in networks of open canals in this paper we present a model for the controlled flow of a fluid through a network of canals using a coupled system of st venant equations we then generalize in a variety of ways recent results of coron d andrea novel and bastin concerning the stabilizability around equilibrium of the flow through a single channel this work is based on the theory of quasilinear hyperbolic systems and in particular on a delicate result of li ta tsien concerning the existence and decay of global classical solutions

adaptive stabilization of n 1 coupled linear hyperbolic systems with uncertain boundary parameters using boundary sensing abstract we design an adaptive control law stabilizing a class of systems of the form of n 1 linear partial differential equations pdes of the hyperbolic type from boundary sensing only we do this by combining a recently derived observer based on swapping design with a backstepping based adaptive control law with time varying gains boundedness of all signals in the closed loop system and asymptotic convergence to zero pointwise in space for the system states are proved the theory is demonstrated in a simulation

existence and exponential stability of a damped wave equation with dynamic boundary conditions and a delay term abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping and a delay term acting on the boundary if the weight of the delay term in the feedback is less than the weight of the term without delay or if it is greater under an assumption between the damping factor and the difference of the two weights we prove the global existence of the solutions under the same assumptions the exponential stability of the system is proved using an appropriate lyapunov functional more precisely we show that even when the weight of the delay is greater than the weight of the damping in the boundary conditions the strong damping term still provides exponential stability for the system

transmission of nonuniform memoryless sources via nonsystematic turbo codes we investigate the joint source channel coding problem of transmitting nonuniform memoryless sources over binary phase shift keying modulated additive white gaussian noise and rayleigh fading channels via turbo codes in contrast to previous work recursive nonsystematic convolutional encoders are proposed as the constituent encoders for heavily biased sources we prove that under certain conditions and when the length of the input source sequence tends to infinity the encoder state distribution and the marginal output distribution of each constituent recursive convolutional encoder become asymptotically uniform regardless of the degree of source nonuniformity we also give a conjecture which is empirically validated on the condition for the higher order distribution of the encoder output to be asymptotically uniform irrespective of the source distribution consequently these conditions serve as design criteria for the choice of good encoder structures as a result the outputs of our selected nonsystematic turbo codes are suitably matched to the channel input since a uniformly distributed input maximizes the channel mutual information and hence achieves capacity simulation results show substantial gains by the nonsystematic codes over previously designed systematic turbo codes furthermore their performance is within 0 74 1 17 db from the shannon limit finally we compare our joint source channel coding system with two tandem schemes which employ a fourth order huffman code performing near optimal data compression and a turbo code that either gives excellent waterfall bit error rate ber performance or good error floor performance at the same overall transmission rate our system offers robust and superior performance at low bers 10 sup 4 while its complexity is lower

performance of parallel concatenated coding schemes in this paper ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance under the assumption of maximum likelihood ml decoding are presented in particular it is proven that in any parallel concatenation scheme with k branches where all k encoders are recursive and the bhattacharyya parameter of the channel is sufficiently small the bit error rate ber and the word error rate go to 0 exactly like n 1 k and n 2 k respectively different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders are considered

outage exponent a unified performance metric for parallel fading channels the parallel fading channel which consists of finite number of subchannels is very important because it can be used to formulate many practical communication systems the outage probability on the other hand is widely used to analyze the relationship among the communication efficiency reliability signal to noise ratio snr and channel fading to the best of our knowledge the previous works only studied the asymptotic outage performance of the parallel fading channels which are only valid for a large number of subchannels or high snrs in this paper a unified performance metric which we shall refer to as the outage exponent will be proposed our approach is mainly based on the large deviations theory and meijer s g function it is shown that the proposed outage exponent is not only an accurate estimation of the outage probability for any number of subchannels any snr and any target transmission rate but also provides an easy way to compute the outage capacity finite snr diversity multiplexing tradeoff and snr gain the asymptotic performance metrics such as the delay limited capacity ergodic capacity and diversity multiplexing tradeoff can be directly obtained by letting the number of subchannels or snr tend to infinity similar to gallager s error exponent a reliable function for parallel fading channels which illustrates a fundamental relationship between the transmission reliability and efficiency can also be defined from the outage exponent therefore the proposed outage exponent provides a complete and comprehensive performance measure for parallel fading channels

marcum q functions and explicit kernels for stabilization of 2 2 linear hyperbolic systems with constant coefficients abstract we find the exact analytical solution to a goursat pde system governing the kernels of a backstepping based boundary control law that stabilizes a constant coefficient 2 2 system of first order hyperbolic linear pdes the solution to the goursat system is related to the solution of a simpler explicitly solvable goursat system through a suitable infinite series of powers of partial derivatives which is summed explicitly in terms of special functions including bessel functions and the generalized marcum q functions of the first order the marcum functions are common in certain applications in communications but have not appeared previously in control design problems the dependence of the explicit solutions with respect to system parameters is analyzed through several examples including the stabilization of a constant equilibrium for a quasi linear plant

on the relaxation approximation of boundary control of the isothermal euler equations we consider the isothermal euler equations without friction that simulate gas flow through a pipe we consider the problem of boundary stabilisation of this system locally around a given stationary state we present a feedback law that is linear in the physical variables and yields exponential decay of the system state for the numerical solution of hyperbolic systems of conservation laws the jin xin relaxation scheme can be used therefore we also consider the boundary stabilisation of the relaxation system by the linear riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system

tight exponential upper bounds on the ml decoding error probability of block codes over fully interleaved fading channels we derive tight exponential upper bounds on the decoding error probability of block codes which are operating over fully interleaved rician fading channels coherently detected and maximum likelihood decoded it is assumed that the fading samples are statistically independent and that perfect estimates of these samples are provided to the decoder these upper bounds on the bit and block error probabilities are based on certain variations of the gallager bounds these bounds do not require integration in their final version and they are reasonably tight in a certain portion of the rate region exceeding the cutoff rate of the channel by inserting interconnections between these bounds we show that they are generalized versions of some reported bounds for the binary input additive white gaussian noise channel

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes