dynamics and performance analysis of analog iterative decoding for low density parity check ldpc codes conventional iterative decoding with flooding or parallel schedule can be formulated as a fixed point problem solved iteratively by a successive substitution ss method in this paper we investigate the dynamics of a continuous time asynchronous analog implementation of iterative decoding and show that it can be approximated as the application of the well known successive relaxation sr method for solving the fixed point problem we observe that sr with the optimal relaxation factor can considerably improve the error rate performance of iterative decoding for short low density parity check ldpc codes compared with ss our simulation results for the application of sr to belief propagation sum product and min sum algorithms demonstrate improvements of up to about 0 7 db over the standard ss for randomly constructed ldpc codes the improvement in performance increases with the maximum number of iterations and by accordingly reducing the relaxation factor the asymptotic result corresponding to an infinite maximum number of iterations and infinitesimal relaxation factor represents the steady state performance of analog iterative decoding this means that under ideal circumstances continuous time asynchronous analog decoders can outperform their discrete time synchronous digital counterparts by a large margin our results also indicate that with the assumption of a truncated gaussian distribution for the random delays among computational modules the error rate performance of the analog decoder particularly in steady state is rather independent of the variance of the distribution the proposed simple model for analog decoding and the associated performance curves can be used as an ideal analog decoder benchmark for performance evaluation of analog decoding circuits

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

self compensation technique for simplified belief propagation algorithm the min sum algorithm is the most common method to simplify the belief propagation algorithm for decoding low density parity check ldpc codes however there exists a performance gap between the min sum and belief propagation algorithms due to nonlinear approximation in this paper a self compensation technique using dynamic normalization is thus proposed to improve the approximation accuracy the proposed scheme scales the min sum algorithm by a dynamic factor that can be derived theoretically from order statistics moreover applying the proposed technique to several ldpc codes for dvb s2 system the average signal to noise ratio degradation which results from approximation inaccuracy and quantization error is reduced to 0 2 db not only does it enhance the error correcting capability of the min sum algorithm but the proposed self compensation technique also preserves a modest hardware cost after realized with 0 13 mum standard cell library the dynamic normalization requires about 100 additional gates for each check node unit in the min sum algorithm

bmo and the regularity criterion for weak solutions to the magnetohydrodynamic equations in this paper we study the regularity criterion for weak solutions to the incompressible magnetohydrodynamic equations we derive the regularity of weak solutions in the marginal class moreover our result demonstrates that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solutions to the magnetohydrodynamic equations

reversible low density parity check codes low density parity check ldpc codes may be decoded using a circuit implementation of the sum product algorithm which maps the factor graph of the code by reusing the decoder for encoding both tasks can be performed using the same circuit thus reducing area and verification requirements motivated by this iterative encoding techniques based upon the graphical representation of the code are proposed code design constraints which ensure encoder convergence are presented and then used to design iteratively encodable codes while also preventing 4 cycle creation we show how the jacobi method for iterative matrix inversion can be applied to finite field matrices viewed as message passing and employed as the core of an iterative encoder we present an algebraic construction of 4 cycle free iteratively encodable codes using circulant matrices analysis of these codes identifies a weakness in their structure due to a repetitive pattern in the factor graph the graph supports pseudo codewords of low pseudo weight in order to remove the repetitive pattern in the graph we propose a recursive technique for generating iteratively encodable codes the new codes offer flexibility in the choice of code length and rate and performance that compares well to randomly generated quasi cyclic and extended euclidean geometry codes

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

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

regularity criteria for the 3d mhd equations involving one current density and the gradient of one velocity component abstract in this paper we consider the cauchy problem for the 3 d mhd equations and provide a regularity criterion involving u 3 and j 3 where u 3 and j 3 are the third component of the velocity and the current density respectively as by products we show that assumptions on two vorticity and one current density component are enough to ensure the smoothness of the solution and improve some previous results skalak 2014 zhou and pokorn 2009 2010 for the navier stokes equations

brief paper comparisons among robust stability criteria for linear systems with affine parameter uncertainties this paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems where the system state matrices considered are affinely dependent on the uncertain parameters at first a robust stability criterion for the class of systems to be affinely quadratically stable aqs is derived based on the vertex separator approach where affine parameter dependent lyapunov functions are exploited to prove stability then comparison results between the robust stability criterion and the existing tests for aqs are given in terms of degree of conservatism a numerical example is given to illustrate the results

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

on the frame error rate of concatenated turbo codes turbo codes with long frame lengths are usually constructed using a randomly chosen interleaver statistically this guarantees excellent bit error rate ber performance but also generates a certain number of low weight codewords resulting in the appearance of an error floor in the ber curve several methods including using an outer code have been proposed to improve the error floor region of the ber curve we study the effect of an outer bch code on the frame error rate fer of turbo codes we show that additional coding gain is possible not only in the error floor region but also in the waterfall region also the outer code improves the iterative app decoder by providing a stopping criterion and alleviating convergence problems with this method we obtain codes whose performance is within 0 6 db of the sphere packing bound at an fer of 10 sup 6

regularity criteria for a lagrangian averaged magnetohydrodynamic α model abstract in this paper we study the n dimensional lagrangian averaged magnetohydrodynamic lamhd model with 5 n 7 throughout the whole space various regularity criteria are established for both the cases with and those without viscosity

on the suboptimality of iterative decoding for turbo like and ldpc codes with cycles in their graph representation in this paper we focus on the suboptimality of iterative decoding on graphs with cycles through examining the use of a reliability based decoding algorithm for some concatenated codes with an interleaver known as turbo like codes the a posteriori probabilities delivered by the iterative decoding are regarded as reliability information and an efficient algorithm for the overall linear block code is applied at certain iterations simulation results show that the suboptimality of iterative decoding due to cycles can be at least partially compensated by this approach some insights about the potential additional coding gains achievable are investigated based on the characteristics of the constituent decoders these characteristics are related to the nature of suboptimality in the overall iterative decoding the effects of some code parameters and channel conditions on the behavior of iterative decoding are also studied for a better understanding of its suboptimality

ad 3 alternating directions dual decomposition for map inference in graphical models we present ad3 a new algorithm for approximate maximum a posteriori map inference on factor graphs based on the alternating directions method of multipliers like other dual decomposition algorithms ad3 has a modular architecture where local subproblems are solved independently and their solutions are gathered to compute a global update the key characteristic of ad3 is that each local subproblem has a quadratic regularizer leading to faster convergence both theoretically and in practice we provide closed form solutions for these ad3 subproblems for binary pairwise factors and factors imposing first order logic constraints for arbitrary factors large or combinatorial we introduce an active set method which requires only an oracle for computing a local map configuration making ad3 applicable to a wide range of problems experiments on synthetic and real world problems show that ad3 compares favorably with the state of the art

algebraic construction of quasi cyclic ldpc codes for the awgn and erasure channels this paper is concerned with construction of quasi cyclic qc low density parity check ldpc codes for three different types of channels the additive white gaussian noise the binary random erasure and the binary burst erasure channels two algebraic methods for systematic construction of qc ldpc codes are presented codes constructed perform well over all three types of channels

robust iterative learning control for linear systems with multiple time invariant parametric uncertainties this article presents a novel robust iterative learning control algorithm ilc for linear systems in the presence of multiple time invariant parametric uncertainties the robust design problem is formulated as a min max problem with a quadratic performance criterion subject to constraints of the iterative control input update then we propose a new methodology to find a sub optimal solution of the min max problem by finding an upper bound of the worst case performance the min max problem is relaxed to be a minimisation problem applying lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities lmis an lmi based ilc algorithm is given afterward and the convergence of the control input as well as the system error are proved finally we apply the proposed ilc to a generic example and a distillation column the numerical results reveal the effectiveness of the lmi based algorithm

a logarithmic regularity criterion for the two dimensional mhd equations abstract in this note we prove a logarithmic regularity criterion for the 2d mhd equations without magnetic diffusion in terms of the magnetic field in homogeneous besov space b 0

stability of polytopes of matrices via affine parameter dependent lyapunov functions asymptotically exact lmi conditions abstract this paper investigates necessary and sufficient conditions for the existence of an affine parameter dependent lyapunov function assuring the hurwitz or schur stability of a polytope of matrices a systematic procedure for constructing a family of linear matrix inequalities conditions of increasing precision is given at each step a set of linear matrix inequalities provides sufficient conditions for the existence of the affine parameter dependent lyapunov function necessity is asymptotically attained through a relaxation based on a generalization of polya s theorem to the case of matrix valued functions numerical experiments illustrate the results

two simple stopping criteria for turbo decoding this paper presents two simple and effective criteria for stopping the iteration process in turbo decoding with a negligible degradation of the error performance both criteria are devised based on the cross entropy ce concept they are as efficient as the ce criterion but require much less and simpler computations

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

some new regularity criteria for the 3d mhd equations abstract in this paper we consider the regularity criteria for solutions to the 3d incompressible magnetohydrodynamics mhd equations the first one involves h u 1 u 2 u and 3 b then the criterion concerning h u and h b 1 b 2 b is presented finally we show that the weak solution u b is actually regular provided that u 3 3 u b and 3 b are in suitable serrin type integrability classes respectively

a new regularity criterion for weak solutions to the viscous mhd equations in terms of the vorticity field abstract in this paper we consider regularity criterion for solutions to the 3d viscous incompressible mhd equations in morrey campanato spaces it is proved that if the vorticity field u belongs to m 2 3 r for 0 r 1 on 0 t then the solution remains smooth on 0 t

lp decoding of regular ldpc codes in memoryless channels we study error bounds for linear programming decoding of regular low density parity check ldpc codes for memoryless binary input output symmetric channels we prove bounds on the word error probability that are inverse doubly exponential in the girth of the factor graph for memoryless binary input awgn channel we prove lower bounds on the threshold for regular ldpc codes whose factor graphs have logarithmic girth under lp decoding specifically we prove a lower bound of 0 735 upper bound of eb n0 2 67 db on the threshold of 3 6 regular ldpc codes whose factor graphs have logarithmic girth our proof is an extension of a recent paper of arora daskalakis and steurer stoc 2009 who presented a novel probabilistic analysis of lp decoding over a binary symmetric channel their analysis is based on the primal lp representation and has an explicit connection to message passing algorithms we extend this analysis to any mbios channel

decoding algorithms for nonbinary ldpc codes over gf q in this letter we address the problem of decoding nonbinary low density parity check ldpc codes over finite fields gf q with reasonable complexity and good performance in the first part of the letter we recall the original belief propagation bp decoding algorithm and its fourier domain implementation we show that the use of tensor notations for the messages is very convenient for the algorithm description and understanding in the second part of the letter we introduce a simplified decoder which is inspired by the min sum decoder for binary ldpc codes we called this decoder extended min sum ems we show that it is possible to greatly reduce the computational complexity of the check node processing by computing approximate reliability measures with a limited number of values in a message by choosing appropriate correction factors or offsets we show that the ems decoder performance is quite good and in some cases better than the regular bp decoder the optimal values of the factor and offset correction are obtained asymptotically with simulated density evolution our simulations on ultra sparse codes over very high order fields show that nonbinary ldpc codes are promising for applications which require low frame error rates for small or moderate codeword lengths the ems decoder is a good candidate for practical hardware implementations of such codes

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

static team problems part ii affine control laws projections algorithms and the legt problem team problems over the set of affine team control laws are solved as constrained parameter optimization problems this methodology eases both the notational and computational difficulties for the lqgt linear quadratic gaussian team and the legt linear exponential gaussian team problems the constrained parameter optimization approach leads to the representation of the optimal team control gains as explicit projections of the optimal centralized gains the projection representation offers insight into the team solution and suggests an algorithm for computing the optimal gains for the legt problem the legt problem behavior is compared to lqgt behavior for an example which consists of a static team with garbled decision implementation

a regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces abstract we consider the regularity criterion for the 3d magneto micropolar fluid equations in triebel lizorkin spaces it is proved that if u l p 0 t f q 2 q 3 0 with 2 p 3 q 2 3 2 q then the solution remains smooth in 0 t as a corollary we obtain the classical beal kato majda criterion that is the condition u l 1 0 t b 0 ensures the smoothness of the solution

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

remarks on the regularity criteria for generalized mhd equations abstract we study the cauchy problem for the generalized mhd equations and prove some regularity criteria involving the integrability of u in the morrey multiplier spaces

a new regularity criterion for the 3d incompressible mhd equations via partial derivatives abstract we consider the regularity criterion for the incompressible mhd equations we show that the weak solution is regular provided that 0 1 3 w 3 w l 5 r 4 r 6 0 t l r r 3 with 4 r or 0 2 3 w 3 w l 11 r 7 r 12 0 t l r r 3 with 5 2 r 4

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

robust performance analysis with lmi based methods for real parametric uncertainty via parameter dependent lyapunov functions robust performance analysis for linear time invariant systems with linear fractional transformation real parametric uncertainty is considered new conditions of robust stability performance based on parameter dependent lyapunov functions are proposed the robust stability performance measures are robust pole location robust h sub spl infin performance and robust h sub 2 performance linear matrix inequality lmi based sufficient conditions for the existence of parameter dependent lyapunov functions are derived by using the quadratic separation concept the performances of the proposed conditions are compared with existing tests