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 expander codes sipser and spielman see ibid vol 42 p 1717 22 nov 1996 have introduced a constructive family of asymptotically good linear error correcting codes expander codes together with a simple parallel algorithm that will always remove a constant fraction of errors we introduce a variation on their decoding algorithm that with no extra cost in complexity provably corrects up to 12 times more errors

a justesen construction of binary concatenated codes that asymptotically meet the zyablov bound for low rate an explicit construction of a sequence of binary codes that asymptotically meet the zyablov bound for rates lower than 0 30 is given by using justesen s construction of concatenation the outer codes are constructed from generalized hermitian curves these outer codes can be described without any algebraic geometry terminology while the proofs of some properties deeply rely on algebraic geometry

h filtering for fuzzy systems with immeasurable premise variables an uncertain system approach this paper discusses a design of stable filters with h disturbance attenuation of takagi sugeno fuzzy systems with immeasurable premise variables when we consider the filter design of takagi sugeno fuzzy systems the selection of premise variables plays an important role if the premise variable is the state of the system then a fuzzy system describes a wide class of nonlinear systems in this case however a filter design of fuzzy systems based on parallel distributed compensator idea is infeasible to avoid such a difficulty we consider the premise variables uncertainties then we consider a robust h filtering problem for such an uncertain system a solution of the problem is given in terms of linear matrix inequalities lmis some numerical examples are given to illustrate our theory

improved nearly mds expander codes a construction of expander codes is presented with the following three properties i the codes lie close to the singleton bound ii they can be encoded in time complexity that is linear in their code length and iii they have a linear time bounded distance decoder by using a version of the decoder that corrects also erasures the codes can replace maximum distance separable mds outer codes in concatenated constructions thus resulting in linear time encodable and decodable codes that approach the zyablov bound or the capacity of memoryless channels the presented construction improves on an earlier result by guruswami and indyk in that any rate and relative minimum distance that lies below the singleton bound is attainable for a significantly smaller alphabet size

ip pspace using error correcting codes the mathbf ip theorem which asserts that mathbf ip mathbf pspace lund et al j acm 39 1992 pp 859 868 shamir j acm 39 1992 pp 878 880 is one of the major achievements of complexity theory the known proofs of the theorem are based on the arithmetization technique which transforms a quantified boolean formula into a related polynomial the intuition that underlies the use of polynomials is commonly explained by the fact that polynomials constitute good error correcting codes however the known proofs seem tailored to the use of polynomials and do not generalize to arbitrary error correcting codes in this work we show that the mathbf ip theorem can be proved by using general error correcting codes and their tensor products we believe that this establishes a rigorous basis for the aforementioned intuition and sheds further light on the mathbf ip theorem

robust h filtering for sampled data fuzzy systems abstract this paper is concerned with robust h filtering for takagi sugeno sampled data fuzzy systems with uncertain parameters takagi sugeno fuzzy system can describe a wide class of nonlinear systems and is widely used in many engineering fields recently system analysis and control design for nonlinear systems based fuzzy system approach have been active the system is usually modelled as a continuous time system while in practical situations the observation is taken at discrete instants such an observation can be represented as a delayed signal first it is shown that the error system which stems from an original fuzzy system and a sampled data filter becomes a system with time varying delay sufficient conditions for the error system to achieve the robust stability with h disturbance attenuation are given in terms of linear matrix inequalities lmis we derive such conditions via output delay system approach under the assumption that sampling time is not greater than some prescribed number based on such conditions we propose a robust h sampled data filter design for a fuzzy system we consider two different cases for the premise variables in our filter design numerical examples are given to illustrate our robust h sampled data filtering

new upper bounds on error exponents we derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels this is an improvement on the best earlier known bounds by shannon gallager berlekamp 1967 and mceliece omura 1977 for the probability of undetected error the new bounds are better than the bounds by levenshtein 1978 1989 and the bound by abdel ghaffar see ibid vol 43 p 1489 502 1997 moreover we further extend the range of rates where the undetected error exponent is known to be exact the new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities

fast decoding of expander codes expander codes are tanner codes defined on sparse graphs that have good expansion properties sipser and spielman 1996 showed that there is a linear time decoding algorithm for expander codes when the vertex expansion is at least 3 4 and the number of errors corrected is a constant fraction of the code length later feldman et al 2007 gave a decoding algorithm that allows the expansion to be 2 3 1 3c where c is the left degree of the underlying bipartite graph at the expense of polynomial time decoding complexity recently viderman 2013 further improved the expansion parameter to 2 3 1 6c and the decoding algorithm runs in linear time these results are for expander codes whose inner codes are parity check codes by using stronger inner codes chilappagari et al 2010 showed that there is a linear time decoding algorithm for every vertex expansion greater than 1 2 in this paper it is shown that for every vertex expansion there is a linear time decoding algorithm for expander codes using inner codes with minimum distance depending on the vertex expansion and that the number of errors corrected is a constant fraction of the code length

list decoding of algebraic geometric codes we generalize sudan s see j compl vol 13 p 180 93 1997 results for reed solomon codes to the class of algebraic geometric codes designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error correction bound d 1 2 d being the minimum distance of the code our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields for the latter problem we design a polynomial time algorithm and show that the resulting overall list decoding algorithm runs in polynomial time under some mild conditions several examples are included

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

robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices randomness is a vital resource for modern day information processing especially for cryptography a wide range of applications critically rely on abundant high quality random numbers generated securely here we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices our approach is secure against the most general adversaries and has the following new features cryptographic level of security tolerating a constant level of imprecision in devices requiring only unit size quantum memory for each device component in an honest implementation and allowing a large natural class of constructions for the protocol in conjunction with a recent work by chung et al l2014r it also leads to robust unbounded expansion using just 2 multipart devices when adapted for distributing cryptographic keys our method achieves for the first time exponential expansion combined with cryptographic security and noise tolerance the proof proceeds by showing that the renyi divergence of the outputs of the protocol for a specific bounding operator decreases linearly as the protocol iterates at the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices

braided block codes a new class of binary iteratively decodable codes with good decoding performance is presented these codes called braided block codes bbcs operate on continuous data streams and are constructed by interconnection of two component block codes bbcs can be considered as convolutional or sliding version of either elias product codes or expander codes in this paper we define bbcs describe methods of their construction analyze code properties and study asymptotic iterative decoding performance

codes on finite geometries new algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented the new construction methods result in a class of multistep majority logic decodable codes and three classes of low density parity check ldpc codes decoding methods for the class of majority logic decodable codes and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their tanner graphs are presented most of the codes constructed can be either put in cyclic or quasi cyclic form and hence their encoding can be implemented with linear shift registers

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

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

linear time encodable decodable codes with near optimal rate we present an explicit construction of linear time encodable and decodable codes of rate r which can correct a fraction 1 r spl epsiv 2 of errors over an alphabet of constant size depending only on spl epsiv for every 0 0 the error correction performance of these codes is optimal as seen by the singleton bound these are near mds codes such near mds linear time codes were known for the decoding from erasures our construction generalizes this to handle errors as well concatenating these codes with good constant sized binary codes gives a construction of linear time binary codes which meet the zyablov bound and also the more general blokh zyablov bound by resorting to multilevel concatenation our work also yields linear time encodable decodable codes which match forney s error exponent for concatenated codes for communication over the binary symmetric channel the encoding decoding complexity was quadratic in forney s result and forney s bound has remained the best constructive error exponent for almost 40 years now in summary our results match the performance of the previously known explicit constructions of codes that had polynomial time encoding and decoding but in addition have linear time encoding and decoding algorithms

expander codes using expander graphs we construct a new family of asymptotically good linear error correcting codes these codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors we present both randomized and explicit constructions of these codes experimental results demonstrate the good performance of the randomly chosen codes

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

robust reliable h control for fuzzy systems with random delays and linear fractional uncertainties this article studies the reliable robust stabilization problem for a class of uncertain takagi sugeno ts fuzzy systems with time varying delays the delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form by implementing a proper novel lyapunov functional together with linear matrix inequality lmi approach a new set of delay dependent sufficient conditions is derived to guarantee the asymptotic stability of ts fuzzy system with a prescribed h performance index further a reliable robust h control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain ts fuzzy system further schur complement and jensen s integral inequality are used to simplify the derivation in the main results the set of sufficient conditions is established using the relationship among the random time varying delay and its lower and upper bounds which can be easily solved by matlab lmi toolbox finally an illustrative example based on the truck trailer model is provided to show the effectiveness of the proposed new design technique

simple and accurate direction of arrival estimator in the case of imperfect spatial coherence we consider the direction finding problem in the imperfect spatial coherence case i e when the amplitude and phase of the wavefront vary randomly along the array aperture this phenomenon can originate from propagation through an inhomogeneous medium it is also encountered in the case of spatially dispersed sources we derive a fast and accurate estimator for the direction of arrival of a single source using a uniform linear array ula of sensors the estimator is based on a reduced statistic obtained from the subdiagonals of the covariance matrix of the array output it only entails computing the fourier transform of an m 1 length sequence where m is the number of array sensors a theoretical analysis is carried out and an expression for the asymptotic variance of the estimator is derived numerical simulations validate the theoretical results and show that the estimator has an accuracy very close to the cramer rao bound

matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts the performance of high resolution direction of arrival doa estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence the original solution to this problem was proposed by paulraj and kailath 1988 but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture a novel solution to this problem is proposed which does not require a priori knowledge of the spatial coherence matrix

subquadratic time encodable codes beating the gilbert varshamov bound we construct explicit algebraic geometry codes built from the garcia stichtenoth function field tower beating the gilbert varshamov bound for alphabet sizes at least 192 messages are identified with functions in certain riemann roch spaces associated with divisors supported on multiple places encoding amounts to evaluating these functions at degree one places by exploiting algebraic structures particular to the garcia stichtenoth tower we devise an intricate deterministic omega 2 runtime exponent encoding and 1 omega 2 expected runtime exponent randomized unique and list decoding algorithms here omega is the matrix multiplication exponent if omega 2 as widely believed the encoding and decoding runtimes are respectively nearly linear and nearly quadratic prior to this work encoding time of code families beating the gilbert varshamov bound were quadratic or worse

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

on trapping sets and guaranteed error correction capability of ldpc codes and gldpc codes the relation between the girth and the guaranteed error correction capability of left regular low density parity check ldpc codes when decoded using the bit flipping serial and parallel algorithms is investigated a lower bound on the size of variable node sets which expand by a factor of at least 3 4 is found based on the moore bound this bound combined with the well known expander based arguments leads to a lower bound on the guaranteed error correction capability the decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets the relation between fixed sets and a class of graphs known as cage graphs is studied upper bounds on the guaranteed error correction capability are then established based on the order of cage graphs the results are extended to left regular and right uniform generalized ldpc codes it is shown that this class of generalized ldpc codes can correct a linear number of worst case errors in the code length under the parallel bit flipping algorithm when the underlying tanner graph is a good expander a lower bound on the size of variable node sets which have the required expansion is established

correcting a fraction of errors in nonbinary expander codes with linear programming a linear programming decoder for nonbinary expander codes is presented it is shown that the proposed decoder has the nearest neighbor certificate properties it is also shown that this decoder corrects any pattern of errors of a relative weight up to approximately 1 4 a b where a and b are the relative minimum distances of the constituent codes

explicit codes achieving list decoding capacity error correction with optimal redundancy in this paper we present error correcting codes that achieve the information theoretically best possible tradeoff between the rate and error correction radius specifically for every 0 r 1 and epsiv 0 we present an explicit construction of error correcting codes of rate that can be list decoded in polynomial time up to a fraction 1 r epsiv of worst case errors at least theoretically this meets one of the central challenges in algorithmic coding theory our codes are simple to describe they are folded reed solomon codes which are in fact exactly reed solomon rs codes but viewed as a code over a larger alphabet by careful bundling of codeword symbols given the ubiquity of rs codes this is an appealing feature of our result and in fact our methods directly yield better decoding algorithms for rs codes when errors occur in phased bursts the alphabet size of these folded rs codes is polynomial in the block length we are able to reduce this to a constant depending on epsiv using existing ideas concerning ldquolist recoveryrdquo and expander based codes concatenating the folded rs codes with suitable inner codes we get binary codes that can be efficiently decoded up to twice the radius achieved by the standard gmd decoding

decentralized h fuzzy filter for nonlinear large scale sampled data systems with uncertain interconnections abstract this paper proposes a decentralized h fuzzy filter technique for nonlinear large scale interconnected systems that are based on the takagi sugeno fuzzy model the large scale system has unknown interconnection terms that are assumed to satisfy the quadratic bounds an error system between the nonlinear large scale system and the decentralized filter is constructed by using the fuzzy lyapunov technique sufficient conditions are proposed for both showing asymptotic stability and guaranteeing h fuzzy filter performance these sufficient conditions are derived in terms of linear matrix inequalities finally simulation examples are given to demonstrate the effectiveness of the proposed technique

using expander graphs to find vertex connectivity the vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial we present the fastest known algorithm for finding for a digraph with n vertices m edges and connectivity the time bound is o n p min 5 2 n3 4 m this improves the previous best bound of o n p min 3 n m for an undirected graph both of these bounds hold with m replaced by n expander graphs are useful for solving the following subproblem that arises in connectivity computation a known set r of vertices contains two large but unknown subsets that are separated by some unknown set s of vertices we must find two vertices of r that are separated by s

decoding of expander codes at rates close to capacity the decoding error probability of codes is studied as a function of their block length it is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small decoding error probability specifically it is assumed that there exists a family of codes of length n and rate r 1 epsiv c c is a capacity of a binary symmetric channel whose decoding probability decreases inverse polynomially in n it is shown that if the decoding probability decreases sufficiently fast but still only inverse polynomially fast in n then there exists another such family of codes whose decoding error probability decreases exponentially fast in n moreover if the decoding time complexity of the assumed family of codes is polynomial in n and 1 epsiv then the decoding time complexity of the presented family is linear in n and polynomial in 1 epsiv these codes are compared to the recently presented codes of barg and zemor error exponents of expander codes ieee transactions on information theory 2002 and concatenated codes serial and parallel ieee transactions on information theory 2005 it is shown that the latter families cannot be tuned to have exponentially decaying in n error probability and at the same time to have decoding time complexity linear in n and polynomial in 1 epsiv

reliability based joint detection decoding algorithm for nonbinary ldpc coded modulation systems this paper studies an extension and improvement of the joint detection decoding algorithm for nonbinary ldpc coded modulation systems the iterative joint detection decoding ijdd algorithm in 1 combines nonbinary ldpc decoding with signal detection based on the hard message passing strategy resulting in significantly reduced decoding complexity however it applies only to majority logic decodable nonbinary ldpc codes with high column weight for nonbinary ldpc codes with low column weight a noticeable performance loss will be incurred to handle this problem we propose a reliability based iterative joint detection decoding also termed improved ijdd algorithm which combines the accumulated reliability of symbols based on the one step majority logic decoding mlgd algorithm and a chase like local list decoding algorithm simulation results show that the improved ijdd algorithm outperforms the ijdd algorithm by about 0 3 db using nonbinary ldpc codes with high column weight and by about 3 db using nonbinary ldpc codes with low column weight d v 4 while maintaining the low complexity of decoding compared to the fft qspa the proposed algorithm has a performance degradation of 0 5 db in the high column weight regime and about 1 db in the low column weight regime

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

deletion codes in the high noise and high rate regimes the noise model of deletions poses significant challenges in coding theory with basic questions like the capacity of the binary deletion channel still being open in this paper we study the harder model of worst case deletions with a focus on constructing efficiently decodable codes for the two extreme regimes of high noise and high rate specifically we construct polynomial time decodable codes with the following tradeoffs for any varepsilon 0 1 codes that can correct a fraction 1 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon over an alphabet of size mathop mathrm poly nolimits 1 varepsilon 2 binary codes of rate 1 tilde o sqrt varepsilon that can correct a fraction varepsilon of deletions and 3 binary codes that can be list decoded from a fraction 1 2 varepsilon of deletions with rate mathop mathrm poly nolimits varepsilon this paper gives the first efficient constructions which meet the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets and correcting a constant fraction of bit deletions with rate approaching 1 over a fixed alphabet the above mentioned results bring our understanding of deletion code constructions in these regimes to a similar level as worst case errors

generalized and doubly generalized ldpc codes with random component codes for the binary erasure channel in this paper a method for the asymptotic analysis of generalized low density parity check gldpc codes and doubly generalized low density parity check d gldpc codes over the binary erasure channel bec based on extrinsic information transfer exit chart is described this method overcomes the problem consisting of the impossibility to evaluate the exit function for the check or variable component codes in situations where the information functions or split information functions for component codes are unknown according to the proposed technique gldpc codes and d gldpc codes where the generalized check and variable component codes are random codes with minimum distance at least 2 are considered a technique is then developed which finds the exit chart for the overall gldpc or d gldpc code by evaluating the expected exit function for each check and variable component code this technique is finally combined with the differential evolution algorithm in order to generate some good gldpc and d gldpc edge distributions numerical results of long random codes are presented which confirm the effectiveness of the proposed approach they also reveal that d gldpc codes can outperform standard ldpc codes and gldpc codes in terms of both waterfall performance and error floor

direction finding for an extended target with possibly non symmetric spatial spectrum we consider the problem of estimating the direction of arrival doa of an extended target in radar array processing two algorithms are proposed that do not assume that the power azimuthal distribution of the scatterers is symmetric with respect to the mass center of the target the first one is based on spectral moments which are easily related to the target s doa the second method stems from a previous paper by the present authors and consists of a least squares fit on the elements of the covariance matrix both methods are simple and are shown to provide accurate estimates furthermore they extend the range of unambiguous doas that can be estimated compared with the same previous paper

linear time encodable and decodable error correcting codes we present a new class of asymptotically good linear error correcting codes these codes can be both encoded and decoded in linear time they can also be encoded by logarithmic depth circuits of linear size and decoded by logarithmic depth circuits of size o nlogn we present both randomized and explicit constructions of these codes

low complexity estimators for distributed sources in antenna array applications the propagation environment is often more complicated than the ordinarily assumed model of plane wavefronts here a low complexity algorithm is suggested for estimating both the doa and the spread angle of a source subject to local scattering using a uniform linear array the parameters are calculated from the estimates obtained using a standard algorithm such as root music to fit a two ray model to the data the algorithm is shown to give consistent estimates and the statistical performance is studied analytically and through simulations

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

a generalization of weighted subspace fitting to full rank models the idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification previously some algorithms have been suggested based on similar ideas for a sensor array processing problem where the underlying data model is not low rank we show that two of these algorithms dspe and dispare fail to give consistent estimates and introduce a general class of subspace fitting like algorithms for consistent estimation of parameters from a possibly full rank data model the asymptotic performance is analyzed and an optimally weighted algorithm is derived the result gives a lower bound on the estimation performance for any estimator based on a low rank approximation of the linear space spanned by the sample data we show that in general for full rank data models no subspace based method can reach the cramer rao lower bound crb

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts eigenstructure subspace methods for direction of arrival estimation are only applicable when each wave front contributes a rank one component to the array covariance this implies that the wave fronts need to have perfect spatial coherence in several practical situations where the wave fronts may only have partial spatial coherence eigenstructure algorithms show poor performance such as overestimation of the number of sources bias and reduced accuracy and resolution in estimating the directions of arrival in this article the performance degradation due to partial spatial coherence is studied and a new approach is proposed that exploits the underlying coherence model to yield asymptotically exact estimates for finite data this method provides improved results only when the number of snapshots exceeds a certain threshold results of computer simulations are also presented

on decoding irregular tanner codes with local optimality guarantees we consider decoding of binary linear tanner codes using message passing iterative decoding and linear programming lp decoding in memoryless binary input output symmetric mbios channels we present new certificates that are based on a combinatorial characterization for the local optimality of a codeword in irregular tanner codes with respect to any mbios channel this characterization is a generalization of arora proc acm symp theory of computing 2009 and vontobel proc inf theory and appl workshop 2010 and is based on a conical combination of normalized weighted subtrees in the computation trees of the tanner graph these subtrees may have any finite height h even equal or greater than half of the girth of the tanner graph in addition the degrees of local code nodes in these subtrees are not restricted to two i e these subtrees are not restricted to skinny trees we prove that local optimality in this new characterization implies maximum likelihood ml optimality and lp optimality and show that a certificate can be computed efficiently we also present a new message passing iterative decoding algorithm called normalized weighted min sum nwms nwms decoding is a belief propagation bp type algorithm that applies to any irregular binary tanner code with single parity check local codes e g low density and high density parity check codes we prove that if a locally optimal codeword with respect to height parameter h exists whereby notably h is not limited by the girth of the tanner graph then nwms decoding finds this codeword in h iterations the decoding guarantee of the nwms decoding algorithm applies whenever there exists a locally optimal codeword because local optimality of a codeword implies that it is the unique ml codeword the decoding guarantee also provides an ml certificate for this codeword finally we apply the new local optimality characterization to regular tanner codes and prove lower bounds on the noise thresholds of lp decoding in mbios channels when the noise is below these lower bounds the probability that lp decoding fails to decode the transmitted codeword decays doubly exponentially in the girth of the tanner graph

approximate maximum likelihood estimators for array processing in multiplicative noise environments we consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise this scenario is encountered for example in communications owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media since the exact maximum likelihood ml estimator is computationally intensive two approximate solutions are proposed originating from the analysis of the high and low signal to noise ratio snr cases respectively first starting with the no additive noise case a very simple approximate ml aml sub 1 estimator is derived the performance of the aml sub 1 estimator in the presence of additive noise is studied and a theoretical expression for its asymptotic variance is derived its performance is shown to be close to the cramer rao bound crb for moderate to high snr next the low snr case is considered and the corresponding aml sub 2 solution is derived it is shown that the approximate ml criterion can be concentrated with respect to both the multiplicative and additive noise powers leaving out a two dimensional 2 d minimization problem instead of a four dimensional 4 d problem required by the exact ml numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis

high rate locally correctable and locally testable codes with sub polynomial query complexity locally correctable codes lccs and locally testable codes ltcs are error correcting codes that admit local algorithms for correction and detection of errors those algorithms are local in the sense that they only query a small number of entries of the corrupted codeword the fundamental question about lccs and ltcs is to determine the optimal tradeoff among their rate distance and query complexity in this work we construct the first lccs and ltcs with constant rate constant relative distance and sub polynomial query complexity specifically we show that there exist lccs and ltcs with block length n constant rate which can even be taken arbitrarily close to 1 and constant relative distance whose query complexity is exp o slog n for lccs and log n o log log n for ltcs in addition to having small query complexity our codes also achieve better tradeoffs between the rate and the relative distance than were previously known to be achievable by lccs or ltcs specifically over large but constant size alphabet our codes approach the singleton bound that is they have almost the best possible relationship between their rate and distance over the binary alphabet our codes meet the zyablov bound such tradeoffs between the rate and the relative distance were previously not known for any o n query complexity our results on lccs also immediately give locally decodable codes with the same parameters

lp decoding corrects a constant fraction of errors we show that for low density parity check ldpc codes whose tanner graphs have sufficient expansion the linear programming lp decoder of feldman karger and wainwright can correct a constant fraction of errors a random graph will have sufficient expansion with high probability and recent work shows that such graphs can be constructed efficiently a key element of our method is the use of a dual witness a zero valued dual solution to the decoding linear program whose existence proves decoding success we show that as long as no more than a certain constant fraction of the bits are flipped by the channel we can find a dual witness this new method can be used for proving bounds on the performance of any lp decoder even in a probabilistic setting our result implies that the word error rate of the lp decoder decreases exponentially in the code length under the binary symmetric channel bsc this is the first such error bound for ldpc codes using an analysis based on pseudocodewords recent work by koetter and vontobel shows that lp decoding and min sum decoding of ldpc codes are closely related by the graph cover structure of their pseudocodewords in their terminology our result implies that that there exist families of ldpc codes where the minimum bsc pseudoweight grows linearly in the block length

a polynomial time algorithm for rayleigh ratio on discrete variables replacing spectral techniques for expander ratio normalized cut and cheeger constant a general form of minimizing the rayleigh ratio on discrete variables is shown here for the first time to be polynomial time solvable this is significant because major problems in clustering partitioning and imaging can be presented as the rayleigh ratio minimization on discrete variables and an orthogonality constraint these challenging problems are modeled as the normalized cut problem the graph expander ratio problem the cheeger constant problem or the conductance problem all of which are np hard these problems have traditionally been solved heuristically using the spectral technique a unified framework is provided here whereby all these problems are formulated as a constrained minimization form of a quadratic ratio referred to here as the rayleigh ratio the quadratic ratio is to be minimized on discrete variables and a single sum constraint that we call the balance or orthogonality constraint when the discreteness constraints on the variables are disregarded the resulting continuous relaxation is solved by the spectral method it is shown here that the rayleigh ratio minimization subject to the discreteness constraints requiring each variable to assume one of two values in b 1 is solvable in strongly polynomial time equivalent to a single minimum s t cut algorithm on a graph of same size as the input graph for any nonnegative value of b this discrete form for the rayleigh ratio problem was often assumed to be np hard not only is it shown here that the discrete rayleigh ratio problem is polynomial time solvable but also the algorithm is more efficient than the spectral algorithm furthermore an experimental study demonstrates that the new algorithm provides in practice an improvement often dramatic on the quality of the results of the spectral method both in terms of approximating the true optimum of the rayleigh ratio problem on both the discrete variables and the balance constraint and in terms of the subjective partition quality a further contribution here is the introduction of a problem the quantity normalized cut generalizing all the rayleigh ratio problems the discrete version of that problem is also solved with the efficient algorithm presented this problem is shown in a companion paper to enable the modeling of features essential to clustering that are valuable in practical applications

spatially coupled ensembles universally achieve capacity under belief propagation we investigate spatially coupled code ensembles for transmission over the binary erasure channel it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble this explains why convolutional ldpc ensembles originally introduced by felstrom and zigangirov perform so well over this channel we show that the equivalent result holds true for transmission over general binary input memoryless output symmetric channels more precisely given a desired error probability and a gap to capacity we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding in fact most codes in this ensemble have this property the quantifier universal refers to the single ensemble code that is good for all channels but we assume that the channel is known at the receiver the key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble we conclude by discussing some interesting open problems

efficient subspace based estimator for localization of multiple incoherently distributed sources in this paper a new subspace based algorithm for parametric estimation of angular parameters of multiple incoherently distributed sources is proposed this approach consists of using the subspace principle without any eigendecomposition of the covariance matrix so that it does not require the knowledge of the effective dimension of the pseudosignal subspace and therefore the main difficulty of the existing subspace estimators can be avoided the proposed idea relies on the use of the property of the inverse of the covariance matrix to exploit approximately the orthogonality property between column vectors of the noise free covariance matrix and the sample pseudonoise subspace the resulting estimator can be considered as a generalization of the pisarenko s extended version of capon s estimator from the case of point sources to the case of incoherently distributed sources theoretical expressions are derived for the variance and the bias of the proposed estimator due to finite sample effect compared with other known methods with comparable complexity the proposed algorithm exhibits a better estimation performance especially for close source separation for large angular spread and for low signal to noise ratio

novel delay dependent robust h control of uncertain systems with distributed time varying delays this paper investigates the problem of delay dependent robust h control for a class of uncertain systems with distributed time varying delays the aim is to design a delay dependent robust h control which ensures robust asymptotic stability of the system the delay derivative dependent robust h control criteria are obtained in terms of linear matrix inequalities lmis numerical examples are given to illustrate the effectiveness of the proposed method the results are also compared with the existing results to show the conservativeness

local correctability of expander codes in this work we present the first local decoding algorithm for expander codes this yields a new family of constant rate codes that can recover from a constant fraction of errors in the codeword symbols and where any symbol of the codeword can be recovered with high probability by reading n e symbols from the corrupted codeword where n is the block length of the code expander codes introduced by sipser and spielman are formed from an expander graph g v e of degree d and an inner code of block length d over an alphabet each edge of the expander graph is associated with a symbol in a string in e will be a codeword if for each vertex in v the symbols on the adjacent edges form a codeword in the inner code we show that if the inner code has a smooth reconstruction algorithm in the noiseless setting then the corresponding expander code has an efficient local correction algorithm in the noisy setting instantiating our construction with inner codes based on finite geometries we obtain novel locally decodable codes with rate approaching one this provides an alternative to the multiplicity codes of kopparty saraf and yekhanin stoc 11 and the lifted codes of guo kopparty and sudan itcs 13

distance properties of expander codes the minimum distance of some families of expander codes is studied as well as some related families of codes defined on bipartite graphs the weight spectrum and the minimum distance of a random ensemble of such codes are computed and it is shown that it sometimes meets the gilbert varshamov gv bound a lower bound on the minimum distances of constructive families of expander codes is derived the relative minimum distance of the expander code is shown to exceed the product bound i e the quantity spl delta sub 0 spl delta sub 1 where spl delta sub 0 and spl delta sub 1 are the minimum relative distances of the constituent codes as a consequence of this a polynomially constructible family of expander codes is obtained whose relative distance exceeds the zyablov bound on the distance of serial concatenations