reliable numerical methods for polynomial matrix triangularization numerical procedures are proposed for triangularizing polynomial matrices over the field of polynomial fractions and over the ring of polynomials they are based on two standard polynomial techniques sylvester matrices and interpolation in contrast to other triangularization methods the algorithms described in this paper only rely on well worked numerically reliable tools they can also be used for greatest common divisor extraction polynomial rank evaluation or polynomial null space computation

abelian avalanches and tutte polynomials abstract we introduce a class of deterministic lattice models of failure abelian avalanche aa models with continuous phase variables similar to discrete abelian sandpile asp models we investigate analytically the structure of the phase space and statistical properties of avalanches in these models we show that the distributions of avalanches in aa and asp models with the same redistribution matrix and loading rate are identical for an aa model on a graph statistics of avalanches is linked to tutte polynomials associated with this graph and its subgraphs in the general case statistics of avalanches is linked to an analog of a tutte polynomial defined for any symmetric matrix

oversampled filter banks as error correcting codes theory and impulse noise correction oversampled filter banks ofbs provide an overcomplete representation of their input signal this paper describes how ofbs can be considered as error correcting codes acting on real or complex sequences very much like classical binary convolutional codes act on binary sequences the structured redundancy introduced by ofbs in subband signals can be used to increase robustness to noise in this paper we define the notions of code subspace syndrome and parity check polynomial matrix for ofbs furthermore we derive generic expressions for projection based decoding suitable for the case when a simple second order model completely characterizes the noise incurred by subband signals we also develop a nonlinear hypotheses test based decoding algorithm for the case when the noise in subbands is constituted by a gaussian background noise and impulsive errors a model that adequately describes the action of both quantization noise and transmission errors simulation results show that the algorithm effectively removes the effect of impulsive errors occurring with a probability of 10 sup 3

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

an extensive search for good punctured rate k k 1 recursive convolutional codes for serially concatenated convolutional codes in many practical applications requiring variable rate coding and or high rate coding for spectral efficiency there is a need to employ high rate convolutional codes cc either by themselves or in a parallel or serially concatenated scheme for such applications in order to keep the trellis complexity of the code constant and to permit the use of a simplified decoder that can accommodate multiple rates a mother cc is punctured to obtain codes with a variety of rates this correspondence presents the results of extensive search for optimal puncturing patterns for recursive convolutional codes leading to codes of rate k k 1 k an integer to be used in serially concatenated convolutional codes sccc the code optimization is in the sense of minimizing the required signal to noise ratio snr for two target bit error rate ber and two target frame error rate fer values we provide extensive sample simulation results for rate k k 1 sccc codes employing our optimized punctured cc

analysis of the effect of impulse noise on multicarrier and single carrier qam systems the paper first shows the equivalence of the bernoulli gaussian impulse noise model in the discrete time domain to the continuous time model of poisson arriving delta functions with random area distributed according to the power rayleigh probability density function this equivalence is then used to develop a closed form expression for the probability of error for single carrier qam that is easily evaluated furthermore the performance of multicarrier modulation mcm is also analyzed using the same impulse noise model and it is shown that in most cases mcm performs better than single carrier systems specifically when the probability of an impulse is not too high and the impulse power is moderate

riemann roch and abel jacobi theory on a finite graph abstract it is well known that a finite graph can be viewed in many respects as a discrete analogue of a riemann surface in this paper we pursue this analogy further in the context of linear equivalence of divisors in particular we formulate and prove a graph theoretic analogue of the classical riemann roch theorem we also prove several results analogous to classical facts about riemann surfaces concerning the abel jacobi map from a graph to its jacobian as an application of our results we characterize the existence or non existence of a winning strategy for a certain chip firing game played on the vertices of a graph

feedback linearization families for nonlinear systems characterizations are developed for parameterized linear dynamic feedback control laws that can arise when linearizing a nonlinear dynamic feedback control law for a specified nonlinear system about a family of constant operating points such characterizations are important in applying the recently developed extended linearization design approach to various types of control problems to illustrate the input output decoupling problem is considered

feedback control of analytic nonlinear systems by extended linearization for mufti input mufti output analytic nonlinear systems a design method based on the family of linearizations of the system parameterized by the family of constant operating points is considered using the cauchy kowalewski theorem it is shown that nonlinear state feedback control laws and output observer feedback control laws exist such that the eigenvalues of the family of closed loop linearizations have specified analytically scheduled values with respect to the family of closed loop operating points

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

divisors on graphs binomial and monomial ideals and cellular resolutions we study various binomial and monomial ideals arising in the theory of divisors orientations and matroids on graphs we use ideas from potential theory on graphs and from the theory of delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions we show that the resolutions of all these ideals are closely related and that their mathbb z graded betti tables coincide as corollaries we give conceptual proofs of conjectures and questions posed by postnikov and shapiro by manjunath and sturmfels and by perkinson perlman and wilmes various other results related to the theory of chip firing games on graphs also follow from our general techniques and results

joint source channel coding using real bch codes for robust image transmission in this paper a new still image coding scheme is presented in contrast with standard tandem coding schemes where the redundancy is introduced after source coding it is introduced before source coding using real bch codes a joint channel model is first presented the model corresponds to a memoryless mixture of gaussian and bernoulli gaussian noise it may represent the source coder the channel coder the physical channel and their corresponding decoder decoding algorithms are derived from this channel model and compared to a state of art real bch decoding scheme a further comparison with two reference tandem coding schemes and the proposed joint coding scheme for the robust transmission of still images has been presented when the tandem scheme is not accurately tuned the joint coding scheme outperforms the tandem scheme in all situations compared to a tandem scheme well tuned for a given channel situation the joint coding scheme shows an increased robustness as the channel conditions worsen the soft performance degradation observed when the channel worsens gives an additional advantage to the joint source channel coding scheme for fading channels since a reconstruction with moderate quality may be still possible even if the channel is in a deep fade

trees parking functions syzygies and deformations of monomial ideals for a graph g we construct two algebras whose dimensions are both equal to the number of spanning trees of g one of these algebras is the quotient of the polynomial ring modulo certain monomial ideal while the other is the quotient of the polynomial ring modulo certain powers of linear forms we describe the set of monomials that forms a linear basis in each of these two algebras the basis elements correspond to g parking functions that naturally came up in the abelian sandpile model these ideals are instances of the general class of monotone monomial ideals and their deformations we show that the hilbert series of a monotone monomial ideal is always bounded by the hilbert series of its deformation then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals in some cases these resolutions coincide with scarf resolutions we prove several formulas for hilbert series of monotone monomial ideals and investigate when they are equal to hilbert series of deformations in the appendix we discuss the abelian sandpile model

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

coding for dpsk noisy phase channels low to moderate complexity coding schemes are suggested and examined for binary dpsk modulation the model of the communication channel consists of both a brownian motion phase noise and an additive white gaussian noise decoding utilizes a mismatched soft decision metric which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation the resulting equivalent binary input output symmetric discrete time coding channel is stationary and memoryless it accounts as well for an underlying time diversity thus providing an effective simple means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels an analytical upper bound on the coded error probability is derived which strictly addresses the brownian motion phase model it features a convenient decoupling of the code structure from the coding channel the latter is completely specified via a single scalar generic parameter which relies on the univariate moments admitted by certain exponential functionals of the brownian motion sample path the exact statistics of which is intractable the theory is illustrated while studying the performance of low constraint length rate 1 n binary convolutional codes which are optimally combined with time diversity the advantages obtained by less trivial forms of code concatenation are examined the approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non binary code

correcting wavelet codes using interleaving and trapping a rate k n wavelet code a form of real convolutional code that encodes k numbers into n numerical code symbols using the present and past input numbers may be used to transport numerical data with redundancy factor rm n rm k such codes offer detection and correction within roundoff tolerances wavelet codes can be processed using two different algebraic representations vector matrix or polyphase polynomial when an interleaver intersperses the code symbols any burst of errors within the interelaver s frame length appears in only one component of the polyphase format a special extended polyphase parity check matrix exposes the error bursts directly for redundancies greater than 1 or a deconvolver operation achieves the same when the redundancy factor is 1 the trapped errors correct the symbols by subtraction simulations verify the effectiveness of this trapping technique

backward adaptive lattice and transversal predictors in adpcm four different backward adaptive predictors and a fixed predictor are compared for use in an adaptive differential pulse code modulation adpcm system for coding speech at 16 kilobits second kbits s for noise free channels the four adaptive predictors a least squares lattice a least mean square lattice a kalman transversal form and a gradient transversal form all exceed the fixed predictor performance as well as the performance of a continuously variable slope delta cvsd modulation system for bit error rates ber s of 10 3or greater the transversal predictor performance falls below that of the fixed predictor and cvsd however the lattice structures maintain their performance advantage the least squares lattice predictor has the best objective and subjective performance for both noiseless and noisy channels all systems perform poorly for a ber of 10 2 to extend the performance of adpcm with a least squares lattice predictor down to a ber of 10 2 the sampling rate is reduced and a selective coding scheme is devised the resulting adpcm system maintains excellent performance through a ber of 10 2and outperforms cvsd for noise free and noisy channels the dynamic range tandeming performance and behavior for noisy inputs for the adpcm system and cvsd are investigated

cellular resolutions of monomial modules we construct a canonical free resolution for arbitrary monomial modules and lattice ideals this includes monomial ideals and defining ideals of toric varieties and it generalizes our joint results with irena peeva for generic ideals bps ps introduction given a field k we consider the laurent polynomial ring t k x 1 1 x 1 n as a module over the polynomial ring s k x1 xn the module structure comes from the natural inclusion of semigroup algebras s k n k z t a monomial module is an s submodule of t which is generated by monomials x x1 1 xan n a z of special interest are the two cases when m has a minimal monomial generating set which is either finite or forms a group under multiplication in the first case m is isomorphic to a monomial ideal in s in the second case m coincides with the lattice module ml s x a l k x b n l t for some sublattice l z whose intersection with n is the origin 0 0 0 we shall derive free resolutions of m from regular cell complexes whose vertices are the generators of m and whose faces are labeled by the least common multiples of their vertices the basic theory of such cellular resolutions is developed in section 1 our main result is the construction of the hull resolution in section 2 we rescale the exponents of the monomials in m so that their convex hull in r is a polyhedron pt whose bounded faces support a free resolution of m this resolution is new and interesting even for monomial ideals it need not be minimal but unlike minimal resolutions it respects symmetry and is free from arbitrary choices in section 3 we relate the lattice module ml to the z l graded lattice ideal il x x a b l s this class of ideals includes ideals defining toric varieties we express the cyclic smodule s il as the quotient of the infinitely generated s module ml by the action of l in fact we like to think of ml as the universal cover of il many questions about il can thus be reduced to questions about ml in particular we obtain the hull resolution of a lattice ideal il by taking the hull resolution of ml modulo l this paper is inspired by the work of barany howe and scarf bhs who introduced the polyhedron pt in the context of integer programming the hull resolution generalizes results in bps for generic monomial ideals and in ps for generic lattice ideals in these generic cases the hull resolution is minimal

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

polynomial ideals for sandpiles and their grobner bases a polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced a grbner basis of this ideal is interpreted combinatorially in terms of well connected subgraphs this gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations

syzygies of oriented matroids we construct minimal cellular resolutions of squarefree monomial ideals arising from hyperplane arrangements matroids and oriented matroids these are stanleyreisner ideals of complexes of independent sets and of triangulations of lawrence matroid polytopes our resolution provides a cellular realization of r stanley s formula for their betti numbers for unimodular matroids our resolutions are related to hyperplane arrangements on tori and we recover the resolutions constructed by d bayer s popescu and b sturmfels we resolve the combinatorial problems posed in 3 by computing mobius invariants of graphic and cographic arrangements in terms of hermite polynomials

new short constraint length convolutional code constructions for selected rational rates corresp new short constraint length convolutional code constructions are tabulated for rates r n k n k 1 2 cdots n 1 with n 2 3 cdots 8 and for constraint lengths k 3 4 cdots 8 these codes have been determined by iterative search based upon a criterion of optimizing the free distance profile specifically these codes maximize the free distance d f while minimizing the number of adversaries in the distance or weight spectrum in several instances we demonstrate the superiority of these codes over previously published code constructions at the same rate and constraint length these codes are expected to have a number of applications including combined source channel coding schemes as well as coding for burst or impulsive noise channels

systematic wavelet subcodes for data protection real number data processing failures are detected by comparing parity values associated with a wavelet code which is most efficient in systematic form any rate k n wavelet code a form of real number convolutional code is manipulated into a systematic wavelet subcode with slightly reduced rate k 1 n staying within the original algebraic structure

improved coding techniques for preceded partial response channels a coset of a convolutional code may be used to generate a zero run length limited trellis code for a 1 d partial response channel the free squared euclidean distance d sub free sup 2 at the channel output is lower bounded by the free hamming distance of the convolutional code the lower bound suggests the use of a convolutional code with maximal free hamming distance d sub max r n for given rate r and number of decoder states n in this paper we present cosets of convolutional codes that generate trellis codes with d sub free sup 2 d sub max r n for rates 1 5 spl les r spl les 7 9 and d sub free sup 2 d sub max r n for r 13 16 29 32 61 64 the tabulated convolutional codes with r spl les 7 9 were not optimized for hamming distance instead a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1 d channel to increase d sub free sup 2 at the channel output the search was limited by only considering cosets with certain structural properties the r spl ges 13 16 codes were obtained using a new construction technique for convolutional codes with free hamming distance 4 newly developed bounds on the maximum zero run lengths of cosets were used to ensure a short maximum run length at the 1 d channel output

breadth first maximum likelihood sequence detection geometry sa b c is an algorithm penetrating a tree or trellis breadth first it performs maximum likelihood sequence detection mlsd under that structural constraint and also under the complexity constraints determined by the parameters b and c first c is the number of partitions into which the states are distributed and b denotes the number of paths in each partition recursively selecting paths which are closest to the received signal in the euclidean distance hamming distance sense guarantees constrained mlsd for the additive white gaussian binary symmetric channel the previously presented vector euclidean distance ved is an important tool for analyzing sa b c over the additive white gaussian noise awgn channel a geometric interpretation of the signals involved clarifies the basic properties of this ved and other relevant general results invariance monotonicity these results also form a basis for the construction of an algorithm for the efficient and fast calculation of minimum veds of interest for large signal to noise ratio snr detection performance this in turn reveals the necessary complexity requirements to meet specified performance requirements for concrete trellis coded systems here the simple example of convolutionally coded rate 1 2 with gray coded quaternary phase shift keying over the awgn channel is considered when c 1 and choosing b spl sim spl radic s s being the number of states in the code trellis gives the same asymptotic detection performance large snr as unconstrained mlsd e g implemented using the viterbi algorithm

a network flow approach to convolutional codes presents an alternative way of looking at convolutional codes as a network of flows from this association previous known classes of nonsystematic convolutional codes are reproduced the authors also present a decomposition of the problem of finding good convolutional codes into well known and structured problems such as the maximum flow problem the knapsack problem and the modular representation of block codes a spanning tree search algorithm is also proposed for finding good codes the authors consider the class of nonsystematic convolutional codes for which the encoders satisfy an equivalent property related to the feasibility of flow finally extensive tables show the new and the previous known codes

projection design for statistical compressive sensing a tight frame based approach in this paper we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error mse performance subject to sensing cost constraints by capitalizing on the mse of the oracle estimator whose performance has been shown to act as a benchmark to the performance of standard sparse recovery algorithms we use the fact that a parseval tight frame is the closest design in the frobenius norm sense to the solution of a convex relaxation of the optimization problem that relates to the minimization of the mse of the oracleestimator with respect to the equivalent sensing matrix subject to sensing energy constraints based on this result we then propose two sensing matrix designs that exhibit two key properties the designs are closed form rather than iterative the designs exhibit superior performance in relation to other designs in the literature which is revealed by our numerical investigation in various scenarios with different sparse recovery algorithms including basis pursuit de noise bpdn the dantzig selector and orthogonal matching pursuit omp

an iterative bayesian algorithm for sparse component analysis in presence of noise we present a bayesian approach for sparse component analysis sca in the noisy case the algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive gaussian noise in general an underdetermined system of linear equations has infinitely many solutions however it has been shown that sufficiently sparse solutions can be uniquely identified our main objective is to find this unique solution our method is based on a novel estimation of source parameters and maximum a posteriori map estimation of sources to tackle the great complexity of the map algorithm when the number of sources and mixtures become large we propose an iterative bayesian algorithm iba this iba algorithm is based on the map estimation of sources too but optimized with a steepest ascent method the convergence analysis of the iba algorithm and its convergence to true global maximum are also proved simulation results show that the performance achieved by the iba algorithm is among the best while its complexity is rather high in comparison to other algorithms simulation results also show the low sensitivity of the iba algorithm to its simulation parameters

trellis coding for partial response channels we consider trellis coding techniques for improving the reliability of digital transmission over noisy partial response channels such channels are commonly encountered in digital communication systems and also play a role in devices for data recording concentrating on the channels with characteristics 1 mp d we study methods to obtain codes which increase free euclidean distance between permitted sequences of channel outputs and avoid the occurrence of unlimited runs of identical outputs at the expense of some loss in data rate one technique employs the concept of set partitioning the other is based on using convolutional codes designed for maximum free hamming distance in conjunction with a precoder both methods lead to essentially equivalent codes

sysygies of unimodular lawrence ideals infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra the quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal which defines a toric subvariety in a product of projective lines connections to graphic arrangements and to beilinson s spectral sequence are explored

minimal free resolutions of the g parking function ideal and the toppling ideal the g parking function ideal mg of a directed multigraph g is a monomial ideal which encodes some of the combinatorial information of g it is an initial ideal of the toppling ideal ig a lattice ideal intimately related to the chip firing game on a graph both ideals were first studied by cori rossin and salvy a minimal free resolution for mg was given by postnikov and shaprio in the case when g is saturated i e whenever there is at least one edge u v for every ordered pair of distinct vertices u and v they also raised the problem of an explicit description of the minimal free resolution in the general case in this paper we give a minimal free resolution of mg for any undirected multigraph g as well as for a family of related ideals including the toppling ideal ig this settles a conjecture of manjunath and sturmfels as well as a conjecture of perkinson and wilmes

binary multilevel coset codes based on reed muller codes we study the construction and decoding of binary multilevel coset codes this construction originally introduced by blokh and zyablov in 1974 and by zinov ev in 1976 shows remarkable analogies with most recent schemes of coded modulations basic elements of the construction are an inner code head of a partition chain having suitable distance properties and a set of outer codes generally nonbinary for each partition level there is an outer code whose alphabet has the same order of the partition in this way it is possible to associate every partition subset to a code symbol it is well known that these codes can be efficiently decoded by the so called multistage decoding we show that good codes in terms of performance complexity can be constructed using reed muller rm codes as inner codes to this aim rm codes are revisited in the framework of the above construction and decoding techniques in particular we describe a family of decoders for rm codes which include forney s 1988 and hemmati s 1989 decoders as special cases finally we present some examples of efficient binary codes based on rm codes and assess their performance via computer simulation

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

instantaneous erasures in oversampled filter banks conditions for output perfect reconstruction in this paper we aim at finding the conditions that an oversampled filter bank ofb should satisfy in order to maintain its perfect reconstruction property when erasures happen in the subband domain this problem has been addressed before mainly from frame theoretic point of view and only for the case of what we call in this paper classic erasure in the frame theoretic approach the stable filter banks are associated with frames in l2 bbz and a subband erasure is defined as the deletion of the frame expansion coefficients corresponding to the frame vectors resulting from each filter and all its translated versions this is equivalent to assuming that all the samples of a subband have been completely lost classic erasure and this is why in this approach it is always assumed that each channel is either working perfectly or not at all in this paper we extend this notion of erasure to a situation where subband channels are allowed to be on or off arbitrarily in each time instance and we define a new type of erasure called instantaneous erasure using an approach based on the time domain analysis of perfect reconstruction property we introduce general conditions for perfect reconstruction of the output and also the sufficient conditions for two classes of filter banks causal ofbs with causal inverse and ofbs with maximum robustness against classic erasure

wavelet codes detection and correction using kalman estimation wavelet codes encoded by uniform oversampled filter banks where the wavelet coefficients represent code symbols are decoded employing kalman fixed lag estimation procedures the code symbol error estimates are based on the mean squared error mse criterion and are first used to detect the presence of large numerical errors then the correction of symbols uses these kalman estimators directly the wavelet code symbols are corrupted by low levels of processing noise continuously and occasionally by large disruptive errors e g impulsive noise the modeling variables have time varying statistics allowing both types of errors to be handled naturally kalman time varying tracking filters which use wavelet syndromes as their measurement inputs develop the fixed lag smoothed estimates for the larger errors the syndromes are also modeled as corrupted by processing noise modeling computational failure errors large and small hypothesis detection methods are used to locate large errors and their statistics must include kalman mismatch characteristics to be valid estimators from several adjacent lag positions assist in the detection procedures simulation results show correction accuracy in the time domain as well as on a mse basis large classes of wavelet codes are designed using binary convolutional codes as starting points from which the proper filter weights for encoding and syndrome evaluating are determined

multilevel coded cpfsk systems for awgn and fading channels in this paper we introduce multilevel coded continuous phase frequency shift keying cpfsk systems for both additive white gaussian noise and fading channels based on multilevel coding and multistage decoding techniques these schemes are designed under the constraint m spl ges 2p for m ary cpfsk with modulation index j p in order to maintain the phase continuity property after multilevel coding we use some specific set partitioning rules we construct examples to show that the proposed systems outperform the corresponding conventional one level schemes for the fading case we consider an ideal fading channel where adjacent fading symbols are assumed to be independent and a correlated fading channel where bit interleavers are needed at each coding level the computer simulation results show that the proposed systems have bit error performance and decoder complexity advantages over the corresponding reference codes taken from the literature it is also shown that there is only a slight degradation on the bit error performance for correlated fading compared to the ideal fading case

systematic dft frames principle eigenvalues structure and applications motivated by a host of recent applications requiring some amount of redundancy frames are becoming a standard tool in the signal processing toolbox in this paper we study a specific class of frames known as discrete fourier transform dft codes and introduce the notion of systematic frames for this class this is encouraged by a new application of frames namely distributed source coding that uses dft codes for compression studying their extreme eigenvalues we show that unlike dft frames systematic dft frames are not necessarily tight then we come up with conditions for which these frames can be tight in either case the best and worst systematic frames are established in the minimum mean squared reconstruction error sense eigenvalues of dft frames and their subframes play a pivotal role in this work particularly we derive some bounds on the extreme eigenvalues dft subframes which are used to prove most of the results these bounds are valuable independently

filter bank frame expansions with erasures we study frames for robust transmission over the internet in our previous work we used quantized finite dimensional frames to achieve resilience to packet losses here we allow the input to be a sequence in l sub 2 z and focus on a filter bank implementation of the system we present results in parallel r sup n or c sup n versus l sub 2 z and show that uniform tight frames as well as newly introduced strongly uniform tight frames provide the best performance

some extended results on the search for good convolutional codes we provide useful results on two classes of convolutional codes binary codes and nonbinary codes the best codes or the best known codes for these two classes of convolutional codes are found by computer search some of them are better than those found in the past we specify these codes by their transfer function matrices distance spectra and information weight spectra furthermore we derive an upper bound on the free distances of binary to m ary codes and q ary to m ary codes numerical values of this bound closely fit the computer searched values

punctured convolutional codes for the 1 d partial response channel a coded 1 d system containing a punctured convolutional encoder is analyzed in general a punctured encoder with 2 sup v states results in a decoder trellis with 2 sup v 1 states and a periodically time varying branch structure a class c of punctured convolutional encoders for which the decoder trellis has a fixed branch structure with 2 sup v states is described an encoder in this class can be combined with a precoder to form a new punctured convolutional encoder that generates the output from the precoder the author determines the set of good variable rate trellis codes for selectable rate encoding and viterbi decoding a set of variable rate trellis codes is generated by a variable rate punctured convolutional encoder in c the author also determines punctured convolutional encoders in c that generate a single good high rate trellis code

rational rate punctured convolutional codes for soft decision viterbi decoding we present rational rate k n punctured convolutional codes n up to 8 k 1 spl middot spl middot spl middot n 1 and constraint length spl nu up to 8 with good performance many of these codes improve the free distance and or weight spectra over previously reported codes with the same parameters the tabulated codes are found by an exhaustive or a random search

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

feedback control of multiinput nonlinear systems by extended linearization control of a nonlinear system is addressed by considering its family of linearizations given that a family of linear state feedback controllers has been designed to meet some linear control objective it is shown how these controllers can be pieced together into an overall nonlinear state feedback controller the resulting closed loop system has the property that its linearizations are equal to the desired linearly controlled systems a similar approach can be used to design nonlinear state estimators the approach is illustrated by applying it to the control of a planar two link manipulator

sequential matrix diagonalization algorithms for polynomial evd of parahermitian matrices for parahermitian polynomial matrices which can be used for example to characterize space time covariance in broadband array processing the conventional eigenvalue decomposition evd can be generalized to a polynomial matrix evd pevd in this paper a new iterative pevd algorithm based on sequential matrix diagonalization smd is introduced at every step the smd algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation a proof of convergence is provided and it is demonstrated that smd establishes diagonalization faster and with lower order operations than existing pevd algorithms

brief paper a velocity algorithm for the implementation of gain scheduled controllers a new method is proposed to implement gain scheduled controllers for nonlinear plants given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points a nonlinear gain scheduled controller is derived that preserves the input output properties of the linear closed loop systems locally about each equilibrium point the key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller for a fairly general class of systems the nonlinear gain scheduled controllers are easy to obtain and their structure is similar to that of the original linear controllers

a riemann roch theorem in tropical geometry recently baker and norine have proven a riemann roch theorem for finite graphs we extend their results to metric graphs and thus establish a riemann roch theorem for divisors on abstract tropical curves

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

trellis codes for 4 ary continuous phase frequency shift keying the approach of morales moreno and pasupathy 1988 is extended for the design of trellis codes for 4 ary continuous phase frequency shift keying cpfsk with modulation index h 1 2 the criterion for comparison of codes is the maximum free euclidean distance for a given rate and the number of states of the signal space code for the same number of states of the signal space code these codes improve the free euclidean distance by up to 1 25 db over previously published results finally the implementation of the combined coding and modulation system is discussed

optimal noise reduction in oversampled pr filter banks this paper studies the optimal noise reduction problem for oversampled filter banks fbs with perfect reconstruction pr constraint both the optimal design and worst case design are considered where the former caters for the noise with known power spectral density psd and the latter for the noise with unknown psd state space based explicit formulae involving only algebraic riccati equation and matrix manipulations are provided for the general iir or fir oversampled pr fbs and the relations between different cases are analyzed and revealed extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness

noise reduction in oversampled filter banks using predictive quantization we introduce two methods for quantization noise reduction in oversampled filter banks these methods are based on predictive quantization noise shaping or linear prediction it is demonstrated that oversampled noise shaping or linear predictive subband coders are well suited for subband coding applications where for technological or other reasons low resolution quantizers have to be used in this case oversampling combined with noise shaping or linear prediction improves the effective resolution of the subband coder at the expense of increased rate simulation results are provided to assess the achievable quantization noise reduction and resolution enhancement and to investigate the rate distortion properties of the proposed methods

on the interpretation of whitney numbers through arrangements of hyperplanes zonotopes non radon partitions and orientations of graphs the doubly indexed whitney numbers of a finite ranked partially ordered set l are the first kind w e x xj x xl e l with ranks i j and the second kind wj the number of x x with x xj when l has a 0 element the ordinary simply indexed whitney numbers are w wo and w wo w building on work of stanley and zaslavsky we show how to interpret the magnitudes of whitney numbers of geometric lattices and semilattices arising in geometry and graph theory for example the number of regions or of k dimen sional faces for any k of an arrangement of hyperplanes in real projective or affine space that do not meet an arbitrary hyperplane in general position the number of vertices of a zonotope p inside the visible boundary as seen from a distant point on a generating line of p the number of non radon partitions of a euclidean point set not due to a separating hyperplane through a fixed point the number of acyclic orientations of a graph stanley s theorem with a new geometrical proof the number with a fixed unique source the number whose set of increasing arcs in a fixed ordering of the vertices has exactly q sources generalizing renyi s enumera tion of permutations with q outstanding elements the number of totally cyclic orientatiofis of a plane graph in which there is no clockwise directed cycle the number of acyclic orientations of a signed graph satisfying conditions analogous to an unsigned graph s having a unique source