decay rate dependent conditions for exponential stability of stochastic neutral systems with markovian jumping parameters abstract this note studies the problem of decay rate dependent exponential stability for neutral stochastic delay systems with markovian jumping parameters first by introducing an operator d x t i as well as a novel lyapunov krasovskii functional sufficient conditions for exponential stability of system with a decay rate are obtained second the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with markovian jumping parameters finally numerical examples are provided to show the effectiveness of the proposed results

optimal control of non homogenous prey predator models during infinite and finite time intervals we propose a lattice to describe dynamics of two animal species population one being a prey and the other a predator the problem of controlling steady states of non homogenous prey predator model during finite and infinite time intervals is studied using lyapunov bellman technique the optimal control law is derived from the conditions that ensure the asymptotic stabilization of the steady states of this model using bellman s equation the densities of both prey and predator populations are obtained as functions of time graphical and numerical example studies of the obtained results are presented

mixed h2 h control of markovian jump time delay systems with uncertain transition probabilities this study addresses the robust stability problem of markovian jump time delay systems with mixed h2 and h control and uncertain transition probabilities in the discrete time domain the transition probabilities are considered to be uncertain but bounded by proposing a new lyapunov functional and applying the free weighting matrix technique we design the mode dependent mixed h2 h controller such that the resultant closed loop systems possess stochastic stability and are prescribed with h performance indices these results generalize several results reported in previous literature which consider the markovian transition probabilities to be known a priori or partially unknown transition probabilities numerical examples and a practical motion control system are presented to illustrate the effectiveness of this technique

corrections and additions to error recovery for variable length codes by j c maxted and j p robinson an error in the subject article is corrected additionally a method of calculating the standard deviation of the expected span of errors is presented for four example codes the standard deviation of the subject article s reduced model is compared to the standard deviation of the subject article s complete model

on the cohomology of stable map spaces we describe an approach to calculating the cohomology rings of stable map spaces m0 0 n d

gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

tight bounds on the redundancy of huffman codes a method for deriving optimal upper bounds on the redundancy of binary huffman codes in terms of the probability p sub 1 of the most likely source letter is presented this method will be used to compute bounds for all p sub 1 or 1 127 which were previously known only for a few special cases furthermore the known optimal lower bound for binary huffman codes is generalized to arbitrary code alphabets and some upper bounds for d ary huffman codes 2 or 1 2

h control for singular markovian jump systems with incomplete knowledge of transition probabilities this paper proposes a h state feedback control for singular markovian jump systems with incomplete knowledge of transition probabilities different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered moreover in contrast to the singular markovian jump systems studied recently the proposed method does not require any tuning parameters that arise when handling non convex terms related to the mode dependent lyapunov matrices and the corresponding self mode transition rates also this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism finally two numerical examples are provided to demonstrate the performance of h mode dependent control

kraft inequality and zero error source coding with decoder side information for certain source coding problems it is well known that the kraft inequality provides a simple sufficient condition for the existence of codes with given codeword lengths motivated by this fact a sufficient condition based on the kraft inequality can also be sought for the problem of zero error instantaneous coding with decoder side information more specifically it can be envisioned that a sufficient condition for the existence of such codes with codeword lengths l x is that for some 0 alphales 1 sigmaxepsivfscr 2 l x lesalpha for each clique fscr in the characteristic graph g of the source side information pair in this correspondence it is shown that 1 if the above is indeed a sufficient condition for a class g of graphs then it is possible to come as close as 1 log2 alpha bits to the asymptotic limits for each graph in g 2 there exist graph classes of interest for which such a can indeed be found and finally 3 no such n can be found for the class of all graphs

minimum expected length of fixed to variable lossless compression without prefix constraints the minimum expected length for fixed to variable length encoding of an n block memoryless source with entropy h grows as nh o 1 where the term o 1 lies between 0 and 1 however this well known performance is obtained under the implicit constraint that the code assigned to the whole n block is a prefix code dropping the prefix constraint which is rarely necessary at the block level we show that the minimum expected length for a finite alphabet memoryless source with known distribution grows as nh 1 2 log n o 1 unless the source is equiprobable we also refine this result up to o 1 for those memoryless sources whose log probabilities do not reside on a lattice

observer based finite time control of time delayed jump systems abstract this paper provides the observer based finite time control problem of time delayed markov jump systems that possess randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process the observer based finite time h controller via state feedback is proposed to guarantee the stochastic finite time boundedness and stochastic finite time stabilization of the resulting closed loop system for all admissible disturbances and unknown time delays based on stochastic finite time stability analysis sufficient conditions that ensure stochastic robust control performance of time delay jump systems are derived the control criterion is formulated in the form of linear matrix inequalities and the designed finite time stabilization controller is described as an optimization one the presented results are extended to time varying delayed mjss simulation results illustrate the effectiveness of the developed approaches

tight upper bounds on the redundancy of huffman codes bounds on the redundancy of huffman codes in terms of the probability p sub 1 of the most likely source letter are provided in particular upper bounds are presented that are sharper than the bounds given recently by r g gallager ibid vol it 24 no 6 p 668 74 nov 1978 and by r m capocelli et al ibid vol it 32 no 6 p 854 857 nov 1986 for an interval 2 2 sup l 1 1 or 2 it is shown that the new bounds are the tightest possible for these intervals

on the redundancy achieved by huffman codes abstract it has been recently proved that the redundancy r of any discrete memoryless source satisfies r 1 h p n where pn is the least likely source letter probability this bound is achieved only by sources consisting of two letters we prove a sharper bound if the number of source letters is greater than two also provided is a new upper bound on r in terms of the two least likely source letter probabilities which improves on a previous result

synchronizing automata with a letter of deficiency 2 we present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of cerny s construction

on the design of variable length error correcting codes a joint source channel coding problem that combines the efficient compression of discrete memoryless sources with their reliable communication over memoryless channels via binary prefix free variable length error correcting codes vlecs is considered under a fixed free distance constraint a priority first search algorithm is devised for finding an optimal vlec with minimal average codeword length two variations of the priority first search based code construction algorithm are also provided the first one improves the resilience of the developed codes against channel noise by additionally considering a performance parameter bdfree without sacrificing optimality in average codeword length in the second variation to accommodate a large free distance constraint as well as a large source alphabet such as the 26 symbol english data source the vlec construction algorithm is modified with the objective of significantly reducing its search complexity while still yielding near optimal codes a low complexity sequence maximum a posteriori map decoder for all vlecs including our constructed optimal code is then proposed under the premise that the receiver knows the number of codewords being transmitted simulations show that the realized optimal and suboptimal vlecs compare favorably with existing codes in the literature in terms of coding efficiency search complexity and error rate performance

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

new bounds on the expected length of optimal one to one codes in this correspondence we consider one to one encodings for a discrete memoryless source which are one shot encodings associating a distinct codeword with each source symbol such encodings could be employed when only a single source symbol rather than a sequence of source symbols needs to be transmitted for example such a situation can arise when the last message must be acknowledged before the next message can be transmitted we consider two slightly different types of one to one encodings depending on whether the empty codeword is used or not and obtain lower and upper bounds on the expected length of optimal one to one codes we first give an extension of a known tight lower bound on the expected length of optimal one to one codes for the case that the the size of the source alphabet is finite and partial information about the source symbol probabilities is available as expected our lower bound is no less than the previously known lower bound obtained without side information about the source symbol probabilities we then consider the case that the source entropy is available and derive arbitrarily tight lower bounds on the expected length of optimal one to one codes we also derive arbitrarily tight lower bounds for the case that the source entropy and the probability of the most likely source symbol are available finally given that the probability of the most likely source symbol is available we obtain an upper bound on the expected length of optimal one to one codes our upper bound is tighter than the best upper bound known in the literature

h_ infty filter design for a class of networked control systems via t s fuzzy model approach this paper is concerned with h design for a class of networked control systems ncss with multiple state delays via the takagi sugeno t s fuzzy model the transfer delays and packet loss that are induced by the limited bandwidth of communication networks are considered the focus of this paper is on the analysis and design of a full order h filter such that the filtering error dynamics are stochastically stable and a prescribed h attenuation level is guaranteed sufficient conditions are established for the existence of the desired filter in terms of linear matrix inequalities lmis an example is given to illustrate the effectiveness and applicability of the proposed design method

shortest synchronizing strings for huffman codes most complete binary prefix codes have a synchronizing string that is a string that resynchronizes the decoder regardless of its previous state this work presents an upper bound on the length of the shortest synchronizing string for such codes two classes of codes with a long shortest synchronizing string are presented it is known that finding a synchronizing string for a code is equivalent to finding a synchronizing string of some finite automaton the cerny conjecture for this class of automata is discussed

algebraic synchronization criterion and computing reset words we refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata we express the condition that an automaton is synchronizing in terms of linear algebra and obtain new upper bounds for automata with a short word of small rank the results are applied to make several improvements in the area in particular we improve the upper bound for reset thresholds of finite prefix codes huffman codes we show that an n state synchronizing decoder has a reset word of length at most o nlog3n in addition to that we prove that the expected reset threshold of a uniformly random synchronizing binary n state decoder is at most o nlog n we prove the ern conjecture for n state automata with a letter of rank 6 n 6 3 in another corollary we show that the probability that the ern conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states and that the expected value of the reset threshold is at most n 3 2 o 1 moreover all of our bounds are constructible we present suitable polynomial algorithms for the task of finding a reset word of length within our bounds

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

robust finite time estimation of markovian jumping systems with bounded transition probabilities this paper studies the finite time state estimation and h filter design problem for a class of uncertain markovian jumping systems mjss with bounded transition probabilities based on the selected lyapunov krasovskii functional the finite time h filter is constructed to derive a sufficient condition such that the filtering error dynamic mjss are finite time bounded and satisfies a prescribed level of h disturbance attenuation in a finite time interval then in terms of linear matrix inequalities lmis techniques the sufficient condition on the existence of finite time h filter is presented and proved the filter matrices can be solved directly by using the existing lmis optimization techniques finally two numerical examples are given to illustrate the effectiveness of the proposed design approach

the synchronization of variable length codes many variable length codes exhibit a tendency for resynchronization to occur automatically following any error however attempts to identify an underlying synchronization mechanism and to accurately predict the expected synchronization delay for even quite specific variable length codes appear to have been largely unsuccessful the present paper explores a novel method for estimating the synchronization performance for a wide variety of variable length codes based on the t codes t codes are a class of self synchronizing codes which typically synchronize within 2 3 codewords by a mechanism that derives from a recursive t augmentation construction it is observed that the t code mechanism for synchronization is followed more or less by other variable length codes wherever substantial numbers of codewords are shared with a t code set t augmentation itself provides a means for assessing the contribution individual codewords make to the overall synchronization process for a t code set thus codeword differences between sets may be specifically evaluated to estimate the synchronization performance of a variable length code set from a closely related t code set

finite time dissipative control for stochastic interval systems with time delay and markovian switching the finite time stochastically boundedness ftsb and the finite time strictly stochastically exponential dissipative ftssed control problems for the stochastic interval systems which are encountered the time delay and markovian switching are investigated in this paper the stochastic delayed interval systems with markovian switching sdisswms are equivalently transformed into a kind of stochastic uncertain time delay systems with markovian switching by interval matrix transformation some sufficient conditions of ftsb and ftssed for the stochastic delayed interval systems with markovian switching are obtained and the ftsb and ftssed controllers are designed by solving a series of linear matrix inequalities which are solvable by lmis toolbox finally a numerical example with simulations is given to illustrate the correctness of the obtained results and the effectiveness of the designed controller

optimum 1 ended binary prefix codes the problem of finding a binary prefix code of minimum average codeword length for a given finite probability distribution subject to the requirement that each codeword must end with a 1 is considered lower and upper bounds to the performance of the optimum code are derived the lower bound is tight for certain probability distributions an algorithm that generates an optimum code for any given distribution is described

more efficient algorithms and analyses for unequal letter cost prefix free coding there is a large literature devoted to the problem of finding an optimal min cost prefix free code with an unequal letter cost encoding alphabet of size while there is no known polynomial time algorithm for solving it optimally there are many good heuristics that all provide additive errors to optimal the additive error in these algorithms usually depends linearly upon the largest encoding letter size this paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite because the largest letter cost is infinite the previous analyses could give infinite error bounds we provide a new algorithm that works with infinite encoding alphabets when restricted to the finite alphabet case our algorithm often provides better error bounds than the best previous ones known

the construction of variable length codes with good synchronization properties variable length codes offer advantages for data compression but are susceptible to loss of synchronization if a bit error occurs this can be mitigated by the use of variable length codes with specific mechanisms for resynchronization such mechanisms exist in the codes known as huffman equivalent he codes and t codes these have been extensively studied in the literature for optimal compression a length vector is obtained from the probabilities of the symbols of the alphabet used however he codes and t codes do not exist for all length vectors in this paper a new class of variable length codes with good synchronization properties is developed these are referred to as ordered termination ot codes ot codes do exist for all length vectors experimental results and some theoretical support suggest that ot codes compare favorably with he and t codes

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

worst case redundancy of optimal binary aifv codes and their extended codes binary almost instantaneous fixed to variable length aifv codes are lossless codes that generalize the class of instantaneous fixed to variable length codes the code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves aifv codes are empirically shown to attain better compression ratio than huffman codes nevertheless an upper bound on the redundancy of optimal binary aifv codes is only known to be 1 which is the same as the bound of huffman codes in this paper the upper bound is improved to 1 2 which is shown to coincide with the worst case redundancy of the codes along with this the worst case redundancy is derived for sources with p max geq 1 2 where p max is the probability of the most likely source symbol in addition we propose an extension of binary aifv codes which use m code trees and allow at most m bit decoding delay we show that the worst case redundancy of the extended binary aifv codes is 1 m for m leq 4

reconstruction of baseline jpeg coded images in error prone environments a two stage method for the reconstruction of missing data in the transmission of baseline jpeg coded images in error prone environments is proposed in the first stage we estimate the values of the missing dc coefficients as effects of errors in estimating the missing dc values will appear as a number of stripes across the image a technique for removing such stripes is also developed in the second stage the data of missing blocks is reconstructed by exploiting the correlation between adjacent blocks simulation results intricate that our reconstruction method performs very well the two key contributions of our method are that it does not assume nondifferential encoding of the dc coefficients and that it performs well in the reconstruction of diagonal edges

generalized multiple description coding with correlating transforms multiple description md coding is source coding in which several descriptions of the source are produced such that various reconstruction qualities are obtained from different subsets of the descriptions unlike multiresolution or layered source coding there is no hierarchy of descriptions thus md coding is suitable for packet erasure channels or networks without priority provisions generalizing work by orchard wang vaishampayan and reibman see proc ieee int conf image processing vol i santa barbara ca p 608 11 1997 a transform based approach is developed for producing m descriptions of an n tuple source m spl les n the descriptions are sets of transform coefficients and the transform coefficients of different descriptions are correlated so that missing coefficients can be estimated several transform optimization results are presented for memoryless gaussian sources including a complete solution of the n 2 m 2 case with arbitrary weighting of the descriptions the technique is effective only when independent components of the source have differing variances numerical studies show that this method performs well at low redundancies as compared to uniform md scalar quantization

bounds on the redundancy of huffman codes corresp new upper bounds on the redundancy of huffman codes are provided a bound that for 2 9 leq p 1 leq 0 4 is sharper than the bound of gallager when the probability of the most likely source letter p 1 is the only known probability is presented the improved bound is the tightest possible for 1 3 leq p 1 leq 0 4 upper bounds are presented on the redundancy of huffman codes when the extreme probabilities p 1 and p n are known

tight bounds on the redundancy of huffman codes hbox h hbox h in this paper we study the redundancy of huffman codes in particular we consider sources for which the probability of one of the source symbols is known we prove a conjecture of ye and yeung regarding the upper bound on the redundancy of such huffman codes which yields in a tight upper bound we also derive a tight lower bound for the redundancy under the same assumption we further apply the method introduced in this paper to other related problems it is shown that several other previously known bounds with different constraints follow immediately from our results

optimal binary one ended codes binary prefix free codes in which all codewords end with a 1 have been introduced by berger and yeung 1990 a recursive method is given here for the construction of all optimal 1 ended codes with n codewords it is shown that the set of codes obtained by the construction contains only optimal codes we also compute recursively the number of essentially different optimal 1 ended codes with n codewords and show that their number grows faster than any polynomial in n

a lower bound on the redundancy of d ary huffman codes corresp a necessary and sufficient condition for the most likely letter of any discrete source to be coded by a single symbol with a d ary huffman code 2 leq d is derived as a consequence a lower bound on the redundancy of a d ary huffman code is established

error recovery for variable length codes when an error occurs in the encoded bit stream produced by a variable length code the decoder may lose synchronization a state model for synchronization recovery is developed and a method for determining the expected span of source symbols lost is presented the performance of various codes with respect to error recovery is discussed two examples are given where equivalent optimal codes have a marked difference in their error recovery characteristics some open problems are indicated

some basic properties of fix free codes a variable length code is a fix free code if no codeword is a prefix or a suffix of any other codeword this class of codes is applied to speed up the decoding process for the decoder can decode from both sides of the compressed file simultaneously we study some basic properties of fix free codes we prove a sufficient and a necessary condition for the existence of fix free codes and we obtain some new upper bounds on the redundancy of optimal fix free codes

asymptotic average redundancy of huffman and other block codes we study asymptotically the redundancy of huffman and other codes it has been known from the inception of the huffman 1952 code that in the worst case its redundancy defined as the excess of the code length over the optimal ideal code length is not more than one however to the best of our knowledge no precise asymptotic results have been reported in literature thus far we consider here a memoryless binary source generating a sequence of length n distributed as binomial n p with p being the probability of emitting 0 based on the results of stubley 1994 we prove that for p 1 2 1 m 1 2 sup 1 m 2 sup m o spl rho sup n spl alpha n m rational where spl alpha log sub 2 1 p p and spl beta log sub 2 1 p spl rho x x is the fractional part of x the appearance of the fractal like function explains the erratic behavior of the huffman redundancy and its resistance to succumb to a precise analysis as a side result we prove that the average redundancy of the shannon block code is as n spl rarr spl infin r sub n sup s 1 2 o 1 spl alpha irrational 1 2 1 m 1 2 o spl rho sup n spl alpha n m rational where spl rho 1 finally we derive the redundancy of the golomb 1966 code for the geometric distribution which can be viewed as a special case of the huffman and shannon codes golomb s code redundancy has only oscillating behavior i e there is not convergent mode these findings are obtained by analytic methods such as theory of distribution of sequences modulo 1 and fourier series

binary prefix codes ending in a 1 binary prefix codes with the constraint that each codeword must end with a 1 have been recently introduced by berger and yeung 1990 we analyze the performance of such codes by investigating their average codeword length in particular we show that a very simple strategy permits the construction of a 1 ended binary prefix code whose average codeword length is less than h 1 for any discrete source with entropy h we also prove a tight lower bound on the optimal average codeword length in terms of h and of the minimum letter probability of the source finally we discuss the problem of finding an optimum feasible code

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

huffman redundancy for large alphabet sources the performance of optimal prefix free encoding for memoryless sources with a large alphabet size is studied it is shown that the redundancy of the huffman code for almost all sources with a large alphabet size n is very close to that of the average distribution of the monotone sources with n symbols this value lies between 0 02873 and 0 02877 bit for sufficiently large n

synchronizing generalized monotonic automata in an earlier paper we have studied reset words for synchronizing automata whose states admit a stable linear order here we show that the same bound on the length of the shortest reset word persists for synchronizing automata satisfying much weaker stability restriction this result supports our conjecture concerning the length of reset words for synchronizing automata accepting only star free languages

performances of linear tools and models for error detection and concealment in subband image transmission we investigate the performances of gaussian modeling and linear prediction tools for error detection and concealment in the transmission of still images we consider the transmission of subband encoded images through two types of channels we model the residual correlation between subband coefficients by considering them as jointly gaussian variables the first transmission medium considered is a packet oriented channel where some packets are lost during transmission the problem is to estimate the values of missing coefficients in this case particular care must be taken while evaluating correlation matrices from incomplete data the other system considered is based on a discrete memoryless noisy channel affecting the data being transmitted the challenge is here first to determine the locations of the errors which is done through hypotheses tests and then to replace them by estimates based on their neighbors the reconstruction via linear prediction is shown to give better results than median filtering based reconstruction error detection through this gaussian model also shows promising results in particular when channel statistics are taken into account in a joint source channel decoding framework

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

on the construction of maximal prefix synchronized codes we present a systematic procedure for mapping data sequences into codewords of a prefix synchronized code ps code as well as for performing the inverse mapping a ps code proposed by gilbert 1960 belongs to a subclass of comma free codes and is useful to recover word synchronization when errors have occurred in the stream of codewords a ps code is defined as a set of codewords with the property that each codeword has a known sequence as a prefix followed by a coded data sequence in which this prefix is not allowed to occur the largest ps code among all ps codes of the same code length is called a maximal prefix synchronized code mps code we develop an encoding and decoding algorithm for gilbert s mps code with a prefix of the form 11 10 and extend the algorithm to the class ps codes of which the prefix is self uncorrelated the computational complexity of the entire mapping process is proportional to the length of the codewords

brief constrained quadratic state feedback control of discrete time markovian jump linear systems in this paper we consider the quadratic optimal control problem of a discrete time markovian jump linear system subject to constraints on the state and control variables it is desired to find a state feedback controller which may also depend on the jump variable that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables related to the state and control variables of the system the transition probability of the markov chain and initial condition of the system may belong to appropriate convex sets we obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities so that convex programming can be used for numerical calculations examples are presented to illustrate the usefulness of the developed results

an error concealment algorithm for images subject to channel errors we present an algorithm to conceal bit errors in still images and image sequences that are coded using the discrete cosine transform dct and variable length codes vlcs no modification is necessary to an existing encoder and no additional bit rate is required the concealment algorithm is kept simple so that real time decoding and concealment is possible a single bit error in these images can cause a block to split into several blocks or several blocks to merge into one this causes the dct coefficients of all subsequent blocks to be correctly decoded but stored in the wrong location in the image furthermore the dc coefficient of all subsequent blocks may be incorrect the error concealment algorithm uses transform domain information to identify the location of the affected blocks and to correct errors the image quality after error concealment is shown to be significantly improved

on the construction of statistically synchronizable codes the problem of constructing statistically synchronizable codes over arbitrary alphabets and for any finite source is considered it is shown how to efficiently construct a statistically synchronizable code whose average codeword length is within the least likely codeword probability from that of the huffman code for the same source moreover a method is given for constructing codes having a synchronizing codeword the method yields synchronous codes that exhibit high synchronizing capability and low redundancy

error recovery of variable length code over bsc with arbitrary crossover probability the error recovery capability of variable length code vlc has been considered as an important performance and design criterion in addition to its coding efficiency however almost all of the existing methods for evaluating the error recovery capability of vlc assume that the transmission fault is a random single bit inversion in this paper we consider a more generalized problem of precisely evaluating the error recovery capability of vlc in the case that the encoded bit stream is transmitted over a bsc with arbitrary crossover probability by making use of the perron frobenius theorem we derive a very simple expression for the exact mean error propagation rate mepr and show that the variance of error propagation rate vepr is zero we also prove that in the regime of very low crossover probability the mean error propagation length mepl derived for single inversion error case approaches a scaled value of the mepr furthermore we briefly discuss the problem of evaluating the error detection capability of non exhaustive code over bsc

best neighborhood matching an information loss restoration technique for block based image coding systems imperfect transmission of block coded images often results in lost blocks a novel error concealment method called best neighborhood matching bnm is presented by using a special kind of information redundancy blockwise similarity within the image the proposed algorithm can utilize the information of not only neighboring pixels but also remote regions in the image very good restoration results are obtained by experiments

synchronization recovery and state model reduction for soft decoding of variable length codes variable length codes vlcs exhibit loss of synchronization problems when transmitted over noisy channels trellis decoding techniques based on maximum a posteriori map estimators are often used to minimize the error rate on the estimated sequence if the number of symbols and or bits transmitted is known by the decoder termination constraints can be incorporated in the decoding process all the paths in the trellis which do not lead to a valid sequence length are suppressed this correspondence presents an analytic method to assess the expected error resilience of a vlc when trellis decoding with a sequence length constraint is used the approach is based on the computation for a given code of the amount of information brought by the constraint it is then shown that this quantity is not significantly altered by appropriate trellis states aggregation this proves that the performance obtained by running a length constrained viterbi decoder on aggregated state models approaches the one obtained with the bit symbol trellis with a significantly reduced complexity it is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size

almost all complete binary prefix codes have a self synchronizing string the probability that a complete binary prefix code has a self synchronizing string approaches one as the number of codewords tends to infinity

error resilient first order multiplexed source codes performance bounds design and decoding algorithms this paper describes a new family of error resilient variable length source codes vlcs the codes introduced can be regarded as generalizations of the multiplexed codes described by je spl acute gou and guillemot they allow to exploit first order source statistics while at the same time being resilient to transmission errors the design principle consists of creating a codebook of fixed length codewords flcs for high priority information and in using the inherent codebook redundancy to describe low priority information the flc codebook is partitioned into equivalence classes according to the conditional probabilities of the high priority source the error propagation phenomenon which may result from the memory of the source coder is controlled by choosing appropriate codebook partitions and index assignment strategies in particular a context dependent index assignment strategy called crossed index assignment is described for the symbol error rate criterion the approach turns out to maximize the cardinality of a set of codewords called the code kernel offering synchronization properties the decoder resynchronization capability is shown to be further increased by periodic use of memoryless multiplexed codes theoretical and practical performances in terms of compression efficiency and error resilience are analyzed

a note on d ary huffman codes an upper bound on the redundancy of d ary huffman codes in terms of the probability p sub 1 of the most likely source letter is provided for large values of p sub 1 the bound improves the one given by r g gallager 1978 additionally some results known for the binary case d 2 are extended to arbitrary d ary huffman codes as a consequence a tight lower bound that corrects a bound recently proposed by j d golic and m m obradovic 1987 is derived

optimal block cosine transform image coding for noisy channels a method is presented for the joint source channel coding optimization of a scheme based on the two dimensional block cosine transform when the output of the encoder is to be transmitted via a memoryless binary symmetric channel the authors approach involves an iterative algorithm for the design of the quantizers in the presence of channel errors used for encoding the transform coefficients this algorithm produces a set of locally optimum in the mean squared error sense quantizers and the corresponding binary codeword assignment for the assumed transform coefficient statistics to determine the optimum bit assignment among the transform coefficients the authors have used an algorithm based on the steepest descent method which under certain convexity conditions on the performance of the channel optimized quantizers yields the optimal bit allocation simulation results for the performance of this locally optimum system over noisy channels have been obtained and appropriate comparisons with a reference system designed for no channel errors have been made it is shown that substantial performance improvements can be obtained by using this scheme furthermore theoretically predicted results and rate distortion theoretic bounds for an assumed two dimensional image model are provided

binary huffman equivalent codes with a short synchronizing codeword for a given set of codeword lengths there are many different optimal variable length codes which are all huffman 1952 equivalent codes some of these codes may contain a synchronizing codeword which resynchronizes the code whenever it is transmitted the shorter the synchronizing codeword the quicker the code will resynchronize ferguson and rabinowitz 1984 suggest the problem of finding for a given set of codeword lengths the binary huffman equivalent code with the shortest synchronizing codeword we consider binary huffman equivalent codes whose shortest codeword has length m 1 and which contain a synchronizing codeword of length m 1 the shortest possible in this case we provide an algorithm for constructing these codes for a given set of codeword lengths if such a code exists we study further properties of these codes and show that when in m spl ges 3 the codes contain more than one synchronizing codeword finally we suggest ways of improving the synchronization properties of the codes and provide some example codes

efficient computation and optimization of the free distance of variable length finite state joint source channel codes this paper considers the optimization of a class of joint source channel codes described by finite state encoders fses generating variable length codes it focuses on fses associated to joint source channel integer arithmetic codes which are uniquely decodable codes by design an efficient method for computing the free distance of such codes using dijkstra s algorithm is proposed to facilitate the search for codes with good distance properties fses are organized within a tree structure which allows the use of efficient branch and prune techniques avoiding a search of the whole tree

the redundancy of an optimal binary fix free code is not greater than 1 bit in the context of fix free codes the most important and immediate consequence of the 3 4 conjecture if it is proven is that the redundancy of an optimal binary fix free code never exceeds 1 bit as with the optimal prefix free codes i e huffman codes in this paper this bound on the redundancy is proven without requiring the conjecture to be true to do so we use two known sufficient conditions for the existence of binary fix free codes to derive an improved upper bound on the redundancy of an optimal fix free code in terms of the largest symbol probability

on the average codeword length of optimal binary codes for extended sources corresp although optimal binary source coding using symbol blocks of increasing length must eventually yield a code having an average codeword length arbitrarily close to the source entropy it is known that the sequence of average codeword lengths need not be nonincreasing the sequence is however bounded above by the average codeword length of the source and certain subsequences must be nondecreasing sufficient conditions are obtained describing sources for which a decrease in average codeword length is achieved when coding pairs of symbols a sufficient condition specifying sources for which no such decrease is possible is also obtained

some tight lower bounds on the redundancy of optimal binary prefix free and fix free codes the tight lower bound on the redundancy of optimal prefix free codes in terms of a given symbol probability not necessarily the largest or the smallest one has been derived in the literature the first goal of this paper is to derive the tight lower bounds in terms of j j 1 known symbol probabilities of the source using some properties of kullback leibler distance since fix free codes are special prefix free codes for which no codeword is a suffix of the other codewords it is clear that all lower bounds on the redundancy of optimal prefix free codes are also valid for fix free ones accordingly the second question of the paper is on the tightness of the derived lower bounds for optimal fix free codes it is proven that these lower bounds are tight for optimal fix free codes if j leq 3 and are not tight for j geq 4 also it is shown that the tight lower bound in terms of the probability of the most likely symbol is the same for optimal prefix free and optimal fix free codes

redundancy related bounds for generalized huffman codes this paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives like the most well known redundancy bounds for minimum average redundancy coding huffman coding these are in terms of a form of entropy and or the probability of an input symbol often the most probable one the bounds here some of which are tight improve on known bounds of the form l h h 1 where h is some form of entropy in bits or in the case of redundancy objectives 0 and l is the length objective also in bits the objectives explored here include exponential average length maximum pointwise redundancy and exponential average pointwise redundancy also called dth exponential redundancy the first of these relates to various problems involving queueing uncertainty and lossless communications the second relates to problems involving shannon coding and universal modeling also explored here for these two objectives is the related matter of individual codeword length

reset sequences for monotonic automata natarajan reduced the problem of designing a certain type of mechanical parts orienter to that of finding reset sequences for monotonic deterministic finite automata he gave algorithms that in polynomial time either find such sequences or prove that no such sequence exists in this paper a new algorithm based on breadth first search is presented that runs in faster asymptotic time than natarajan s algorithms and in addition finds the shortest possible reset sequence if such a sequence exists tight bounds on the length of the minimum reset sequence are given the time and space bounds of another algorithm given by natarajan are further improved that algorithm finds reset sequences for arbitrary deterministicfinite automata when all states are initially possible

map decoding of variable length codes with self synchronization strings maximum a posteriori probability map decoding of huffman equivalent variable length codes vlcs has two undesired features one is the high decoding complexity and the other is the discrepancy between the objective of map decoding and the levenshtein distance which is commonly used as the performance metric in this correspondence improvement over these two issues is targeted through extracting self synchronization information in vlc coded sequence and incorporating it into map decoding it shown that self synchronization strings ssss are concatenation of huffman codewords and can be readily found occurrence probabilities of ssss are then analyzed by using this self synchronization information map decoding is split into multiple decoding of short data segments so that both decoding performance improvement and complexity reduction are obtained simulation results demonstrate the effectiveness of the proposed method

adaptive minimum symbol error rate decision feedback equalization for multilevel pulse amplitude modulation the design of decision feedback equalizers dfes is typically based on the minimum mean square error mmse principle as this leads to effective adaptive implementation in the form of the least mean square algorithm it is well known however that in certain situations the mmse solution can be distinctly inferior to the optimal minimum symbol error rate mser solution we consider the mser design for multilevel pulse amplitude modulation block data adaptive implementation of the theoretical mser dfe solution is developed based on the parzen window estimate of a probability density function furthermore a sample by sample adaptive mser algorithm called the least symbol error rate lser is derived for adaptive equalization applications the proposed lser algorithm has a complexity that increases linearly with the equalizer length computer simulation is employed to evaluate the proposed alternative mser design for equalization application with multilevel signaling schemes

picard group of moduli of hyperelliptic curves the main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves we compute their picard groups giving explicit description of the generators we get an application to the non existence of a tautological family over the coarse moduli space

on line adaptive canonical prefix coding with bounded compression loss semistatic minimum redundancy prefix mrp coding is fast compared with rival coding methods but requires two passes during encoding its adaptive counterpart dynamic huffman coding requires only one pass over the input message for encoding and decoding and is asymptotically efficient dynamic huffman 1952 coding is however notoriously slow in practice by removing the restriction that the code used for each message symbol must have minimum redundancy and thereby admitting some compression loss it is possible to improve the speed of adaptive mrp coding this paper presents a controlled method for trading compression loss for coding speed by approximating symbol frequencies with a geometric distribution the result is an adaptive mrp coder that is asymptotically efficient and also fast in practice

some upper bounds on the redundancy of optimal binary fix free codes in order to investigate the cost of employing fix free codes instead of the well established prefix free codes some upper bounds on the redundancy of the optimal fix free codes and their difference with the corresponding huffman codes are presented unlike the conventional approach which is based on some shannon like suboptimal codes we examine the redundancy of a better huffman like code an algorithm is proposed for deriving optimal binary codeword lengths with kraft sum 5 8 for a given probability distribution the existence of a fix free code with such codelengths is guaranteed by yekhanin s theorem it is shown that the redundancy of this fix free code is at most 0 8 bit greater than that of the huffman code and does not exceed 8 3 log3 1 0817 bits this upper bound is 4 3 log 5 3 0 5964 bit less than the best known one if the 3 4 conjecture is proved sometime in the future the presented upper bound on the redundancy of the optimal fix free codes i e 1 0817 will be improved by only 5 3 log3 0 0817 in addition to these general bounds all known upper bounds in terms of the largest the smallest and an arbitrary given symbol probability are substantially improved