trellis coded differentially coherent tcdc mpsk with carrier phase noise the authors consider trellis coded m ary phase shift keying mpsk when used with differentially coherent demodulation over a carrier phase noise dominated channel a tight upper bound to the probability of error is introduced this bound shows the presence of an irreducible probability of error when compared to coherently demodulated trellis coded mpsk the irreducible probability of error of the differentially coherent scheme is much lower this improved robustness to carrier phase noise is obtained at the expense of signal to noise ratio snr coding gain numerical results for two ungerboeck codes with differentially coherent mpsk demodulation show poor snr coding gain a modification of ungerboeck codes which makes them more suitable for use with differentially coherent demodulation is shown to increase the snr gain while maintaining good robustness to carrier phase noise

cones and decomposition of sub and supermartingales abstract we study sub and supermartingales with values in the class f c of all convex fuzzy subsets of a banach space having compact support the terms sub and super are understood with respect to a partial order not necessarily inclusion in this general framework orders with respect to which a doob type decomposition can hold are naturally associated to convex subcones with a special property termed f c properness decomposition theorems into the sum or difference of a martingale and a compensator are proven in the sub case the martingale need exist only in a superspace of f c

fuzzy set valued gaussian processes and brownian motions gaussian processes and brownian motion are concepts and tools in modelling important uncertain systems in many areas in view of uncertainty complexity in many real world problems we extend these tools to the case where stochastic processes can take on fuzzy sets as values in this paper we discuss fuzzy set valued gaussian processes based on the results of s li y ogura v kreinovich limit theorems and applications of set valued and fuzzy set valued random variables kluwer academic publishers dordrecht 2002 s li y ogura h t nguyen gaussian processes and martingales for fuzzy valued variables with continuous parameter inform sci 133 2001 7 21 s li y ogura f n proske m l puri central limit theorems for generalized set valued random variables j math anal appl 285 2003 250 263 n n lyashenko on limit theorems for sums of independent compact random subsets in the euclidean space j soviet math 20 1982 2187 2196 and m l puri d a ralescu the concept of normality for fuzzy random variables ann probab 13 1985 1373 1379 we also introduce the concept of fuzzy set valued brownian motion and then prove several properties of such processes

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

convergence theorem for fuzzy martingales abstract we study fuzzy set valued measures in a banach space and their relationships to fuzzy random variables our main result is a convergence theorem for fuzzy martingales our tool is a radon nikodym type theorem for fuzzy measures which are absolutely continuous with respect to probability measures

characterization of compact subsets of fuzzy sets a characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space rn the metric for which is the supremum over the hausdorff distances between corresponding level sets it is shown that a closed subset is compact if and only if it is uniformly support bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

tcm with differential encoding set partitioning trellis designs and distance analysis differential encoding de is a classical technique at the transmitter that allows simple noncoherent detection at the receiver on the other hand trellis coded modulation tcm is a bandwidth efficient technique which offers reliable data transmission in this paper we aim to find the best concatenation order of tcm and de for channel phase coherence over n 2 symbols besides the well known tcm followed by de called tcm de we propose a new trellis coding extension of de which extends our earlier work called differential trellis coded modulation dtcm dtcm is tcm with de defined in states where distinct states may have distinct de functions we propose design methods of de functions for noncoherently non catastrophic dtcm for both tcm de and dtcm we propose additive distance measures and set partitioning based on the proposed set partitioning trellis codes are designed or searched for both tcm de and dtcm both minimum distances and simulation results show that tcm de outperforms dtcm and the obtained new codes are better than the original codes

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

separability for graph convergence of sequences of fuzzy valued random variables abstract we prove that the graph convergence in hausdorff metric or kuratowski mosco topology of a sequence of fuzzy sets follows from the convergence of the sequences of the level sets for countable dense levels as an application we give a strong law of large numbers for fuzzy valued random variables including the case when the level sets may not be bounded

existence and uniqueness of solution for fuzzy random differential equations with non lipschitz coefficients in this paper a class of fuzzy random differential equations with non lipschitz coefficients is studied the existence and uniqueness of solutions for fuzzy random differential equations with non lipschitz coefficients is first proved then the dependence of fuzzy random differential equations on initial values is discussed finally the non confluence property of the solution for fuzzy random differential equation is investigated our main tool is the gronwall lemma

m ary phase coding for the noncoherent awgn channel this work considers coded m ary phase shift keying mpsk schemes with noncoherent detection a class of block codes called module phase codes is described the algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection it is shown that differential encoding may be viewed as a specific code from a particular class of module phase codes two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded mpsk are presented in the first class of module phase codes the coding gain is achieved at the expense of bandwidth expansion in the second class however the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth finally an integrated demodulation decoding technique based on a modification of information set decoding is presented it is shown that this reduced complexity suboptimal decoding strategy performs nearly as well as maximum likelihood decoding

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

noncoherent block coded tapsk for coherent detection block coded modulation is a bandwidth efficient scheme in this paper we propose theorems about the error performance of block coded modulation using m ary phase shift keying mpsk for noncoherent detection based on these theorems we propose a novel block coded modulation scheme for noncoherent detection called noncoherent block coded mpsk the proposed scheme provides flexible designs of noncoherent block codes with different code rate block length and error performance good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes moreover noncoherent block codes of this new scheme can be decoded by multistage decoding which has the advantage of low complexity and satisfactory error performance in this paper two algorithms of multistage decoding for noncoherent detection are proposed as well the error performance of some designed codes and decoding algorithms is verified by computer simulation

a hybrid method for systems of closely spaced dielectric spheres and ions we develop an efficient semianalytical spectrally accurate and well conditioned hybrid method for the study of electrostatic fields in composites consisting of an arbitrary distribution of dielectric spheres and ions that are loosely or densely close to touching packed we first derive a closed form formula for the image potential of a general multipole source of arbitrary order outside a dielectric sphere based on this formula a hybrid method is then constructed to solve the boundary value problem by combining these analytical methods of image charges and image multipoles with the spectrally accurate mesh free method of moments the resulting linear system is well conditioned and requires many fewer unknowns on material interfaces as compared with standard boundary integral equation methods in which the formulation becomes increasingly ill conditioned and the number of unknowns also increases sharply as the spheres approach each other or ions approach the spheres due to the geometric and physical

overview on the development of fuzzy random variables this paper presents a backward analysis on the interpretation modelling and impact of the concept of fuzzy random variable after some preliminaries the situations modelled by means of fuzzy random variables as well as the main approaches to model them are explained we also summarize briefly some of the probabilistic studies concerning this concept as well as some statistical applications

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

on borel measurability and large deviations for fuzzy random variables fuzzy random variables are a special case of measurable mappings taking on values in a non separable metric space due to that non separability the two main definitions in the literature turn out not to be equivalent we give an easy necessary and sufficient condition for their equivalence an intermediate result of independent value is a characterization of separable subsets of that metric space several probabilistic applications are proposed notably a generalization to this setting of the large deviations principle of bolthausen

on embedding problems of fuzzy number spaces iv in this paper we are going to follow the preceding papers to investigate the embedding problem of fuzzy number space ne 1 by means of a concrete embedding operator using the embedding operator some subclasses of ne 1 and metrices on ne 1 are also investigated

stochastic integral with respect to set valued square integrable martingales in this paper we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set valued square integrable martingale secondly we shall prove the representation theorem of set valued square integrable martingale thirdly we shall give the definition of stochastic integral of a stochastic process with respect to a set valued square integrable martingale and the representation theorem of this kind of integrals finally we shall prove that the stochastic integral is a set valued sub martingale

strong laws of large numbers for independent fuzzy set valued random variables abstract in this paper we shall present strong laws of large numbers slln s for independent not necessary identically distributed fuzzy set valued random variables whose base space is a separable banach space or an euclidean space in the sense of the extended hausdorff metric d h we apply the method to the sequence of independent identically distributed fuzzy set valued random variables to give a simple proof of slln s

theoretical analysis and performance limits of noncoherent sequence detection of coded psk a theoretical performance analysis of noncoherent sequence detection schemes previously proposed by the authors for combined detection and decoding of coded m ary phase shift keying m psk is presented a method for the numerical evaluation of the pairwise error probability for which no closed form expressions exist is described the classical union bound is computed and results are compared with computer simulations an upper bound on this pairwise error probability is also presented this upper bound may be effectively used for the definition of an equivalent distance which may be useful in exhaustive searches for optimal codes using this bound it is proven that in the general coded case the considered noncoherent decoding schemes perform as close as desired to an optimal coherent receiver when a phase memory parameter is sufficiently large in the case of differentially encoded m psk a simple expression of the asymptotic bit error probability is derived which is in agreement with simulations for high as well as low signal to noise ratio snr

a convergence theorem of fuzzy valued martingales in the extended hausdorff metric h in this paper we shall give a new embedding method to prove a convergence theorem for fuzzy valued random variables in the sense of the extended hausdorff metric h without the restriction of fuzzy sets satisfying the lipschitz condition

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

further results on differential encoding by a table recently we proposed a novel differential encoder by a look up table in this paper we present further research results on this subject we first propose a bit assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance then differential encoding for multiple symbol differential detection is proposed after that we indicate that differential encoding by a table is equivalent to differential encoding by a trellis so we propose a novel differential detector which uses the viterbi algorithm on the trellis a theorem about the sufficient number of states for various modulations is proposed in addition we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding for this noncoherent trellis coding scheme we propose augmented state viterbi decoding finally we extend the proposed differential encoding and detection to differential space time modulation dstm we propose a new definition of dstm by which the set of transmitted blocks is determined first the differential encoding is implemented by a look up table which can be optimized the proposed dstm has satisfactory error performance without constellation expansion

gaussian processes and martingales for fuzzy valued random variables with continuous parameter abstract the purpose of this paper is to discuss fuzzy valued gaussian processes and martingales with continuous parameter we mainly obtain a representation theorem for fuzzy valued gaussian processes after proving a new embedding theorem based on previous results about set valued and fuzzy valued martingales cf s li y ogura j fuzzy math 4 1996 905 s li y ogura fuzzy sets and systems 101 1999 453 s li y ogura ann probab 26 1998 1384 1402 s li y ogura in proc ifsa 97 vol 4 1997 pp 9 13 s li y ogura in c bertoluzza m a gil d a ralescu eds statistical modeling analysis and management of fuzzy data physica in press y ogura s li fuzzy sets and systems in press we prove optional sampling theorems for set valued and fuzzy valued martingales with continuous parameter

bandwidth efficient noncoherent trellis coded mpsk in this letter we propose a novel bandwidth efficient noncoherent trellis coded mpsk scheme in which a particularly designed differential encoder is added in front of the trellis encoder with this differential encoder trellis coded mpsk proposed by ungerboeck is no longer noncoherently catastrophic and thus achieves better error performance moreover new trellis codes which for the proposed scheme have better bit error rates than ungerboeck s codes are found by computer searches

on the method of images for systems of closely spaced conducting spheres in this paper a new formalism is developed to generate the image of a multipole expansion of arbitrary order in a conducting sphere a method of images based on this formalism is subsequently combined with the method of moments to solve boundary value problems for systems of closely spaced conducting spheres the effectiveness of the new hybrid method is demonstrated through several numerical examples

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

convergence of set valued and fuzzy valued martingales the purpose of this paper is to prove the convergence theorems of set valued and fuzzy valued martingales in kuratowski mosco sense without assuming that their values are compact or of compact level sets

differential encoding by a look up table for quadrature amplitude modulation in this paper we propose a novel differential encoder for qam quadrature amplitude modulation by a look up table instead of a rule using a table for differential encoding has the advantages of both low complexity and good error performance we propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two codewords with small noncoherent distance for 16qam and 32qam we show that the differential encoders obtained by the proposed algorithms are optimal in terms of minimum noncoherent distance differential detectors for qam including a reduced complexity two symbol detector and multiple symbol detectors are proposed as well simulation results of 16qam show that the proposed differential encoder provides significant gain over existent differential encoders as expected by distance analysis and the proposed low complexity multiple symbol differential detector can further improve the error performance

limit theorems for fuzzy random variables a strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables whose values are fuzzy sets with compact levels the proofs are based on embedding theorems as well as on probability techniques in banach space