a note on the set theoretical defuzzification the set theoretic defuzzification sd method has been claimed to be a rational defuzzification method which is exclusively based on the fuzzy set theory j valente de oliveira fuzzy sets and systems 76 1995 63 however this paper shows the examples that the method is not applicable with general t norms and t conorms for normal fuzzy sets we show that the sd values of a normalized fuzzy set are located outside the support of the given fuzzy set with the min type t norm operator for non normal fuzzy sets we show that the defuzzification values of certain kinds of non normal fuzzy sets are unit value regardless of the support of the fuzzy set finally we show that the sd method does not satisfy two of three basic constraints for rational defuzzification operator which is proposed by runkler and glesner proc 2nd ieee internat conf on fuzzy systems p 1161

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

a proposal for a defuzzification strategy by the concept of sensitivity analysis abstract a systematic procedure is proposed for defuzzifying fuzzy subsets and interval values employing the concept of sensitivity analysis with a kind of minmax principle such that the defuzzification minimizes the sensitivity rating the discrepancy between a would be most appropriate defuzzified value and the unknown ideal value of defuzzification in the possible worst case a criterion of defuzzification can be built into the sensitivity to give a rationale to the defuzzified value as examples defuzzification with respect to a criterion of distance and minimization problems of two types of functions with fuzzy parameters are discussed

a bounded distance decoding algorithm for the leech lattice with generalizations an algorithm is given that decodes the leech lattice with not much more than twice the complexity of soft decision decoding of the golay code the algorithm has the same effective minimum distance as maximum likelihood decoding and increases the effective error coefficient by less than a factor or two the algorithm can be recognized as a member of the class of multistage algorithms that are applicable to hierarchical constructions it is readily generalized to lattices that can be expressed in terms of binary code formulas and in particular to construction b lattices

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

further asymptotic upper bounds on the minimum distance of trellis codes asymptotic upper bounds on the minimum distance of trellis codes are derived a universal bound and bounds specific to phase shift keying psk and quadrature amplitude modulation qam signal sets are obtained

combining beamforming and space time coding using noisy quantized feedback the goal of combining beamforming and spacetime coding is to obtain full diversity order and to provide additional received power array gain compared to conventional space time codes in this work a class of code constellations is proposed called generalized partly orthogonal designs pods and both high rate and low rate feedback information is incorporated with possible feedback errors a binary symmetric channel bsc model characterizes feedback errors two cases are studied first when the bsc bit error probability is known a priori to the transmission ends and second when it is not known exactly based on a minimum pairwise error probability pep design criterion we design a channel optimized vector quantizer covq for feedback information and a precoder matrix codebook to adjust the transmission codewords the attractive property of our combining scheme is that it converges to conventional space time coding with low rate and erroneous feedback and to directional beamforming with high rate and error free feedback this scheme also shows desirable robustness against feedback channel modeling mismatch

on the spectrum of distances of a multilevel code decoded by a multistage decoder in this correspondence we are concerned with the error rates contributed by component codes in a multilevel code decoded by a multistage decoder these error rates are required for estimating the performance of the structure but more importantly they can serve as a design tool for achieving high coding gain the latter objective can be reached by approaching a balance among these error rates for evaluating the error rate contributed by a component code it is essential to calculate the corresponding spectrum of euclidean distances a method for computing this spectrum is developed in this correspondence the method is general and applicable to any signal constellation and convolutional as well as block component codes the error coefficient available in the literature for some multilevel codes with an infinite size signal constellation is shown to be significantly different from that of a practical finite constellation note that the complete spectrum is essential when codewords of a component code with hamming distance beyond the minimum distance affect the error rate see e g turbo codes

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

a set theoretical defuzzification method a defuzzification method coinciding with the result of the subsethood theorem and including a family of averaging methods like mean of maxima and center of gravity as special cases is presented the defuzzification method named subsethood defuzzification sd method has the advantage of being exclusively based on set theoretical operations giving thus an insight on the nature of the computations involved in one of the most controversial stages of the fuzzy controller architecture in addition the sd method allows its customization also in the aim of set theory customization is believed as a necessary feature as the defuzzification problem seems ill defined and application dependent

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

similarity measure between fuzzy sets and between elements abstract two similarity measures are proposed one for the similarity between fuzzy sets and the other between elements in fuzzy sets with and example it is shown that the proposed measures can be used in the behavior analysis in an organization

diversity embedded space time codes rate and diversity impose a fundamental tradeoff in wireless communication high rate space time codes come at a cost of lower reliability diversity and high reliability diversity implies a lower rate however wireless networks need to support applications with very different quality of service qos requirements and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them in this paper we design high rate space time codes that have a high diversity code embedded within them this allows a form of communication where the high rate code opportunistically takes advantage of good channel realizations while the embedded high diversity code provides guarantees that at least part of the information is received reliably we provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint the nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white gaussian noise awgn channel that are matched to binary partitions of quadrature amplitude modulation qam and phase shift keying psk constellations the importance of set partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain we investigate the systems implications of embedded diversity codes by examining value to unequal error protection rate opportunism and packet delay optimization these applications demonstrate that diversity embedded codes have the potential to outperform traditional single layer codes in moderate signal to noise snr regimes

multilevel trellis coded modulations for the rayleigh fading channel the authors present coded 8 phase shift keyed 8 psk modulations for the rayleigh fading channel the schemes are based on multilevel trellis coded modulation constructions and utilize maximum free hamming distance binary convolutional codes as building blocks a suboptimal multistage decoder that utilizes interstage interleaving and iterative decoding is proposed and evaluated examples are constructed to show that the proposed schemes outperform the best modified codes of the ungerboeck type due to significantly higher implicit time diversity yielding seven branches of built in time diversity whereas the ungerboeck code yields four branches of time diversity for a 64 state system the transmission delay is higher however the new schemes can provide three levels of unequal error protection when 8 psk or 8 differential phase shift keying 8 dpsk modulations are used they provide 10 14 db channel signal to noise ratio gain over uncoded 4 dpsk at a bit error rate of 10 sup 3 for a modest decoding complexity

performance evaluation of coded modulation schemes based on binary lattices we describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding these techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based multilevel coded modulation schemes can also be described through a trellis by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum likelihood decoding using the viterbi algorithm and for computing the error probability an upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels and is applicable to both maximum likelihood and staged decoding

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

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

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

on trellis codes with a delay processor and a signal mapper it is already known that a trellis code t which is constructed by using the encoder of a convolutional code c with short constraint length followed by a delay processor and a signal mapper is equivalent to a trellis code with large constraint length in this paper we derive a new lower bound on the free distance of t which in some cases is better than the previously derived bound moreover instead of the decoding used in earlier publications we apply iterative decoding on both tailbiting and zero tail representations of t to take advantage of the new lower bound and in the meantime to decrease the associated error coefficient caused by the decoding used in earlier publications comparisons among various designs of such a trellis code and some well known coding methods are also provided

multilevel coded modulation for unequal error protection and multistage decoding ii asymmetric constellations in this paper theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection uep and multistage decoding are presented it is shown that nonstandard signal set partitionings and multistage decoding provide excellent uep capabilities beyond those achievable with conventional coded modulation the coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits the large effective error coefficients normally associated with standard mapping by set partitioning are reduced by considering nonstandard partitionings of the underlying signal set the bits to signal mappings induced by these partitionings allow the use of soft decision decoding of binary block codes moreover parallel operation of some of the staged decoders is possible to achieve high data rate transmission so that there is no error propagation between these decoders hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels the error performance of specific examples of multilevel codes over 8 psk and 64 qam signal sets are simulated and compared with theoretical upper bounds on the error performance

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

graph based iterative decoding algorithms for parity concatenated trellis codes we construct parity concatenated trellis codes in which a trellis code is used as the inner code and a simple parity check code is used as the outer code from the tanner wiberg loeliger 1981 1996 graph representation several iterative decoding algorithms can be derived however since the graph of the parity concatenated code contains many short cycles the conventional min sum and sum product algorithms cannot achieve near optimal decoding after some simple modifications we obtain near optimal iterative decoders the modifications include either a introducing a normalization operation in the min sum and sum product algorithms or b cutting the short cycles which arise in the iterative viterbi algorithm iva after modification all three algorithms can achieve near optimal performance but the iva has the least average complexity we also show that asymptotically maximum likelihood ml decoding and a posteriori probability app decoding can be achieved using iterative decoders with only two iterations unfortunately this asymptotic behavior is only exhibited when the bit energy to noise ratio is above the cutoff rate simulation results show that with trellis shaping iterative decoding can perform within 1 2 db of the shannon limit at a bit error rate ber of 4 spl times 10 sup 5 for a block size of 20000 symbols for a block size of 200 symbols iterative decoding can perform within 2 1 db of the shannon limit

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

multilevel construction of block and trellis group codes the theory of group codes has been shown to be a useful starting point for the construction of good geometrically uniform codes in this paper we study the problem of building multilevel group codes i e codes obtained combining separate coding at different levels in such a way that the resulting code is a group code a construction leading to multilevel group codes for semi direct and direct products is illustrated the codes that can be obtained in this way are identified new geometrically uniform euclidean space codes obtained from multilevel codes over abelian and nonabelian groups are presented

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

a multiple criteria active learning method for support vector regression abstract this paper presents a novel active learning method developed in the framework of e insensitive support vector regression svr for the solution of regression problems with small size initial training data the proposed active learning method selects iteratively the most informative as well as representative unlabeled samples to be included in the training set by jointly evaluating three criteria i relevancy ii diversity and iii density of samples all three criteria are implemented according to the svr properties and are applied in two clustering based consecutive steps in the first step a novel measure to select the most relevant samples that have high probability to be located either outside or on the boundary of the e tube of svr is defined to this end initially a clustering method is applied to all unlabeled samples together with the training samples that are inside the e tube those that are not support vectors i e non svs then the clusters with non svs are eliminated the unlabeled samples in the remaining clusters are considered as the most relevant patterns in the second step a novel measure to select diverse samples among the relevant patterns from the high density regions in the feature space is defined to better model the svr learning function to this end initially clusters with the highest density of samples are chosen to identify the highest density regions in the feature space then the sample from each selected cluster that is associated with the portion of feature space having the highest density i e the most representative of the underlying distribution of samples contained in the related cluster is selected to be included in the training set in this way diverse samples taken from high density regions are efficiently identified experimental results obtained on four different data sets show the robustness of the proposed technique particularly when a small size initial training set are available

space time trellis codes over rapid rayleigh fading channels with channel estimation part ii performance analysis and code design for non identical channels we consider the maximum likelihood ml receiver design performance analysis and code design for space time trellis codes sttc over non identical rapid fading channels with imperfect channel state information csi the exact pairwise error probability pep and pep bounds for the ml receiver are obtained a new code design criterion exploiting the statistical information of the channel estimates is proposed which can minimize the performance loss caused by channel estimation error new codes are obtained via an iterative search algorithm with reduced complexity under actual channel estimation conditions our codes perform better than the existing codes in the literature which are designed on the assumption of identical channels and perfect csi at the receiver more performance gain can be achieved by our codes when the degree of imbalance among the links is higher

active learning and basis selection for kernel based linear models a bayesian perspective we develop an active learning algorithm for kernel based linear regression and classification the proposed greedy algorithm employs a minimum entropy criterion derived using a bayesian interpretation of ridge regression we assume access to a matrix bbrn n for which the i j th element is defined by the kernel function k i j bbr with the observed data i bbrd we seek a model m i yi where yi is a real valued response or integer valued label which we do not have access to a priori to achieve this goal a submatrix il ib bbrn m is sought that corresponds to the intersection of n rows and m columns of indexed by the sets il and ib respectively typically m n and n n we have two objectives i determine the m columns of indexed by the set ib that are the most informative for building a linear model m 1 i ib t yi without any knowledge of yi i 1n and ii using active learning sequentially determine which subset of n elements of yi i 1n should be acquired both stopping values ib m and il n are also to be inferred from the data these steps are taken with the goal of minimizing the uncertainty of the model parameters x as measured by the differential entropy of its posterior distribution the parameter vector x bbrm as well as the model bias bbr is then learned from the resulting problem yil il ibx 1 the remaining n n responses labels not included in yil can be inferred by applying x to the remaining n n rows of ib we show experimental results for several regression and classification problems and compare to other active learning methods

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

the error probability of m ary psk block coded modulation schemes a tight upper bound on the decoding error probability is derived for block coded modulation structures where an m ary phase shift keying m psk signal constellation is employed this bound called a tangential sphere bound is tight for very low as well as for high signal to noise ratios snrs berlekamp s tangential union bound previously derived for binary codes can be derived for an m psk block coded modulation structure as well however it is proven that our tangential sphere bound is tighter than berlekamp s 1980 tangential bound for particular schemes it is shown that for low snrs our bound is considerably tighter than the tangential bound as one of the examples a multistage decoder is considered

new multilevel codes over gf q set partitioning is applied to multidimensional signal spaces over gf q i e gf sup n1 q n1 or d are presented these codes use reed solomon codes as component codes longer multilevel block codes are also constructed using q ary block codes with block length longer than q 1 as component codes some quaternary multilevel block codes are presented with the same length and number of information symbols as but larger distance than the best previously known quaternary one level block codes it is proved that if all the component block codes are linear the multilevel block code is also linear low rate q ary convolutional codes word error correcting convolutional codes and binary to q ary convolutional codes can also be used to construct multilevel trellis codes over gf q or binary to q ary trellis codes

the cutoff rate for on off keying it is well known that on off keying ook i e the transmission of a pulse for a data one mark and transmission of no signal for a data zero space exhibits a 3 db inferiority to antipodal signalling in terms of the signal to noise ratio required to achieve a specified bit error probability when the channel is characterized by the cutoff rate r sub 0 this 3 db inferiority persists in the sense that the required e sub b n sub 0 to operate at a given value of r sub 0 is 3 db greater for the ook channel than for the antipodal channel however it is shown that if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks part of this penalty is recovered in fact it is shown that in the limit of low r sub 0 there is no penalty in signal to noise ratio even at rates of realistic interest the penalty is significantly less than the expected 3 db

on block coded modulation with interblock memory block coded modulation with interblock memory bcmim is a variation of block coded modulation bcm which is designed for multilevel coding by providing interblock memory between adjacent blocks the coding rate of a bcmim scheme can be increased without decreasing the minimum squared euclidean distance msed as compared to the original bcm in an early version of bcmim interblock coding is provided only between the first two coding levels of adjacent blocks in this paper we design bcmim with a more general form for which interblock coding can be introduced among many coding levels in this way we can further increase the coding rate of bcmim without decreasing the msed we provide many examples to show the advantages of bcmim with the general form most of the examples are designed based on multidimensional signal sets since a multidimensional signal set can provide more coding levels than a two dimensional 2 d signal set

recursive space time trellis codes using differential encoding differential space time modulation dstm has been recently proposed by hughes and hochwald and sweldens when the channel information is not known at the receiver where the demodulation is in fact the same as the coherent demodulation of space time block coding by replacing the channel matrix with the previously received signal matrix on the other hand the dstm also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver which is the interest of this paper this recursive structure of the dstm has been adopted lately by schlegel and grant in joint with a conventional binary code and joint iterative decoding demodulation with a superior performance the number of states of the trellis from the recursive structure depends on both the memory size which is fixed in this case and the unitary space time code ustc when a ustc for the dstm forms a group the number of states is the same as the size of the ustc otherwise the number of the states is the size of the semi group generated by the ustc from all the multiplications of the matrices in the ustc it is well known in the conventional convolutional coding cc or the trellis coded modulation tcm the free hamming or euclidean distance or the performance increases when the number of states increases by adding more memory with a properly designed cc or tcm in this paper we systematically study and design the ustc dstm for the recursive space time trellis modulation and show that the diversity product increases when the number of states increases which is not because of the memory size but because of the different ustc designs that generate different sizes of semi groups we propose a new ustc design criterion to ensure that the trellis structure improves the diversity product over the ustc as a block code based on the new criterion we propose a new class of ustc design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas we then follow schlegel and grant s approach for joint encoding and iterative decoding of a binary coded dstm turbo space time coding and numerically show that our new ustc designs for the recursive space time trellis modulation outperforms the group ustc used by schlegel and grant

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

a study of defuzzification with experts knowledge for deteriorating repairable systems abstract this paper presents ideas on the applications of fuzzy concepts to decision making for deteriorating repairable systems a non homogeneous poisson process nhpp with a power law intensity function is used in this study in general classical bayesian decision methods presume that future states of nature can be characterized as probability events however we do not know what the future will entail probabilistically so we devise a method to consider experts opinions which are usually the absence of sharply defined criteria and to develop a fuzzy bayesian decision process for dealing with such situations two cases of the discrimination problem with deteriorating repairable systems are studied 1 fuzzy states and exact information and 2 fuzzy states and fuzzy information the fuzzy decomposition and arithmetic derivation of the experts opinion are presented to facilitate the development of the bayesian decision process for deteriorating repairable systems

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

statistical analysis of the product high order ambiguity function the high order ambiguity function haf was introduced for the estimation of polynomial phase signals pps embedded in noise since the haf is a nonlinear operator it suffers from noise masking effects and from the appearance of undesired cross terms and possibly spurious harmonics in the presence of multicomponent mc signals the product haf phaf was then proposed as a way to improve the performance of the haf in the presence of noise and to solve the ambiguity problem in this correspondence we derive a statistical analysis of the phaf in the presence of additive white gaussian noise awgn valid for high signal to noise ratio snr and a finite number of data samples the analysis is carried out in detail for single component pps but the multicomponent case is also discussed error propagation phenomena implicit in the recursive structure of the phaf based estimator are explicitly taken into account the analysis is validated by simulation results for both single and multicomponent ppss

on the performance evaluation of trellis codes generating function techniques for analyzing the error event and the bit error probabilities for trellis codes are considered the conventional state diagram approach for linear codes where the number of states is equal to the number of trellis states cannot be applied directly to arbitrary trellis codes and instead a state diagram where the number of states is equal to the square of the number of trellis states must be used it is shown that for an interesting class of trellis codes a modified generating function can be defined for which the number of states em is equal to the number of trellis states the class of codes considered includes trellis codes of rate r n 1 n based upon set partitioning whenever the first partition breaks the signal constellation into two subsets which have the same configuration matrix i e the same ordered set of mutual distances the complexity of calculating this modified generating function is the same as for the ordinary generating function of a convolutional code with the same number of trellis states bounds on the performance of some interesting codes are given based upon this method

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

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

two level coding based on trellis coded modulation and reed solomon codes a number of two level codes based on trellis coded modulation tcm schemes and their matched single or double error correcting reed solomon codes using qam constellations are presented and evaluated compared to the well known 4d 16 state tcm scheme with a comparable bandwidth efficiency these two level codes provide greater immunity from both gaussian and impulse noise at the cost of a reasonably higher complexity and a longer decoding delay on the order of a few hundred symbols the authors also show how to cope with phase ambiguities of the constellation in these two level codes both rotationally invariant coding and rotation detecting techniques are considered

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

a novel weighted multilevel space time trellis coding scheme it has been shown that when perfect or partial channel state information csi is available at the transmitter the performance and capacity of a space time coded system can be further improved multilevel space time trellis codes mlsttc s are capable of simultaneously providing bandwidth efficiency diversity improvement and coding gain with significantly reduced decoding complexity especially for larger constellations and higher throughputs in this paper we present a design of combined multilevel space time trellis codes and beam forming based on feedback from receiver henceforth referred to as weighted multilevel space time trellis codes wmlsttcs the channel profile is used to provide a beam forming scheme that achieves the better performance by properly weighting transmitted signals weights are selected that matches best with a channel profile feedback from the receiver indicative of long term characteristics of the wireless channel wmlsttcs provide improvement in performance of mlsttcs

lattice codes and generalized minimum distance decoding for ofdm systems lattice coding of orthogonal frequency division multiplexing ofdm systems is considered mapping of multilevel construction lattices to ofdm blocks is shown and a methodology for probabilistic analysis of multistage generalized minimum distance gmd decoding of the received ofdm blocks is shown as a case study transmission of points from a 128 dimensional barnes wall lattice is considered tight approximations to the system error rate are obtained and verified by simulation it appears that gmd decoding of lattice encoded ofdm provides high coding gain at low complexity

generalized minimum distance decoding of euclidean space codes and lattices it is shown that multistage generalized minimum distance gmd decoding of euclidean space codes and lattices can provide an excellent tradeoff between performance and complexity we introduce a reliability metric for gaussian channels that is easily computed from an inner product and prove that a multistage gmd decoder using this metric is a bounded distance decoder up to the true packing radius the effective error coefficient of multistage gmd decoding is determined two simple modifications in the gmd decoding algorithm that drastically reduce this error coefficient are proposed it is shown that with these modifications gmd decoding achieves the error coefficient of maximum likelihood decoding for block codes and for generalized construction a lattices multistage gmd decoding of the lattices d sub 4 e sub 8 k sub 12 bw sub 16 and spl lambda sub 24 is investigated in detail for k sub 12 bw sub 16 and spl lambda sub 24 the gmd decoders have considerably lower complexity than the best known maximum likelihood or bounded distance decoding algorithms and appear to be the most practically attractive decoders available for high dimensional codes and lattices spl ges 64 dimensions maximum likelihood decoding becomes infeasible while gmd decoding algorithms remain quite practical as an example we devise a multistage gmd decoder for a 128 dimensional sphere packing with a nominal coding gain of 8 98 db that attains an effective error coefficient of 1365760 this decoder requires only about 400 real operations in addition to algebraic errors and erasures decoding of certain bch and hamming codes it therefore appears to be practically feasible to implement algebraic multistage gmd decoders for high dimensional sphere packings and thus achieve high effective coding gains

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

tuning of fuzzy models by fuzzy neural networks it is relatively easy to construct a rough fuzzy model with expert knowledge it is difficult however to fine tune the parameters of the fuzzy model in order to get improved behavior for the purpose of tackling this problem we propose a fuzzy neural network model the proposed model utilizes a prior expert knowledge for target systems and embodies fuzzy models which consist of fuzzy rules whose antecedent and consequent are fuzzy sets the model is equipped with a fuzzy inferencing and tuning mechanism for model parameters by learning it allows us to tune such parameters of fuzzy models as linguistic terms and relative rule importance in addition to show its applicability we perform some experiments and present the results

an approach to ungerboeck coding for rectangular signal sets corresp a method of finding good ungerboeck codes for large rectangular quadrature amplitude modulation qam signal sets is described using the concept of euclidean weights due to ungerboeck we prove that a 2 n point basic constellation may be employed to determine exactly the free distance for an ungerboeck coded rectangular 2 m point set when m n 1 bits are uncoded and the remaining bits pass through a rate n 1 n convolutionai encoder it is shown that rate 2 3 encoders may be used to achieve most of the theoretically possible coding gain in the proposed scheme where the effect of the error coefficient on the coding gain has been considered

trellis codes for the optical direct detection channel it is observed that the reduced complexity minimum distance search method of zehavi and wolf 1987 can be extended from codes designed using the squared euclidean distance measure to any measure which is additive over the code branches c n georghiades 1989 has derived such a metric for codes for the direct detection optical channel the search method is applied to find codes for four and eight point overlapping pulse position modulation oppm with large minimum distance and a small number of codewords at that distance

block coded psk modulation using two level group codes over dihedral groups a length n group code over a group g is a subgroup of g sup n under component wise group operation group codes over dihedral groups d sub m with 2m elements that are two level constructible using a binary code and a code over z sub m residue class integer ring modulo m as component codes are studied for arbitrary m a set of necessary and sufficient conditions on the component codes for the two level construction to result in a group code over d sub m are obtained the conditions differ for m odd and even using two level group codes over d sub m as label codes the performance of a block coded modulation scheme is discussed under all possible matched labelings of 2m apsk and 2m spsk asymmetric and symmetric psk signal sets in terms of the minimum squared euclidean distance matched labelings that lead to automorphic euclidean distance equivalent codes are identified it is shown that depending upon the ratio of hamming distances of the component codes some labelings perform better than others the best labeling is identified under a set of restrictive conditions finally conditions on the component codes for phase rotational invariance properties of the signal space codes are discussed

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed

techniques of bounding the probability of decoding error for block coded modulation structures two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented the first bound which is applicable to the additive white gaussian noise awgn channel is tighter than the well known union bound and the minimum distance bound especially for low signal to noise ratio it is shown that for the leech lattice this upper bound is very close to a sphere lower bound for the second upper bound which is applicable to any memoryless channel not necessarily awgn a method of random coset coding is presented for the awgn channel a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code which is required for the computation of the first upper bound

an adaptive approach to defuzzification based on level sets abstract we look at the process of defuzzification used in fuzzy logic controllers we provide a parametrized formulation for this procedure based upon the use of level sets which we call generalized level set defuzzification we show that the commonly used defuzzification procedures mean of maxima and center of area are special cases of this general procedure and are simply distinguished by the choice of the parameter we provide a simple algorithm for adaptive choice of the best defuzzification procedure

computing upper bounds to error probability of soft decision decoding of reed solomon codes based on the ordered statistics algorithm this correspondence presents performance analysis of symbol level soft decision decoding of q ary maximum distance separable mds codes based on the ordered statistics algorithm the method we present is inspired by the one recently proposed by agrawal and vardy 2000 who approximately evaluate the performance of generalized minimum distance decoding the correspondence shows that in our context the method allows us to compute the exact value of the probability that the transmitted codeword is not one of the candidate codewords this leads to a close upper bound on the performance of the decoding algorithm application of the ordered statistics algorithm to mds codes is not new nevertheless its advantages seem not to be fully explored we show an example where the decoding algorithm is applied to singly extended 16 ary reed solomon rs codes in a 128 dimensional multilevel coded modulation scheme that approaches the sphere lower bound within 0 5 db at the word error probability of 10 sup 4 with manageable decoding complexity