the l fuzzy hypermodules in this paper we introduce the concept of l fuzzy hypermodules over an l fuzzy hyperring and investigate some of their properties we provide the notion of l fuzzyr subhypermodules of an l fuzzy r hypermodule and derive a kind of l fuzzy quotient hypermodule by using an l fuzzy r subhypermodule we also study the properties of l fuzzy a regular relation on l fuzzy r hypermodules and investigate l fuzzy hypermodule strong homomorphism

triangulated categories and kac moody algebras by using the ringel hall algebra approach we find a lie algebra arising in each triangulated category with t 2 1 where t is the translation functor in particular the generic form of the lie algebras determined by the root categories the 2 period orbit categories of the derived categories of finite dimensional hereditary associative algebras gives a realization of all symmetrizable kac moody lie algebras

block transmission over dispersive channels transmit filter optimization and realization and mmse dfe receiver performance optimal transmit filters for packet based data transmission on dispersive gaussian noise linear time invariant channels are derived by maximizing the mutual information subject to a fixed input power budget a quasi stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case for situations of most practical interest moreover this quasi stationary approximation results in efficiently computed lattice or pole zero implementations of the transmit filter by considering the popular finite impulse response minimum mean square error decision feedback equalizer fir mmse dfe as a receiver structure we show that transmitter optimization results in an appreciable improvement in the decision point signal to noise ratio finally we show that as the output blocklength becomes infinite the optimum finite dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well known water pouring distribution

block based eigensystem of the 1 spl plusmn d and 1 d sup 2 partial response channels we find analytical expressions for the block based input and output eigenvectors and eigenvalues of the systems with responses 1 spl plusmn d and 1 d sup 2 the input eigenvectors form an orthonormal basis which is the optimum modulator for a channel with that transfer function the output eigenvectors form an orthonormal basis with the same spectral nulls as the corresponding system this basis can be used to produce line codes with spectral nulls the eigenvectors are sinusoids this reduces the computational complexity by allowing for fast transform algorithms to perform the modulation for a block of data

optimization of signal sets for partial response channels i numerical techniques given a linear time invariant discrete time channel the problem of constructing n input signals of finite length k that maximize minimum l sub 2 distance between pairs of outputs is considered two constraints on the input signals are considered a power constraint on each of the n inputs hard constraint and an average power constraint over the entire set of inputs soft constraint the hard constraint problem is equivalent to packing n points in an ellipsoid in min k n 1 dimensions to maximize the minimum euclidean distance between pairs of points gradient based numerical algorithms and a constructive technique based on dense lattices are used to find locally optimal solutions to the preceding signal design problems two numerical examples are shown for which the average spectrum of an optimized signal set resembles the water pouring spectrum that achieves shannon capacity assuming additive white gaussian noise

discrete time signal design for maximizing separation in amplitude given a discrete time linear shift invariant channel with finite impulse response the problem of designing finite length input signals with bounded amplitude l sub spl infin norm such that the corresponding output signals are maximally separated in amplitude l sub spl infin sense is considered in general this is a nonconvex optimization problem and appears to be computationally difficult an optimization algorithm that seems to perform well is described optimized signal sets and associated minimum distances minimum l sub spl infin separation between two distinct channel outputs are presented for some example impulse responses a conjectured upper bound on the minimum distance is given that is easily computed given the impulse response of the channel the number of inputs and the input length this upper bound is shown to be valid for a limited class of impulse response functions

coset codes for partial response channels or coset codes with spectral nulls known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls by using coset precoding and running digital sum feedback any desired tradeoff can be achieved between the power and spectra of the relevant sequences up to the optimum tradeoff possible a fundamental theorem specifying this optimum tradeoff is given a maximum likelihood sequence estimation mlse decoder for the original code may be used for the adapted code and such a decoder then attains the minimum squared distance of the original code these methods sometimes generate codes with greater minimum squared distance than that of the original code this distance can be attained by augmented decoders although such decoders inherently require long decoding delays and may be subjected to quasi catastrophic error propagation the authors conclude that at least for sequences supporting large numbers of bits per symbol coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels or for sequences with spectral nulls as they do in the ordinary memoryless case

redefined fuzzy hv submodules and many valued implications this paper considers a relationship between fuzzy sets and algebraic hyperstructures a generalization of ideas presented by davvaz b davvaz fuzzy h v submodules fuzzy sets syst 117 2001 477 484 and bhakat and das s k bhakat p das email protected q fuzzy subgroup fuzzy sets syst 80 1996 359 368 is presented in fact the main purpose of this paper is to introduce and study a new sort of fuzzy h v submodule of an h v module called email protected q fuzzy h v submodules these fuzzy h v submodules are characterized by their level h v submodules the concept of a fuzzy h v submodule with thresholds is introduced and some interesting properties are investigated

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

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

the optimum combination of block codes and receivers for arbitrary channels a determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal to noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum this permits representing the channel as a set of parallel uncoupled subchannels with uncorrelated noise the representation is used to calculate the capacity of an arbitrary block coded time discrete channel it is shown that substantial coding gains compared to symbol by symbol processing can be achieved the block code used can be concatenated with trellis coded modulation so that the two coding gains are additive

bounds on maximum throughput for digital communications with finite precision and amplitude constraints the problem of finding the maximum achievable data rate over a linear time invariant channel is considered under constraints different from those typically assumed the limiting factor is taken to be the accuracy with which the receiver can measure the channel output more precisely the following problem is considered given a channel with known impulse response h t a transmitter with an output amplitude constraint and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t sub 0 by at least some small positive constant d what is the maximum number of messages n sub max that can be transmitted in a given time interval 0 t lower bounds on n sub max can be easily computed by constructing a particular set of inputs to the channel the main result is an upper bound on n sub max for arbitrary h t the upper bound depends on the spread of h t which is the maximum range of values the channel output may take at some time t sub 0 0 given that the output takes on a particular value alpha at time t 0 numerical results are shown for different impulse responses including two simulated telephone subscriber loop impulse responses

optimization of signal sets for partial response channels ii asymptotic coding gain for pt i see ibid vol 37 no 5 p 1327 141 1991 for a linear time invariant discrete time channel with a given transfer function h f and information rate r bits t where t is the symbol interval an optimal signal set of length k is defined to be a set of 2 sup rk inputs of length k that maximizes the minimum l sub 2 distance between pairs of outputs the author studies the minimum distance between outputs or equivalently the coding gain of optimal signal sets as k to infinity he shows how to estimate the coding gain relative to single step detection of an optimal signal set length k when k is large

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

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

elliptic lie algebras and tubular algebras abstract this article is to study relations between tubular algebras of ringel and elliptic lie algebras in the sense of saito yoshii using the explicit structure of the derived categories of tubular algebras given by happel ringel we prove that the elliptic lie algebra of type d 4 1 1 e 6 1 1 e 7 1 1 or e 8 1 1 is isomorphic to the ringel hall lie algebra of the root category of the tubular algebra with the same type as a by product of our proof we obtain a chevalley basis of the elliptic lie algebra following indecomposable objects of the root category of the corresponding tubular algebra this can be viewed as an analogue of the frenkel malkin vybornov theorem in which they described a chevalley basis for each untwisted affine kac moody lie algebra by using indecomposable representations of the corresponding affine quiver

hall algebras hereditary algebras and quantum groups let r be an associative hereditary algebra over a finite field k and let r fin be the full subcategory of r mod whose objects are those left r modules x which are finite as sets ix oc assume also that r isfinitary in c ringel s sense i e that iext l s s c for all simple s s in r fin this condition is met for example if r is finitely generated as k algebra 4 pp 435 436 let be the set of all isomorphism classes in r fin if 2 e then u will denote an r module in class 2 the class of all zero left r modules is denoted 0 let i c be the set of all isomorphism classes of simple modules in r fin thus u i e i is a complete set of simple finite left r modules we identify the grothendieck group k0 r fin with the free abelian group e1 v i v e 7z having i as free basis so that if x e r fin then the corresponding element of k0 r fin is the dimension vector dimx y i vii where for each i e vi is the multiplicity of the simple module u in any composition series of x clearly d imx lies in the subsemigroup

optimization of a lattice based constellation for signaling over a partial response channel this article discusses the problem of optimizing a lattice based signal constellation for signaling over a partial response channel the objective is to minimize the probability of error which is determined by the combined effects of the additive gaussian noise and channel memory

sphere packing upper bounds on the free distance of trellis codes sphere packing arguments are used to develop upper bounds on the free distance of trellis codes a general bounding procedure is presented sphere packing bounds including bounds on the density of infinite regions packings for hypercubes and packings on the surface of a unit sphere are then used to produce bounds for a wide variety of trellis codes among the applications are convolutional codes ungerboeck codes for phase shift keying and quadrature amplitude modulation coset codes and continuous phase modulation codes the new bounds are significantly tighter than existing bounds in many cases of practical interest

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

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

design of channel estimate dependent space time block codes so far the assumption of no channel knowledge at the transmitter has generally been inherent in the design of space time codes this paper on the other hand assumes that quantized channel information obtained from a feedback link is available at the transmitter and investigates how such channel information can be incorporated into the design of unstructured space time block codes efficient codes are found by means of a gradient search over a continuous alphabet simulation results for an uncorrelated rayleigh fading scenario using two and four transmit antennas and one receive antenna show the benefits of the code designs

f polygroups ii first a product between two f subpolygroups of a given f polygroup is defined and then a necessary and sufficient condition is given in order that the product be an f subpolygroup then by considering the notion of homomorphism of f polygroups some related results are obtained finally the concept of quotient f polygroup is defined and then some theorems are proved

lattice structure on fuzzy congruence relations of a hypergroupoid in this manuscript we first define the notion of fuzzy left right congruence relation on a hypergroupoid and then we investigate the lattice structure of the set of these fuzzy relations finally we show that a special class of fuzzy equivalence relations on the hypergroupoid forms a distributive lattice

some remarks on congruences obtained from the l fuzzy nakano hyperoperation in this paper we study relations which are congruences with respect to and p where p is the p cut of the l fuzzy hyperoperation the main idea is to start from an equivalence relation r 1 which is a congruence with respect to and 1 and for each email protected x construct an equivalence relation r p which is a congruence with respect to and p furthermore for each email protected r p we construct a quotient hyperoperation p and we show that the hyperalgebra x r p p is a join space and the hyperalgebra x r p p p is a hyperlattice

fuzzy hyperlattices in this paper we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices moreover we define and analyze the hypercongruence on hyperlattices and the fuzzy strong hypercongruence on fuzzy hyperlattices and we study the interrelation between the fuzzy hypercongruence on fuzzy hyperlattices and the homomorphism of fuzzy hyperlattices also a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained finally we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices respectively

the l fuzzy nakano hypergroup in this paper we start with a lattice x and define in terms of a family of crisp hyperoperations p one hyperoperation for each p x we show that for every p the hyperalgebra x p is a join space and the hyperalgebra x p is very similar to a hyperlattice then we use the hyperoperations p as p cuts to introduce an l fuzzy hyperoperation and show that x is an l fuzzy join space and the hyperalgebra x p is very similar to an l fuzzy hyperlattice

lie algebras graded by finite root systems and the intersection matrix algebras of slodowy this paper is about toroidal lie algebras certain intersection matrix lie algebras defined by slodowy and their relationship to one another and to certain lie algebra analogues of steinberg groups the main result of the paper is the identification of the intersection matrix algebras arising from multiply affinized cartan matrices of types a d and e with certain steinberg lie algebras and toroidal lie algebras propositions 5 9 and 5 10 a major part of the paper studies and classifies lie algebras graded by finite root systems these become the princi pal tool in our analysis of intersection matrix algebras each lie algebra graded by a simply laced finite root system of rank 2 has attached to it an algebra which according to the type and rank is either commutative and associative only associative or alternative all these possibilities occur in our description of inter section matrix algebras let r be any associative algebra with identity not necessarily finite dimen sional over a field k of characteristic 0 for each positive integer n the associative algebra m r of n n matrices with coefficients in r forms a lie algebra over k under the commutator product we denote this lie algebra by ol r let eis be the i j matrix unit of m r and assume that n 2 the subalgebra e r of oi r generated by the elements reis r r i 4 j is an ideal of 91 r and is perfect i e it is its own derived algebra now any perfect lie algebra o has a universal central extension also perfect called a universal covering algebra u c a of o ga so in particular e r has a u c a that we will denote by t r we define 112 r by the exact sequence 0 1 0 f2 r t r e r 0 dedicated to our teacher maria j wonenburger both authors gratefully acknowledge the support of the natural sciences and engineering research council of canada

noncommutative projective curves and quantum loop algebras we show that the hall algebra of the category of coherent sheaves on a weighted projective line over a finite field provides a realization of the quantized enveloping algebra of a certain nilpotent subalgebra of the affinization of the corresponding kac moody algebra in particular this yields a geometric realization of the quantized enveloping algebra of elliptic or 2 toroidal algebras of types d 4 1 1 e 1 1 6 e 1 1 7 and e 8 1 1 in terms of coherent sheaves on weighted projective lines of genus one or equivalently in terms of equivariant coherent sheaves on elliptic curves

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained

maximizing the output energy of a linear channel with a time and amplitude limited input the problem of maximizing the output energy of a linear time invariant channel given that the input signal is time and amplitude limited is considered it is shown that a necessary condition for an input mu to be optimal assuming a unity amplitude constraint is that it satisfy the fixed point equation sgn f mu where the functional f is the convolution of mu with the autocorrelation function of the channel impulse response it is also shown that all solutions to this equation for which mod mu mod 1 almost everywhere correspond to local maxima of the output energy iteratively recomputing mu from the fixed point equation leads to an algorithm for finding local optima numerical results are given for the cases where the transfer function is ideal low pass and has two poles these results support the conjecture that in the ideal low pass case the optimal input signal is a single square pulse a generalization of the preceding fixed point condition is also derived for the problem of maximally separating n outputs of a discrete time linear time invariant channel