constrained capacities for faster than nyquist signaling this paper deals with capacity computations of faster than nyquist ftn signaling it shows that the capacity of ftn is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc ftn signals can in fact achieve the ultimate capacity for the signal power spectral density psd the paper lower and upper bounds the ftn capacity under the constraint of finite input alphabet it is often higher than the capacity for comparable orthogonal pulse systems sometimes it is superior to all forms of orthogonal signaling with the same psd

on the general linear group and hochschild homology our main result here is a rational computation of the homology of the adjoint action of the infinite general linear group of an arbitrary ring before stating the result we establish some notation and conventions rings are associative and with unit if a is a ring then gl a uk 0glk a is its infinite general linear group an a bimodule is an abelian group b which is both a left a module and a right a module and satisfies alb a2 al ba2 for ai ea be b for example b a if b is an a bimodule then m b uk omk b is the infinite additive group of matrices with entries in b conjugation defines an action the adjoint action of gl a on m b note that an a q bimodule is just an a bimodule which is also a rational vector space if b is an a q bimodule then hj a c q b denotes the hochschild homology of a q with coefficients in b our main result it appears in slightly more detailed form as theorem v 3 is

continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

dynamical and cohomological obstructions to extending group actions motivated by a question of ghys we study obstructions to extending group actions on the boundary partial m of a 3 manifold to a c 0 action on m among other results we show that for a 3 manifold m the s 1 times s 1 action on the boundary does not extend to a c 0 action of s 1 times s 1 via homeomorphisms that are isotopic to the identity as a discrete group on m except in the trivial case m cong d 2 times s 1

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

sequential sequence estimation for channels with intersymbol interference of finite or infinite length a sequential sequence estimator for channels with finite or infinite intersymbol interference isi is proposed it consists of a whitened matched filter followed by a sequential algorithm a key component of a sequential estimator is a suitable metric that accounts for the unequal search depth this metric is derived for the isi channel computer simulations for three different channels show that the sequential sequence estimator has considerably less computational complexity than a maximum likelihood sequence estimator using the viterbi algorithm mlse va while still maintaining the optimum estimation performance of the mlse va a performance not achievable with any reduced state viterbi algorithm

contractive type non self mappings on metric spaces of hyperbolic type abstract let x d be a metric space of hyperbolic type and k a nonempty closed subset of x in this paper we study a class of mappings from k into x not necessarily self mappings on k which are defined by the contractive condition 2 1 below and a class of pairs of mappings from k into x which satisfy the condition 2 28 below we present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of ciric l b ciric quasi contraction non self mappings on banach spaces bull acad serbe sci arts 23 1998 25 31 l b ciric j s ume m s khan h k t pathak on some non self mappings math nachr 251 2003 28 33 rhoades b e rhoades a fixed point theorem for some non self mappings math japon 23 1978 457 459 and many other authors some examples are presented to show that our results are genuine generalizations of known results from this area

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

infinite loop spaces and positive scalar curvature we study the homotopy type of the space of metrics of positive scalar curvature on high dimensional compact spin manifolds hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable space from the real k theory spectrum our main results concern the nontriviality of this map we prove that for 2n ge 6 the natural ko orientation from the infinite loop space of the madsen tillmann weiss spectrum factors up to homotopy through the space of metrics of positive scalar curvature on any 2n dimensional spin manifold for manifolds of odd dimension 2n 1 ge 7 we prove the existence of a similar factorisation when combined with computational methods from homotopy theory these results have strong implications for example the secondary index map is surjective on all rational homotopy groups we also present more refined calculations concerning integral homotopy groups to prove our results we use three major sets of technical tools and results the first set of tools comes from riemannian geometry we use a parameterised version of the gromov lawson surgery technique which allows us to apply homotopy theoretic techniques to spaces of metrics of positive scalar curvature secondly we relate hitchin s secondary index to several other index theoretical results such as the atiyah singer family index theorem the additivity theorem for indices on noncompact manifolds and the spectral flow index theorem finally we use the results and tools developed recently in the study of moduli spaces of manifolds and cobordism categories the key new ingredient we use in this paper is the high dimensional analogue of the madsen weiss theorem proven by galatius and the third named author

surgery and duality surgery as developed by browder kervaire milnor novikov sullivan wall and others is a method for comparing homotopy types of topological spaces with difieomorphism or homeomorphism types of manifolds of dimension 5 in this paper a modiflcation of this theory is presented where instead of flxing a homotopy type one considers a weaker information roughly speaking one compares n dimensional compact manifolds with topological spaces whose k skeletons are flxed where k is at least n 2 a particularly attractive example which illustrates the concept is given by complete intersections by the lefschetz hyperplane theorem a complete intersection of complex dimension n has the same n skeleton as n and one can use the modifled theory to obtain information about their difieomorphism type although the homotopy classiflcation is not known the theory reduces this classiflcation result to the determination of complete intersections in a certain bordism group this was under certain restrictions carried out in tr the restrictions are if d d1 dr is the total degree of a complete intersection x n1 dr of complex dimension n then the assumption is that for all primes p with p pi1 n 1 the total degree d is divisible by p 2n 1 2pi1 1 theorem a two complete intersections x n

bandwidth efficient coded modulation with optimized linear partial response signals we study the design of optimal signals for bandwidth efficient linear coded modulation previous results show that for linear channels with intersymbol interference isi reduced search decoding algorithms have near maximum likelihood error performance but with much smaller complexity than the viterbi decoder consequently the controlled isi introduced by a lowpass filter can be practically used for bandwidth reduction such spectrum shaping filters comprise an explicit coded modulation for which we seek the optimal design we simultaneously constrain the bandwidth and maximize the minimum euclidean distance between signals we show that under quite general assumptions the problem can be formulated as a linear program and solved with well known efficient optimization techniques numerical results are presented and the performance of the optimal signals measured by their combined bandwidth and noise immunity is analyzed the new codes are comparable to set partition tcm trellis codes tests of an m algorithm decoder confirm this and show that the performance occurs at small detection complexity

a simple and effective precoding scheme for noise whitening on intersymbol interference channels a precoding scheme for noise whitening on intersymbol interference isi channels is presented this scheme is compatible with trellis coded modulation and unlike tomlinson precoding allows constellation shaping it can be used with almost any shaping scheme including the optimal svq shaping as opposed to trellis precoding which can only be used with trellis shaping the implementation complexity of this scheme is minimal only three times that of the noise prediction filter hence effective noise whitening can be achieved by using a high order predictor

on the minimum distance problem for faster than nyquist signaling the authors reconsider the problem of determining the minimum distance between output sequences of an ideal band limiting channel that are generated by uncoded binary sequences transmitted at a rate exceeding the nyquist rate for signaling rates up to about 25 faster than the nyquist rate it is shown that the minimum distance does not drop below the value which it would have in the ideal case wherein there is not intersymbol interference mathematically the problem is to decide if the best l sup 2 fourier approximation to the constant 1 on the interval sigma pi sigma pi 0 0 with coefficients restricted to be 1 or 0 occurs when all coefficients are zero this is shown to be optimal for 0 802

the homotopy type of the cobordism category the embedded cobordism category under study in this paper generalizes the category of conformal surfaces introduced by g segal in s2 in order to formalize the concept of field theories our main result identifies the homotopy type of the classifying space of the embedded d dimensional cobordism category for all d for d 2 our results lead to a new proof of the generalized mumford conjecture somewhat different in spirit from the original one presented in mw

non binary and precoded faster than nyquist signaling faster than nyquist ftn signaling is an important method of narrowband coding the concept is extended here to non binary signal constellations these are much more bandwidth efficient than binary ones a powerful method of finding the minimum distance for binary and non binary ftn is presented preceding ftn transmissions with short linear filters proves to be an effective way to gain distance a shannon limit to bit error rate is derived that applies for ftn tests of an m algorithm receiver are performed and compared to this limit

on symbol error probability bounds for isi like channels some issues with forney s upper and lower bounds 1972 for the symbol error probability in systems with memory e g intersymbol interference channels have been pointed out in the literature we expound on these issues for the upper bound we show that although the most commonly cited proofs are not logically consistent the bound is true for more general conditions the reasoning leading to the lower bound is shown to be flawed and in general to lead to invalid lower bounds we suggest a lower bound based on mazo s bound 1975 as an alternative

on the minimum length error event of minimum euclidean weight let eta denote the length of the shortest error event achieving the minimum detection distance of maximum likelihood signal detection for an impulse response having memory v a family of impulse responses where eta is of order v sup 2 is exhibited this in turn shows that some difficulty can arise in computing the minimum detection distance

rhoades type fixed point theorems for a pair of nonself mappings abstract using suitable conditions of weak commutativity we prove theorems for a pair of nonself mappings which generalize earlier results due to rhoades and assad et al some illustrative examples and applications are also discussed

optimal transmit filters for isi channels under channel shortening detection we consider channels affected by intersymbol interference with reduced complexity mutual information optimized channel shortening detection for such settings we optimize the transmit filter taking into consideration the reduced receiver complexity constraint as figure of merit we consider the achievable information rate of the entire system and with functional analysis we establish a general form of the optimal transmit filter which can then be optimized by standard numerical methods as a corollary to our main result we obtain some insight of the behavior of the standard waterfilling algorithm for intersymbol interference channels with only some minor changes the general form we derive can be applied to multiple input multiple output channels with intersymbol interference to illuminate the practical use of our results we provide applications of our theoretical results by deriving the optimal shaping pulse of a linear modulation transmitted over a bandlimited additive white gaussian noise channel which has possible applications in the faster than nyquist time packing technique

common fixed points of almost generalized contractive mappings in ordered metric spaces the existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature

cobordism categories and moduli spaces of odd dimensional manifolds abstract we prove that the stable moduli space of n 1 connected n parallelizable 2 n 1 dimensional manifolds is homology equivalent to an infinite loopspace for n 4 n 7 the main novel ingredient is a version of the cobordism category incorporating surgery data in the form of lagrangian subspaces

some common fixed point theorems for weakly compatible mappings abstract jungck s g jungck compatible mappings and common fixed points int j math math sci 9 1986 771 779 notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non self mappings in complete convex metric spaces we improve on the method of proof used by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 and ahmed and rhoades a ahmed b e rhoades some common fixed point theorems for compatible mappings indian j pure appl math 32 2001 1247 1254 and obtain generalization of some known results in particular a theorem by rhoades b e rhoades a fixed point theorem for non self set valued mappings int j math math sci 20 1997 9 12 is generalized and improved

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

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

multistream faster than nyquist signaling we extend mazo s concept of faster than nyquist ftn signaling to pulse trains that modulate a bank of subcarriers a method called two dimensional ftn signaling the signal processing is similar to orthogonal frequency division multiplex ofdm transmission but the subchannels are not orthogonal despite nonorthogonal pulses and subcarriers the method achieves the isolated pulse error performance it does so in as little as half the bandwidth of ordinary ofdm euclidean distance properties are investigated for schemes based on several basic pulses the best have gaussian shape an efficient distance calculation is given concatenations of ordinary codes and ftn are introduced the combination achieves the outer code gain in as little as half the bandwidth receivers must work in two dimensions and several iterative designs are proposed for ftn with outer convolutional coding

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

minimum distance analysis of a certain class of 2 d isi channels we perform a minimum distance analysis of a class of two dimensional intersymbol interference isi channels applicable to multitrack magnetic recording and orthogonal frequency division multiplex transmission systems exact minimum distance for a wide class of isi responses is derived the fundamental analytical technique is to transform the channel into an equivalent minimum phase channel the results improve upon the prior work of soljanin and georghiades

an extension of the simplex algorithm for semi infinite linear programming we present a primal method for the solution of the semi infinite linear programming problem with constraint index sets we begin with a detailed treatment of the case whens is a closed line interval in a characterization of the extreme points of the feasible set is given together with a purification algorithm which constructs an extreme point from any initial feasible solution the set of points ins where the constraints are active is crucial to the development we give in the non degenerate case the descent step for the new algorithm takes one of two forms either an active point is dropped or an active point is perturbed to the left or right we also discuss the form of the algorithm when the extreme point solution is degenerate and in the general case when the constraint index set lies in p the method has associated with it some numerical difficulties which are at present unresolved hence it is primarily of interest in the theoretical context of infinite dimensional extensions of the simplex algorithm

on computing the minimum distance for faster than nyquist signaling the degradation suffered when pulses satisfying the nyquist criterion are used to transmit binary data at a rate faster than the nyquist rate over the ideal band limited brick wall channel is studied the minimum distance between received signals is used as a performance criterion it is well known that when nyquist pulses i e pulses satisfying the nyquist criterion are sent at the nyquist rate the minimum distance between signal points is the same as the pulse energy the main result is to show that the minimum distance between received signals is the same as the pulse energy for rates of transmission about 25 beyond the nyquist rate which is the best possible result in fact one can even identify the precise error event and signaling rate that causes the minimum distance to be no longer equal to the pulse energy the mathematical formulation of the problem is analyzed

common fixed point theorems for non self mappings in metric spaces of hyperbolic type in this paper the concept of a pair of non linear contraction type mappings in a metric space of hyperbolic type is introduced and the conditions guaranteeing the existence of a common fixed point for such non linear contractions are established presented results generalize and improve some of the known results an example is constructed to show that our theorems are genuine generalizations of the main theorems of assad ciric khan et al rhoades and imdad and kumar one of the possible applications of our results is also presented

limited search trellis decoding of convolutional codes the least storage and node computation required by a breadth first tree or trellis decoder that corrects t errors over the binary symmetric channels is calculated breadth first decoders work with code paths of the same length without backtracking the viterbi algorithm is an exhaustive trellis decoder of this type other schemes look at a subset of the tree or trellis paths for random tree codes theorems about the asymptotic number of paths required and their depth are proved for concrete convolutional codes the worst case storage for t error sequences is measured in both cases the optimal decoder storage has the same simple dependence on t the m algorithm and algorithms proposed by g j foschini ibid vol it 23 p 605 9 sept 1977 and by s j simmons phd diss queens univ kingston ont canada are optimal or nearly so they are all far more efficient than the viterbi algorithm

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

on the complexity of bounded distance decoding for the awgn channel earlier work has derived the storage complexity of the bounded distance decoder bdd for binary channel convolutional codes we extend this work to the gaussian noise channel and to partial response codes we show that the storage requirement spl sim 2 sup 1 r 1 sup t paths for rate r convolutional codes over the binary channel becomes spl sim 2 sup 2rt over the gaussian channel where the decoder must correct t errors thus convolutional coding over the gaussian channel is not only 3 db more energy efficient but its decoding is simpler as well next we estimate the path storage for partial response codes i e real number convolutional codes over the gaussian channel the growth rate depends primarily on the bandwidth of the code a new optimization procedure is devised to measure the maximum storage requirement in gaussian noise for these two code types an analysis based on difference equations predicts the asymptotic storage growth for partial response codes

geometric transfer and the homotopy type of the automorphism groups of a manifold introduction for m a compact manifold with or without boundary in one of the categories diff pl or top we denote by a m the semisimplicial ss group of automorphisms of m i e the group of diffeomorphisms pl homeomorphisms or homeomorphisms resp in this paper we describe in the stability range and localized away from two the homotopy structure of a m we do this in terms of a m the ss group of block automorphisms whose homotopy structure is a sophisticated formulation of surgery theory abk and some new homotopy functors 5 theorem c the functors 5 and 5 l here considered have already been studied in the pl category by hatcher h from a different point of view the present geometric description is appropriate to the description of the homotopy structure of a m and enables us to produce a natural map b sc x 5 x from the associative monoid of simple homotopy equivalence of x to 5 x which will be important for our study besides the geometric topology results blr two ideas partially developed in bli are basic the first is the transfer map and stability for concordances described in the pl context by hatcher and in the differentiable context in bli the second is the splitting of a z 1 weak commutative topological group with involution as a product up to homotopy of two pieces the symmetric respectively antisymmetric parts applied to our situation those parts manifest very different behavior the results of this paper have been sketched by the first author in the survey paper b there is an overlap between some but not all results of a and results of hatcher h2 published in the same volume as b the results of this paper are stated in the next section statement of results and the proofs are given in subsequent sections we continue this section with a description of the notations used

a new description of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four his method is to specify an underlying convolutional code and a rule mapping by set partitioning that maps the output of this code onto a fixed signal constallation a new description of a trellis code is given that combines these two steps into one the new description is analytic rather than graphical many practical codes can be described very simply and strict bounds on performance can be obtained a method for differential encoding trellis codes is presented that was suggested by the authors representation

asymptotic error performance of modulation codes in the presence of severe intersymbol interference the minimum distance and hence the asymptotic error probability of trellis modulation codes that have been subjected to severe channel filtering are evaluated a general algorithm is proposed for this purpose and applied to one class of coded modulations using a frequency domain interpretation of the euclidean distance it is shown that under extreme channel band limitations the error event that causes the minimum distance is characterized by a spectral null at dc numerical results show that for filtered continuous phase modulation codes decreasing the modulation index or smoothing the frequency pulse does not improve the error performance for some of these modulations channel filtering can actually improve the minimum distance bandpass and low pass filtering are contrasted the numerical results are explained by power spectrum considerations

homological stability for moduli spaces of high dimensional manifolds i s galatius was partially supported by nsf grants dms 1105058 and dms 1405001 the european research council erc under the european union s horizon 2020 research and innovation pro gramme grant agreement no 682922 as well as the danish national research foundation through the centre for symmetry and deformation dnrf92 and erc 682992 o randal williams was partially supported by the herchel smith fund and epsrc grant ep m027783 1

pair of non self mappings and common fixed points we study quasi contraction type non self mappings on takahashi convex metric spaces and common fixed point theorems for a pair of maps results generalizing and unifying fixed point theorems of imdad and kumar das and naik jungck ciric ume khan and pathak and ciric are established

multi valued non self mappings on convex metric spaces abstract in this paper we prove common fixed point theorems for a pair of multi valued non self mappings in metrically convex metric spaces our results generalize and extend both theorems of itoh comment math univ carolin 18 1977 247 and khan pacific j math 95 1981 337 the theorem of assad boll un math ital 4 1973 1 the theorem of rhoades comment math univ carolin 37 1996 401 and the main theorem of assad and kirk pacific j math 43 1972 535

some topological properties of kahler manifolds and homogeneous spaces on donne des calculs explicites des groupes d homotopie rationnels du monoide topologique de toutes les auto equivalences d homotopie d une variete de kahler homogene

reduced complexity sequence detection for nonminimum phase intersymbol interference channels controlled intersymbol interference may be used to design bandwidth efficient coded modulation schemes the performance of the optimum receiver depends only on the free distance of the code and is independent of its phase large reductions in receiver complexity are obtained by using reduced search detection techniques like the m algorithm ma however we show that ma detector performance depends critically on phase and is characterized by the partial energy of the encoder or channel the minimum phase encoder needs by far the least detector searching we propose modifications to the receiver so that the reduced search can operate on all nonminimum phase channels at this same low complexity

maximum likelihood sequence detection for intersymbol interference channels a new upper bound on error probability maximum likelihood sequence detection of digital signaling subject to intersymbol interference and additive white gaussian noise is considered a new approach to the error probability analysis results in an upper bound which is tighter than the forney bound in addition in the case of infinite length intersymbol interference a locally convergent bound is shown to hold under fairly general assumptions on the signal autocorrelation

fixed point theorem for two non self mappings in cone metric spaces in this paper we extend a fixed point theorem of imdad and kumar for a pair of non self maps to non normal cone spaces

binary symbol recovery via ell_ infty minimization in faster than nyquist signaling systems the issue of binary symbol detection in faster than nyquist signaling systems also known as overcomplete frame modulated digital transmission systems is addressed in this paper through convex relaxation the original combinatorial optimization problem is transformed to an l minimization problem following this idea we further propose lp approximation algorithms to efficiently tackle such a convex optimization problem for noiseless case the recoverability of l minimization is analyzed it is shown that the binary symbol vector b can be completely recovered via l minimization if and only if there is a vector in the row space of the transmission matrix located in the same quadrant as b otherwise complete reconstruction via l minimization is hopeless at the same time we give an upper bound to the reconstruction probability for noisy case the reconstruction probability is analyzed via the probability distribution function of indefinite quadratic form in gaussian vectors numerical results are provided to study the detection performance of l minimization it is shown that compared with semidefinite programming algorithm and linear minimum mean squared error lmmse method the proposed l minimization detection achieves a better performance complexity trade off

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

stable moduli spaces of high dimensional manifolds we prove an analogue of the madsen weiss theorem for high dimensional manifolds in particular we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of sn sn in the limit g to infty rationally it is a polynomial ring in certain explicit generators giving a high dimensional analogue of mumford s conjecture

homological stability and stable moduli of flat manifold bundles abstract we prove that the group homology of the diffeomorphism group of g s n s n int d 2 n as a discrete group is independent of g in a range provided that n 2 this answers the high dimensional version of a question posed by morita about surface diffeomorphism groups made discrete the stable homology is isomorphic to the homology of a certain infinite loop space related to the haefliger s classifying space of foliations one geometric consequence of this description of the stable homology is a splitting theorem that implies certain classes called generalized mumford morita miller classes lift to a secondary r z invariants for flat g s n s n bundles provided g 0

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

the stable mapping class group and q ℂp in t2 it was shown that the classifying space of the stable mapping class groups after plus construction b has an infinite loop space structure this result and the tools developed in bm to analyse transfer maps are used here to show the following splitting theorem let p p e 0 e p 2 be the adams splitting of the p completed suspension spectrum of p then for some infinite loop space w p b p e 0 e p 3 w p where e i denotes the infinite loop space associated to the spectrum e i the homology of e i is known and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group this splitting also detects all the miller morita mumford classes our results suggest a homotopy theoretic refinement of the mumford conjecture the above p adic splitting uses a certain infinite loop map b p 1 that induces an isomorphims in rational cohomology precisely if the mumford conjecture is true we suggest that might be a homotopy equivalence

iterative construction of fixed points of nonself mappings in banach spaces the purpose of this paper is to study the iterative methods for constructing fixed points of nonself mappings in banach spaces the concept of the class of asymptotically q g weakly contractive nonself mappings is introduced and a new iterative algorithm for finding fixed points of this class of mappings is studied several strong convergence results on this algorithm are established under different conditions

the effect of signaling rate on information rate for single carrier linear transmission systems we consider the effect of signaling rate baud rate on the information rate of single carrier linear transmission systems with gaussian inputs several different communication scenarios are investigated correlated or uncorrelated symbols a fixed modulation pulse or a modulation pulse varying with the signaling rate and frequency selective or flat channels for uncorrelated symbols we show that the information rate grows monotonically with signaling rate for some cases while it can in fact decrease in other cases sufficient conditions on the modulation pulse and the channel impulse response are derived so that the information rate is increasing with increased signaling rate especially these conditions give criterias for when non orthogonal signaling is beneficial compared to orthogonal signaling in the case of flat fading for modulation pulses varying with the signaling rate it is shown that there are pulses for which the information rate is non decreasing with increasing signaling rate when correlation between symbols is allowed we show that one can guarantee increasing information rate with increased signaling rate no matter the pulse channel shape except for some hypothetical special cases by signaling with an snr above a certain finite threshold

abelian quotients of mapping class groups of highly connected manifolds we compute the abelianisations of the mapping class groups of the manifolds w g 2n g s n times s n for n ge 3 and g ge 5 the answer is a direct sum of two parts the first part arises from the action of the mapping class group on the middle homology and takes values in the abelianisation of the automorphism group of the middle homology the second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable j homomorphism we relate its calculation to a purely homotopy theoretic problem

exploiting faster than nyquist signaling faster than nyquist signaling introduces intersymbol interference but increases the bit rate while preserving the signaling bandwidth for sinc pulses it has been established that with a small increase in the signaling rate beyond the nyquist rate there is no reduction in the minimum euclidean distance for binary signaling we generalize these observations to the family of raised cosine pulses the structure of the error events that reduce the minimum distance is examined and constrained coding ideas are suggested that theoretically allow even faster signaling then we propose ways of achieving these gains practically by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding turbo equalization

practically realizable digital transmission significantly below the nyquist bandwidth proposes a practically realizable digital signaling scheme that requires a bandwidth significantly below the nyquist limit and at the same time achieves the same asymptotic performance as memoryless pam a five step iterative procedure for constructing such schemes is presented and examples that occupy down to about 60 percent of the nyquist bandwidth are demonstrated using this simple procedure practical receiver structures are also briefly discussed

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

time frequency packing for linear modulations spectral efficiency and practical detection schemes we investigate the spectral efficiency achievable by a low complexity symbol by symbol receiver when linear modulations based on the superposition of uniformly time and frequency shifted replicas of a base pulse are employed although orthogonal signaling with gaussian inputs achieves capacity on the additive white gaussian noise channel we show that when finite order constellations are employed by giving up the orthogonality condition thus accepting interference among adjacent signals we can considerably improve the performance even when a symbol by symbol receiver is used we also optimize the spacing between adjacent signals to maximize the achievable spectral efficiency moreover we propose a more involved transmission scheme consisting of the superposition of two independent signals with suitable power allocation and a two stage receiver showing that it allows a further increase of the spectral efficiency finally we show that a more involved equalization algorithm based on soft interference cancellation allows to achieve an excellent bit error rate performance even when error correcting codes designed for the gaussian noise limited channel are employed and thus does not require a complete redesign of the coding scheme

an upper bound for the pseudoisotopy stable range we prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than 2n 2 in order to do so we define new characteristic classes for block bundles extending our earlier work with ebert and prove their non triviality we also explain how similar methods show that mathrm top 2n mathrm o 2n is rationally 4n 5 connected