quasi multiplicativity of typical cocycles we show that typical in the sense of bonatti and viana ergod theory dyn syst 24 5 1295 1330 2004 and avila and viana port math 64 311 376 2007 holder and fiber bunched text gl d mathbb r valued cocycles over subshifts of finite type are uniformly quasi multiplicative with respect to all singular value potentials we prove the continuity of the singular value pressure and its corresponding necessarily unique equilibrium state for such cocycles and apply this result to repellers moreover we show that the pointwise lyapunov spectrum is closed and convex and establish partial multifractal analysis on the level sets of pointwise lyapunov exponents for such cocycles

renormalization theory of self avoiding walks which cross a square the renormalization group theory is used to calculate the critical behaviour of selfwoiding walks which cross a square this problem which has been proposed recently is especially well suited for a renormalization group analysis the fixed endpoint diagonal span trademark of the square crossing walks leads naturally to a well defined renormaliz ation scheme unlike other finite lattice renormalization schemes for self avoiding walks this square crossing renormalization is exact in the sense that the finite lattice square is uniquely defined the spanning rule is unambiguous and the end to end correlations are exactly preserved the results for the critical point are in excellent agreement with series analysis estimates and support a conjecture on its exact value

self avoiding walks that cross a square the authors consider self avoiding walks that traverse an l l square lattice whittington and guttmann 1990 have proved the existence of a phase transition in the infinite l limit at a critical value of the step fugacity they make several finite size scaling predictions for the critical region using the relation between self avoiding walks and the n vector model of magnetism adsorbing as well as nonadsorbing boundaries are considered the predictions are in good agreement with numerical data for l or 9

self avoiding walk on critical percolation cluster abstract we consider the asymptotic behavior of long self avoiding walks and chains on critical percolation clusters pointing out various potentially important but often neglected subtle features of the problem we also present the results of our exact enumeration for a three dimensional lattice which address some of these points

two dimensional lattice vesicles and polygons we consider a lattice model of two dimensional vesicles in which the boundary of the vesicle is the perimeter of a self avoiding polygon embeddable in the square lattice with fixed boundary length m we incorporate an osmotic pressure difference by associating a fugacity with the area enclosed by the polygon we derive rigorous results concerning the behaviour of the associated free energy and the form of the phase diagram by deriving exact values ofthe numbers of polygons with m edges which enclose area n and analysing the resulting series we obtain the free energy the phase boundary and various scaling exponents and amplitudes numerically

diversity order gain for narrow band multiuser communications with pre combining group detection in narrow band multiuser communication systems with fading diversity it is shown that pre combining group detection can bridge the diversity order gap in performance between the optimum and linear detectors for a system with m diversity channels the group detector diversity order is m g where g is the interfering group size a design parameter group detection thus provides a more substantial improvement in performance in narrow band channels over linear detection than in wide band channels in which the diversity orders of the optimal and linear detectors are equal here the complexity of the receiver is a new parameter which in addition to the number of antennas can be used to control the diversity order exact formulas for the pairwise error probabilities and bounds for the bit error rate are obtained and numerical results are shown

adsorption and collapse of self avoiding walks in three dimensions a monte carlo study we consider self avoiding walks on the simple cubic lattice with a unit degree vertex at the origin and confined to the half space in addition the walks interact with the plane z 0 and have a vertex vertex interaction within the walk so that the walk can adsorb at the surface z 0 and also undergo collapse we investigate the interaction between collapse and adsorption using monte carlo methods and explore the form of the phase diagram

equilibrium states for factor maps between subshifts abstract let x y be a factor map where x x and y y are subshifts over finite alphabets assume that x satisfies weak specification let a a 1 a 2 r 2 with a 1 0 and a 2 0 let f be a continuous function on x with sufficient regularity holder continuity for instance we show that there is a unique shift invariant measure on x that maximizes f d a 1 h x a 2 h 1 y in particular taking f 0 we see that there is a unique invariant measure on x that maximizes the weighted entropy a 1 h x a 2 h 1 y which answers an open question raised by gatzouras and peres 1996 in 15 an extension is given to high dimensional cases as an application we show that for each compact invariant set k on the k torus under a diagonal endomorphism if the symbolic coding of k satisfies weak specification then there is a unique invariant measure supported on k so that dim h dim h k

statistical precoding with decision feedback equalization over a correlated mimo channel the decision feedback df transceiver combining linear precoding and df equalization can establish point to point communication over a wireless multiple input multiple output channel matching the df transceiver design parameters to the channel characteristics can improve system performance but requires channel knowledge we consider the fast fading channel scenario with a receiver capable of tracking the channel state variations accurately while the transmitter only has long term channel distribution information the receiver design problem given channel state information is well studied in the literature we focus on transmitter optimization which amounts to designing a statistical precoder to assist the channel tailored df equalizer we develop a design framework that encompasses a wide range of performance metrics common cost functions for precoder optimization are analyzed thereby identifying a structure of typical cost functions transmitter design is approached for typical cost functions in general and we derive a precoder design formulation as a convex optimization problem two important subclasses of cost functions are considered in more detail first we explore a symmetry of df transceivers with a uniform subchannel rate allocation and derive a simplified convex optimization problem which can be efficiently solved even as system dimensions grow second we explore the tractability of a certain class of mean square error based cost functions and solve the transmitter design problem with a simple algorithm that identifies the convex hull of a set of points in r2 the behavior of df transceivers with optimal precoders is investigated by numerical means

group detection for synchronous gaussian code division multiple access channels the concept of group detection is introduced to address the design of suboptimum multiuser detectors for code division multiple access cdma channels a group detection scheme consists of a bank of p group detectors one each for detecting the information symbols of users in each group of a p group partition of the k simultaneously transmitting users in a parallel group detection scheme these group detectors operate independently whereas in a sequential scheme each group detector uses the decisions of the previous group detectors to successively cancel the interference from those users group detectors based on the generalized likelihood ratio test glrt are obtained for the synchronous gaussian cdma channel the complexity of these detectors is exponential in the group size whereas that of the optimum detector is exponential in k since the partition of users is a design parameter group sizes can be chosen to satisfy a wide range of complexity constraints a key performance result is that the glrt group detectors are optimally group near far resistant furthermore upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived these bounds reveal that the sequential group detectors can under certain conditions perform as well as glrt group detectors of much larger group sizes group detection provides a unifying approach to multiuser detection when the users are partitioned into k single user groups the glrt a modified form of glrt and the sequential group detectors reduce to previously proposed suboptimal detectors namely the decorrelator the two stage detector and the decorrelating decision feedback detector respectively for the other nontrivial partitions the group detectors are new and have a performance that is commensurate with their complexity

self avoiding walks which cross a square the authors consider self avoiding walks on the square lattice which are confined to lie in or on the boundary of a square with vertices at 0 0 0 l l 0 and l l they ask for the number of such walks which begin at the origin and end at the vertex l l especially in the large l limit similarly they ask for the mean number of steps in such walks as a function of l at fixed l the authors also associate a fugacity with the number of steps of the walk and ask how the system behaves as a function of this fugacity they provide some rigorous results in particular proving that there is a phase transition at some particular value of the fugacity and supplement these with the analysis of series data for the problem

composite models of polygons a composite polygon is composed of a lattice polygon in the square lattice which contains in its interior an internal structure which may also be a lattice polygon or a lattice tree or a lattice animal or a lattice disc or a collection of these the properties of composite polygons are considered in this manuscript in particular i shall consider the growth constants and generating functions of these models as well as the statistical mechanics of interacting models of composite polygons it is shown that there is an adsorption transition of the internal structure on the containing polygon and a transition which corresponds to the inflation of the containing polygon by the internal structure

optimal detection ordering for coded v blast optimum ordering strategies for the coded vertical bell labs layered space time v blast architecture with capacity achieving temporal codes on each stream are analytically studied including 4 different power rate allocation strategies among data streams compact closed form solutions are obtained for the case of zero forcing zf v blast with two transmit antennas and necessary optimality conditions are found for the general case the optimal rate allocation is shown to have a major impact stronger streams are detected last while the optimal power allocation does not alter the original foschini ordering stronger streams are detected first sufficient conditions for the optimality of the greedy ordering are established it is optimal for the zf v blast under an optimal rate allocation with two transmit antennas at any snr and with any number of antennas in the low and high snr regimes it satisfies the necessary optimality conditions for larger systems at any snr and is nearly optimal in many cases an snr gain of ordering is introduced and studied including closed form expressions as well as lower and upper bounds and the conditions for their achievability for the minimum mean square error mmse v blast under an optimal rate allocation any ordering is shown to deliver the same system capacity all the results also apply to a multiple access channel with the successive interference cancelation receiver

asymptotics of knotted lattice polygons we use monte carlo methods to investigate the asymptotic behaviour of the number and mean square radius of gyration of polygons in the simple cubic lattice with fixed knot type let be the number of n edge polygons of a fixed knot type in the cubic lattice and let be the mean square radius of gyration of all the polygons counted by if we assume that where is the growth constant of polygons of knot type and is the entropic exponent of polygons of knot type then our numerical data are consistent with the relation where is the unknot and is the number of prime factors of the knot if we assume that then our data are consistent with both and being independent of these results support the claims made in janse van rensburg and whittington 1991a 24 3935 and orlandini et al 1996 29 l299 1998 topology and geometry in polymer science ima volumes in mathematics and its applications berlin springer

critical behaviour of self avoiding walks that cross a square consider the set of all self avoiding walks in the square lattice which start at 0 0 end at l l and are entirely contained in the square 0 l 0 l associate a fugacity x with each step of the walk whittington and guttmann 1990 showed that the dominant walks have o l steps when x is small and o l2 steps when x is large and they conjectured that there is a single transition point at x mu 1 where mu is the inverse of the connective constant for unconstrained self avoiding walks we present a rigorous proof of this conjecture and its analogue in higher dimensions we also discuss what can be said rigorously about two scaling exponents associated with this phase transition and compare this with analogous results that have been obtained exactly and rigorously on the discrete sierpinski gasket by hattori hattori and kusuoka 1990

optimization of ldpc codes for modulation and detection in layered multi antenna architectures in this paper we first perform the density evolution of ldpc codes in layered multi antenna architectures using bit interleaved coded modulation and detection based on successive decoding and interference cancellation the noise thresholds of ldpc codes are shown to be achieved within 1 2 db of the capacity for these architectures we then present a rate allocation method which optimizes the performance of a layered architecture and find good degree distributions for ldpc codes with the rates allocated by our method simulation results show that the performance for an optimized layered architecture is better by 4 db than that for the layered architecture using ldpc codes with the same rate in all layers

on the critical behaviour of self avoiding walks for pt i see ibid vol 22 p 1839 1989 for the self avoiding walk problem the coefficients of the chain generating function and of the generating function for the sum of square end to end distances have been extended to 20 terms for the triangular lattice to 27 terms for the diamond lattice to 21 terms for the simple cubic lattice and to 16 terms for the bcc lattice precise estimates of the critical points are obtained and for the exponents we find that gamma 1 161 or 0 002 and nu 0 592 or 0 003 encompasses all the three dimensional lattice data

asymptotic performance analysis of coded blast architectures with statistical rate and power allocations in this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in bell labs layered space time blast architectures employing successive decoding and interference cancellation we then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of blast architectures since the methods are developed by using ergodic capacity and outage capacity functions of the layers the allocated rates and powers depend only on a given channel statistic finally we prove that the rate allocation yields a better asymptotic performance than the power allocation numerical results show that blast architectures with the rate and power allocation perform better by 4 db and 3 db respectively than a blast architecture with the same rate and power in all layers

self avoiding walks interacting with a surface discusses two models of polymer adsorption in one model a self avoiding walk on a d dimensional lattice interacts with a d 1 dimensional hyperplane in the other model this walk must also lie in or on one side of this hyperplane both models exhibit non analytic behaviour corresponding to a phase transition but these phase transitions do not occur at the same point the authors give numerical estimates of the locations of these transitions

interacting self avoiding walks and polygons in three dimensions self interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the point we consider self avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon we prove that these walks and polygons have the same limiting free energy if the interactions between nearest neighbour vertices are repulsive the attractive interaction regime is investigated using monte carlo methods and we find evidence that the limiting free energies are also equal here in particular this means that these models have the same point in the asymptotic limit the dimensions and shapes of walks and polygons are also examined as a function of the interaction strength

gibbs measures for fibred systems abstract we consider a topological dynamical system t y y on a metric space y which forms a fibre bundle over another dynamical system if t is fibrewise expanding and exact along fibres and if is a holder continuous function we prove the existence of a system of conditional measures called a family of gibbs measures where the jacobian is determined by this theorem reduces to ruelle s perron frobenius theorem when the base of the fibred system consists of a single point the method of proof does not use any form of symbolic representation we also study continuity properties of a family of gibbs measures over the base and give applications to the equilibrium theory of higher dimensional complex dynamics

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

on optimum power allocation for the v blast a unified analytical framework for optimum power allocation in the unordered v blast algorithm and its comparative performance analysis are presented compact closed form approximations for the optimum power allocation are derived based on average total and block error rates the choice of the criterion has little impact on the power allocation and overall the optimum strategy is to allocate more power to lower step transmitters and less to higher ones high snr approximations for optimized average block and total error rates are given the snr gain of optimization is rigorously defined and studied using analytical tools including lower and upper bounds high and low snr approximations the gain is upper bounded by the number of transmit antennas for any modulation format and type of fading channel while the average optimization is less complex than the instantaneous one its performance is almost as good at high snr a measure of robustness of the optimized algorithm is introduced and evaluated the optimized algorithm is shown to be robust to perturbations in individual and total transmit powers based on the algorithm robustness a pre set power allocation is suggested as a low complexity alternative to the other optimization strategies which exhibits only a minor loss in performance over the practical snr range

the hausdorff and dynamical dimensions of self affine sponges a dimension gap result we construct a self affine sponge in mathbb r 3 whose dynamical dimension i e the supremum of the hausdorff dimensions of its invariant measures is strictly less than its hausdorff dimension this resolves a long standing open problem in the dimension theory of dynamical systems namely whether every expanding repeller has an ergodic invariant measure of full hausdorff dimension more generally we compute the hausdorff and dynamical dimensions of a large class of self affine sponges a problem that previous techniques could only solve in two dimensions the hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge implying that sponges with a dimension gap represent a nonempty open subset of the parameter space

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

analysis on the diversity multiplexing tradeoff for ordered mimo sic receivers the diversity multiplexing tradeoff for multiple input multiple output mimo point to point channels and multiple access channels were first proposed and studied by zheng and tse recently while the optimal tradeoff curves for mimo channels have been explicitly explored those corresponding to some suboptimal and practical mimo schemes are still open one such important problem is the diversity multiplexing tradeoff for a v blast type system employing ordered successive interference cancellation sic receivers with zero forcing zf or minimum mean square error mmse processing at each stage in this paper we take a novel geometrical approach and rigorously verify that under general settings the optimal ordering rule for a v blast sic receiver will not improve its performance regarding diversity multiplexing tradeoff in point to point channels the same geometrical tool is then applied to mimo spatial division multiple access channels leading to some first results in this area particularly we reveal that when the rates of data streams are fixed i e zero spatial multiplexing gain the diversity order is not improved by user ordering

the error probability of the fixed complexity sphere decoder the fixed complexity sphere decoder fsd has been previously proposed for multiple input multiple output mimo detection in order to overcome the two main drawbacks of the sphere decoder sd namely its variable complexity and its sequential structure although the fsd has shown remarkable quasi maximum likelihood ml performance and has resulted in a highly optimized real time implementation no analytical study of its performance existed for an arbitrary mimo system herein the error probability of the fsd is analyzed proving that it achieves the same diversity as the maximum likelihood detector mld independent of the constellation used in addition it can also asymptotically yield ml performance in the high signal to noise ratio snr regime those two results together with its fixed complexity make the fsd a very promising algorithm for uncoded mimo detection

new approach for error compensation in coded v blast ofdm systems in this paper we investigate coded layered space time architectures for frequency selective fading multiple input multiple output orthogonal frequency division multiplexing ofdm channels by computing outage capacity formulas we will show that the capacity of the vertical bell labs layered space time v blast architecture can closely approach the shannon capacity in the frequency selective ofdm environment motivated by the capacity analysis we propose pragmatic approaches which preserve the optimality of the layered space time concept we present methods to prevent the error propagation from catastrophically affecting the signal detection in subsequent layers first we start with a comprehensive signal modeling which includes error propagation we derive an improved signal detector and describe the optimal soft bit log likelihood ratio value computation method by taking decision errors into account for soft input channel decoding then to further enhance the v blast performance we show that cancellation using decoded decisions from previous layers makes the decision errors almost completely disappear so that the layered space time architecture can approach the attainable channel capacity finally simulations confirm that the proposed schemes show a significant performance improvement over the conventional methods

punctured discs on the square lattice the authors study the perimeter length of self avoiding surfaces on the square lattice they prove that surfaces with area n containing h boundary components have a mean perimeter length of order n they arrive at this result by studying the incidence of 4 cycles in two dimensional site animals

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

multifractal formalism for almost all self affine measures we conduct the multifractal analysis of self affine measures for almost all family of affine maps besides partially extending falconer s formula of lq spectrum outside the range 1 q 2 the multifractal formalism is also partially verified

adsorption and collapse of self avoiding walks at a defect plane we consider self avoiding walks and polygons on the simple cubic lattice with a vertex vertex interaction i e a contact interaction which also interact with a defect plane z 0 the walks or polygons can undergo a collapse transition and can also adsorb at the defect plane for the polygon case we prove that the limiting free energy exists and show that there is an adsorption transition for each finite value of the vertex vertex interaction we use monte carlo methods to investigate the form of the phase diagram for the walk problem

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

infinite to one codes and markov measures we study the structure of infinite to one continuous codes between subshifts of finite type and the behaviour of markov measures under such codes we show that if an infinite to one code lifts one markov measure to a markov measure then it lifts each markov measure to uncountably many markov measures and the fibre over each markov measure is isomorphic to any other fibre calling such a code markovian we characterize markovian codes through pressure we show that a simple condition on periodic points necessary for the existence of a code between two subshifts of finite type is sufficient to construct a markovian code several classes of markovian codes are studied in the process of proving illustrating and providing contrast to the main results a number of examples and counterexamples are given in particular we give a continuous code between two bernoulli shifts such that the defining vector of the image is not a clustering of the defining vector of the domain

knots in self avoiding walks discusses the existence of knots in random self avoiding walks on a lattice using kesten s 1963 pattern theorem it is shown that almost all sufficiently long self avoiding walks on the three dimensional simple cubic lattice contain a knot

an analysis of the mimo sdma channel with space time orthogonal and quasi orthogonal user transmissions and efficient successive cancellation decoders we consider space time transceiver architectures for space division multiple access sdma fading channels with simultaneous transmissions from multiple users each user has up to four transmit antennas and employs a space time orthogonal or a quasi orthogonal design as an inner code at the multiple antenna receiver efficient successive group interference cancellation strategies based on zero forcing or minimum mean square error mmse filtering are employed in some fixed or channel dependent order these strategies are efficient in the sense that they exploit the special structure of the inner codes to yield much higher diversity orders than would be otherwise possible while at the same time preserving what we call the decoupling property of the constituent inner codes which enables the use of low complexity outer encoders decoders for each user motivated by the special structure of the effective channel matrix induced by the inner codes we obtain several new distribution results on the qr and eigenvalue decompositions of certain structured random matrices these results are the key to a comprehensive performance analysis of the proposed multiuser transceiver architectures including the characterization of diversity multiplexing tradeoff dmt curves and exact per user bit error rates bers without making simplifying assumptions about error propagation

lyapunov spectrum of asymptotically sub additive potentials for general asymptotically sub additive potentials resp asymptotically additive potentials on general topological dynamical systems we establish some variational relations between the topological entropy of the level sets of lyapunov exponents measure theoretic entropies and topological pressures in this general situation most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub additive case and in the case that the entropy map is not upper semi continuous

exact transfer matrix enumeration and critical behaviour of self avoiding walks across finite strips we use a transfer matrix with suitably defined vertex weights to algebraically enumerate n step self avoiding walks confined to cross an l m rectangle on the square lattice we construct the exact generating functions for self avoiding walks from the south west to south east corners for l 1 2 3 4 5 and infinite height m corresponding to a half strip we also consider the number of n sided polygons rooted to the south west corner of the half strip and give a formulation to treat self avoiding walks across the full strip in each case the exact generating functions are ratios of polynomials in the step fugacity we investigate the singularity structure of the generating functions along with the finite size scaling in m of the singularity in the analogue of the heat capacity we find the critical exponents gamma 1 and gamma 2 for the half and open strip along with nu 1 2 these results are indicative of the one dimensional or gaussian nature of self avoiding walks in infinitely long but finitely wide strips

optimal precoder design for correlated mimo communication systems using zero forcing decision feedback equalization we consider the design of the precoder for a multi input multi output mimo communication system equipped with a decision feedback equalizer dfe receiver for such design problems perfect knowledge of the channel state information csi at both the transmitter and the receiver is usually required however in the environment of wireless communications it is often difficult to provide sufficiently timely and accurate feedback of csi from the receiver to the transmitter for such designs to be practically viable in this paper we consider the optimum design of a precoder for a wireless communication link having m transmitter antennas and n receiver antennas m n in which the channels are assumed to be flat fading and may be correlated we assume that full knowledge of csi is available at the receiver at the transmitter however only the first and second order statistics of the channels are available our goal here is to come up with an efficient design of the optimal precoder for such a mimo system by minimizing the average arithmetic mean squared error mse of zero forcing zf decision feedback detection subject to a constraint on the total transmitting power applying some of the properties of the matrix parameters this nonconvex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method the performance of the mimo system equipped with this optimum precoder and a zf dfe has also been found to be comparable and in some cases superior to that of v blast which necessitates optimally ordered successive interference cancellation based on the largest postdetection signal to noise ratio snr in terms of tradeoff between performance and implementation simplicity our new system is certainly an attractive alternative

an iterative extension of blast decoding algorithm for layered space time signals we propose an iterative extension of the bell laboratory layered space time blast algorithm and its variant vertical blast vblast a characteristic feature of the blast type algorithm is that symbol decisions with low reliability are fed back to decode other symbols both performance analysis based on gaussian approximation of residual interference and simulation results demonstrate that error propagation due to unreliable decision feedback can severely limit system performance the extended algorithm exploits inherent signal diversity in blast to mitigate residual interference thus overcoming the performance bottleneck due to error propagation it yields an impressive performance gain over blast in particular the extension of blast with zero forcing interference nulling admits a simple qr implementation and exhibits excellent performance with low complexity

monte carlo study of 3d vesicles abstract a model of vesicles on a cubic lattice is studied by monte carlo methods vesicles have spherical topology and are made of lattice plaquettes an osmotic pressure difference acts between interior and exterior results are given for critical properties in the deflated regime

mimo transceivers with decision feedback and bit loading theory and optimization this paper considers mimo transceivers with linear precoders and decision feedback equalizers dfes with bit allocation at the transmitter zero forcing zf is assumed considered first is the minimization of transmitted power for a given total bit rate and a specified set of error probabilities for the symbol streams the precoder and dfe matrices are optimized jointly with bit allocation it is shown that the generalized triangular decomposition gtd introduced by jiang li and hager offers an optimal family of solutions the optimal linear transceiver which has a linear equalizer rather than a dfe with optimal bit allocation is a member of this family this shows formally that under optimal bit allocation linear and dfe transceivers achieve the same minimum power the dfe transceiver using the geometric mean decomposition gmd is another member of this optimal family and is such that optimal bit allocation yields identical bits for all symbol streams no bit allocation is necessary when the specified error probabilities are identical for all streams the qr based system used in vblast is yet another member of the optimal family and is particularly well suited when limited feedback is allowed from receiver to transmitter two other optimization problems are then considered a minimization of power for specified set of bit rates and error probabilities the qos problem and b maximization of bit rate for fixed set of error probabilities and power it is shown in both cases that the gtd yields an optimal family of solutions

adsorption and collapse of self avoiding walks and polygons in three dimensions we consider self avoiding walks and polygons on the simple cubic lattice confined to the half space and interacting with the plane z 0 in addition there is a short range vertex vertex interaction in the walk or polygon which can lead to a collapse transition we explore the interaction between collapse and adsorption in these systems and discuss the form of the phase diagram key results include a proof of the existence of an adsorption transition for polygons for every value of the vertex vertex interaction a corresponding proof for walks when the vertex vertex interaction term is repulsive and a proof that if polygons exhibit a collapse transition then the phase boundary between the expanded and desorbed phase and the collapsed and desorbed phase must be a straight line

bending rigidity driven transition and crumpling point scaling of lattice vesicles the crumpling transition of three dimensional 3d lattice vesicles subject to a bending fugacity ensuremath rho exp ensuremath kappa mathit k mathit bt is investigated by monte carlo methods in a grand canonical framework by also exploiting conjectures suggested by previous rigorous results a critical regime with scaling behavior in the universality class of branched polymers is found to exist for ensuremath rho ensuremath gtrsim mathrm ensuremath rho mathit c for ensuremath rho mathrm ensuremath rho mathit c the vesicles undergo a first order transition that has remarkable similarities to the line of droplet singularities of inflated 2d vesicles at the crumpling point ensuremath rho mathrm ensuremath rho mathit c which has a tricritical character the average radius and the canonical partition function of vesicles with n plaquettes scale as mathit n ensuremath nu mathit c and mathit n mathrm ensuremath mathrm ensuremath theta mathit c respectively with ensuremath nu mathit c 0 4825 ifmmode pm else textpm fi 0 0015 and mathrm ensuremath theta mathit c 1 78 ifmmode pm else textpm fi 0 03 these exponents indicate a new class distinct from that of branched polymers for scaling at the crumpling point textcopyright 1996 the american physical society

analysis of decision feedback detection for mimo rayleigh fading channels and the optimization of power and rate allocations for an uncoded k transmit n receive antenna coherent narrow band communication system employing a decorrelating decision feedback detector d dfd the exact average over channel realizations joint error probability jep as well as the average per symbol error probabilities seps are derived without making any simplifying assumptions on error propagation it is proved that the diversity orders of the jep and the sep of every symbol is limited by error propagation to n k 1 based on our exact error probability analysis however we suggest an optimization of jep over nonnegative quadrature amplitude modulation qam constellation sizes rates and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment in fact the jep of such an optimized design has the much improved diversity order of n which is also the diversity order obtained through the optimum maximum likelihood ml detector moreover it is seen that these simple optimized designs can achieve a significant fraction of the spl epsi outage capacity even without outer codes it is also known but only through simulations that when the symbols are detected in certain channel realization dependent orders it is possible to improve substantially over fixed order detection in the case of the equal rate and equal power assignment we provide an analysis for a recently proposed channel dependent ordering rule and show that it does not provide an improvement of the diversity order of the jep beyond n k 1 another ordering rule that was proposed earlier to maximize the worst case post detection signal to noise ratio snr under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption while efficiently computable this ordering rule is seen to perform almost as well as the optimal channel dependent ordering rule that minimizes the conditional jep and hence the jep nevertheless a multiple input multiple output mimo system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower jep than that of the equal power equal rate system where transmitters are detected in a channel dependent order optimal or otherwise

relative pressure relative equilibrium states compensation functions and many to one codes between subshifts soit s x x t y y des applications continues d espaces metrisables compacts et soit x y une surjection continue avec t o s t o on etudie la notion de pression relative et on etudie certaines fonctions de pression relative maximales qui s associent aux etats d equilibres relatifs on relie ces idees a la notion de fonction de compensation et on montre qu une fonction de compensation existe toujours quand s et t sont des sous decalages

dimension theory of iterated function systems let si l i 1 be an iterated function system ifs on d with attractor k let denote the one sided full shift over the alphabet 1 l we define the projection entropy function h on the space of invariant measures on e associated with the coding map k and develop some basic ergodic properties about it this concept turns out to be crucial in the study of dimensional properties of invariant measures on k we show that for any conformal ifs respectively the direct product of finitely many conformal ifss without any separation condition the projection of an ergodic measure under is always exactly dimensional and its hausdorff dimension can be represented as the ratio of its projection entropy to its lyapunov exponent respectively the linear combination of projection entropies associated with several coding maps furthermore for any conformal ifs and certain affine ifss we prove a variational principle between the hausdorff dimension of the attractors and that of projections of ergodic measures 2008 wiley periodicals inc

structure of equilibrium states on self affine sets and strict monotonicity of affinity dimension a fundamental problem in the dimension theory of self affine sets is the construction of high dimensional measures which yield sharp lower bounds for the hausdorff dimension of the set a natural strategy for the construction of such high dimensional measures is to investigate measures of maximal lyapunov dimension these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by falconer whilst the existence of these equilibrium states has been well known for some years their structure has remained elusive particularly in dimensions higher than two in this article we give a complete description of the equilibrium states of the singular value function in the three dimensional case showing in particular that all such equilibrium states must be fully supported in higher dimensions we also give a new sufficient condition for the uniqueness of these equilibrium states as a corollary giving a solution to a folklore open question in dimension three we prove that for a typical self affine set in r 3 removing one of the affine maps which defines the set results in a strict reduction of the hausdorff dimension