iterative tree automata abstract the iterative tree automaton is introduced as a binary tree connected network with sequential input and output at the root of the tree the real and linear time computational power of this type of systolic system as a language acceptor is studied it is shown that for real time computations the arity of the tree is essential while this is not the case for linear time computations our main result is that every t n time nondeterministic turing machine can be simulated by an ita in deterministic ct n time a number of properties of real and linear time ita are proved

sub gaussian estimates of heat kernels on infinite graphs we prove that a two sided sub gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the green kernel admits a uniform polynomial decay

sequential machine characterizations of trellis and cellular automata and applications we look at a simple but general model of a systolic system called a trellis automaton ta a ta is equivalent in computational power to a one dimensional unbounded cellular automaton ca a model of parallel computation which has been studied extensively in the literature different varieties of ta s are equivalent to corresponding variations of ca s we present for the first time sequential machine characterizations of ta s ca s the sequential machines are useful and powerful tools for investigating properties of ta s ca s they ar easy to program because unlike the parallel models one does not have to deal with the problem of synchronization several applications are given in particular we prove a new speed up theorem which is stronger than what has previously been shown

inegalites de sobolev produit sur les groupes de lie nilpotents on generalise dans le cadre des groupes de lie nilpotents reels et connexes l inegalite classique due a gagliardo et nirenberg

random walks on discrete groups of polynomial volume growth let mu be a probability measure with finite support on a discrete group gamma of polynomial volume growth the main purpose of this paper is to study the asymptotic behavior of the convolution powers mu n of mu if mu is centered then we prove upper and lower gaussian estimates we prove a central limit theorem and we give a generalization of the berry esseen theorem these results also extend to noncentered probability measures we study the associated riesz transform operators the main tool is a parabolic harnack inequality for centered probability measures which is proved by using ideas from homogenization theory and by adapting the method of krylov and safonov this inequality implies that the positive mu harmonic functions are constant finally we give a characterization of the mu harmonic functions which grow polynomially

topological transformations as a tool in the design of systolic networks abstract we introduce the notion of computational network cn which is a general model of an arbitrary finite or infinite system of parallel synchronized processors systolic network our basic and very useful tools are topological transformations of the space time diagrams unrollings of computations on cn we show that the topological transformations on unrollings can be used to design systolic networks to give simple proofs of their correctness and to demonstrate the equivalence of different networks for example we usedthe transformation technique to give a concise proof of a strengthened version of leiserson s and saxe s retiming lemma and systolic conversion theorem as a practical application we show the correctness of a simple algorithm for distributed sorting on a systolic ring many other examples are given

systolic trellis automata stability decidability and complexity systolic trellis automata are models of hexagonally connected and triangularly shaped systolic arrays this paper studies the problems of stability decidability and complexity for them the original definition of systolic trellis automata requires that an input string is fed to a specific row of processors here it is shown that given a homogeneous trellis automaton we can construct an equivalent one stable or superstable which allows to feed the input string to any sufficiently long row of processors moreover some closure and decidability results for trellis automata are established and the computational complexity of languages accepted by trellis automata is investigated

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

the mimo arq channel diversity multiplexing delay tradeoff in this paper the fundamental performance tradeoff of the delay limited multiple input multiple output mimo automatic retransmission request arq channel is explored in particular we extend the diversity multiplexing tradeoff investigated by zheng and tse in standard delay limited mimo channels with coherent detection to the arq scenario we establish the three dimensional tradeoff between reliability i e diversity throughput i e multiplexing gain and delay i e maximum number of retransmissions this tradeoff quantifies the arq diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain interestingly arq diversity appears even in long term static channels where all the retransmissions take place in the same channel state furthermore by relaxing the input power constraint allowing variable power levels in different retransmissions we show that power control can be used to dramatically increase the diversity advantage our analysis reveals some important insights on the benefits of arq in slow fading mimo channels in particular we show that 1 allowing for a sufficiently large retransmission delay results in an almost flat diversity multiplexing tradeoff and hence renders operating at high multiplexing gain more advantageous 2 mimo arq channels quickly approach the ergodic limit when power control is employed finally we complement our information theoretic analysis with an incremental redundancy lattice space time ir last coding scheme which is shown through a random coding argument to achieve the optimal tradeoff s an integral component of the optimal ir last coding scheme is a list decoder based on the minimum mean square error mmse lattice decoding principle for joint error detection and correction throughout the paper our theoretical claims are validated by numerical results

coded modulation with mismatched csit over mimo block fading channels reliable communication over delay constrained multiple input multiple output mimo block fading channels with discrete inputs and mismatched imperfect channel state information at the transmitter csit is studied the csit mismatch is modeled as gaussian random variables whose variances decay as a power of the signal to noise ratio snr a special focus is placed on the large snr decay of the error and outage probabilities when power control with long term power constraints is used without explicitly characterizing the corresponding power allocation algorithms we derive the outage exponent as a function of the system parameters including the csit noise variance exponent and the exponent of the peak power constraint it is shown that csit even if noisy is always beneficial and leads to important gains in terms of exponents

efficient simulations of simple models of parallel computation by time bounded atms and space bounded tms abstract we present efficient time bounded atm and space bounded tm simulations of one way conglomerates owcs which are interconnected networks of finite state machines that allow only one way communication between adjacent nodes in particular we show that owcs with depth d n and operating in time t n can be simulated by atms in time o d n log t n and hence by a tm with the same amount of space this extends ruzzo s result that boolean circuits of depth d n can be simulated by o d n time bounded atms and refines gold schlager s result that two way conglomerates operating in t n time can be simulated by t n space bounded tms by exploiting the regularity of interconnections in some owcs we obtain more efficient space bounded tm simulations for example using the atm result a k dimensional one way mesh array of nk nodes would require n2 space on a tm such an array can run in cn time in the worst case we show that the 7space can be reduced to n 2 1 k

analysis of multiple antenna systems with finite rate feedback using high resolution quantization theory this paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple antenna systems with finite rate feedback inspired by the results of classical high resolution quantization theory the problem of finite rate quantized communication system is formulated as a general fixed rate vector quantization problem with side information available at the encoder or the quantizer but unavailable at the decoder the framework of the quantization problem is sufficiently general to include quantization schemes with general non mean squared distortion functions and constrained source vectors asymptotic distortion analysis of the proposed general quantization problem is provided by extending the vector version of the bennett s integral specifically tight lower and upper bounds of the average asymptotic distortion are proposed sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed rate quantization problems the proposed general methodology provides a powerful analytical tool to study a wide range of finite rate feedback systems to illustrate the utility of the framework we consider the analysis of a finite rate feedback multiple input single output miso beamforming system over independent and identically distributed i i d rayleigh flat fading channels numerical and simulation results are presented that further confirm the accuracy of the analytical results

isoperimetric inequalities and markov chains soit a i j i j n la matrice stochastique d une chaine de markov reversible sur n 1 2 soit n 2 tel que f r c f d f c 0 n ou r 2n n 2 ou c 0 est independant de f et ou r indique la norme dans l r n d pour la mesure i i alors on a sup i j j 1 a i j 0 n 2

nonlinear damped wave equations for the sub laplacian on the heisenberg group and for rockland operators on graded lie groups abstract in this paper we study the cauchy problem for the semilinear damped wave equation for the sub laplacian on the heisenberg group in the case of the positive mass we show the global in time well posedness for small data for power like nonlinearities we also obtain similar well posedness results for the wave equations for rockland operators on general graded lie groups in particular this includes higher order operators on r n and on the heisenberg group such as powers of the laplacian or the sub laplacian in addition we establish a new family of gagliardo nirenberg inequalities on a graded lie groups that play a crucial role in the proof but which are also of interest on their own if g is a graded lie group of homogeneous dimension q and a 0 1 r q a and 1 p q r q q a r then we have the following gagliardo nirenberg type inequality u l q g u l a r g s u l p g 1 s for s 1 p 1 q a q 1 p 1 r 1 0 1 provided that a q 1 p 1 r 0 where l a r is the homogeneous sobolev space of order a over l r if a q 1 p 1 r 0 we have p q r q q a r and then the above inequality holds for any 0 s 1

triangle cellular automata this paper introduces a special class of cellular automata called triangle cellular automata which accept as input strings of length a power of two in particular we study the special case in which state information can only move upward through a complete binary tree of finite state automata it is shown that this class of cellular automata can accept various string languages in o log n time where n is the length of the input string defining the initial states of the leaf vertices in the tree extensions to two dimensions defining a pyramid cellular automaton are also given

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

fundamental solution for the q laplacian and sharp moser trudinger inequality in carnot groups abstract for a general carnot group g with homogeneous dimension q we prove the existence of a fundamental solution of the q laplacian u q and a constant a q 0 such that exp a q u q is a homogeneous norm on g this implies a representation formula for smooth functions on g which is used to prove the sharp carnot group version of the celebrated moser trudinger inequality

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

nondeterministic probabilistic and alternating computations on cellular array models abstract a new mechanism for introducing nondeterminism on the cellular automaton model is introduced it is shown that this form of nondeterminism corresponds to the traditional notion in the unbounded time case but there appear to be differences when real time or linear time cellular automata are considered the notion is then generalised to include probabilistic and alternating computations restricted nondeterminism classes are also defined and studied in an attempt to refine the power of nondeterminism

the hardy inequality and nonlinear parabolic equations on carnot groups abstract in this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation u t g p u v x u p 1 in 0 t 1 p 2 u x 0 u 0 x 0 in u x t 0 on 0 t where g p is the p sub laplacian on a carnot group g and v l loc 1

low complexity classes of multidimensional cellular automata in this paper multidimensional cellular automaton are considered we investigate the hierarchy designed by the low complexity classes when the dimensionality is increased whether this hierarchy is strict is an open problem however we compare different variants and study their closure properties we present also a correspondence between a main variant of multidimensional real time cellular automata and one way multihead alternating finite automata

analysis on lie groups theorie locale diffusion de la chaleur sur des groupes de lie connexes la theorie globale les inegalites de sobolev bases graduees sur des corps lisses construction des bases graduees estimation locale du noyau diffusion de la chaleur demonstration de l inegalite de sobolev locale formes de dirichlet sur des groupes le semi groupe de convolution les conditions de sobolev modifiees

bennett s integral for vector quantizers this paper extends bennett s 1948 integral from scalar to vector quantizers giving a simple formula that expresses the rth power distortion of a many point vector quantizer in terms of the number of points point density function inertial profile and the distribution of the source the inertial profile specifies the normalized moment of inertia of quantization cells as a function of location the extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increase precise conditions are given for the convergence of distortion suitably normalized to bennett s integral previous extensions did not include the inertial profile and consequently provided only bounds or applied only to quantizers with congruent cells such as lattice and optimal quantizers the new version of bennett s integral provides a framework for the analysis of suboptimal structured vector quantizers it is shown how the loss in performance of such quantizers relative to optimal unstructured ones can be decomposed into point density and cell shape losses as examples these losses are computed for product quantizers and used to gain further understanding of the performance of scalar quantizers applied to stationary memoryless sources and of transform codes applied to gaussian sources with memory it is shown that the short coming of such quantizers is that they must compromise between point density and cell shapes

a linear speed up theorem for cellular automata abstract ibarra 1985 showed that given a cellular automaton of range 1 recognizing some language in time n 1 r n we can obtain another ca of range 1 recognizing exactly the same language but in time n 1 r n k k 2 arbitrary their proof proceeds indirectly through the simulation of cas by a special kind of sequential machines the stms and we think it misses that way some of the deep intuition of the problem we therefore provide here a direct proof of this result extended to the case of cas of arbitrary range involving the explicit construction of a ca working in time n 1 r n k this speeded up automaton first gathers the cells of the line k by k in n 1 steps which then enables it to start computing by leaps of k steps thus completing the r n remaining steps in time r n k the major problem arising from the obligation to pass from one phase to the other synchronously is solved using a synchronization process derived from the solutions of the well known firing squad synchronization problem fssp

the streaming dmt of fading channels we study sequential transmission of a stream of messages over a block fading multi input multi output mimo channel a new message arrives in each coherence block and the decoder is required to output each message after a delay of t coherence blocks we establish the optimal diversity multiplexing tradeoff dmt and show that it can be achieved using a simple interleaving of messages the converse is based on an outage amplification technique which appears to be new we also discuss another coding scheme based on a sequential tree code this coding scheme only requires the knowledge of delay at the decoder and yet realizes the optimal dmt we finally discuss some extensions when multiple messages at uniform intervals arrive within each coherence period

small time gaussian estimates of heat diffusion kernels ii the theory of large deviations la deuxieme partie d un article etudiant le noyau de chaleur d un operateur differentiel d ordre 2 sur une variete c

stein weiss inequalities for the fractional integral operators in carnot groups and applications in this article we consider the fractional integral operator i on any carnot group x1d53e i e nilpotent stratified lie group in the weighted lebesgue spaces l p x x1d53e we establish stein weiss inequalities for i and obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional integral operator i from the spaces l p x x1d53e to l q x x1d53e and from the spaces l 1 x x1d53e to the weak spaces wl q x x1d53e by using the stein weiss inequalities in the limiting case we prove that the modified fractional integral operator is bounded from the space l p x x1d53e to the weighted bounded mean oscillation bmo space bmo x x1d53e where q is the homogeneous dimension of x1d53e as applications of the properties of the fundamental solution of sub laplacian on x1d53e we prove two sobolev stein embedding theorems on weighted lebesgue and weighted besov spaces in the carnot group setting as another application we prove the boundedness of i from the weighted besov

on source transmission over mimo channels with limited feedback the problem of source channel coding over a multiple antenna mimo channel with quantized channel state information at the transmitter csit is considered upper bounds on the distortion exponents achieved with partial csit under a long term power constraint are developed it is shown that the distortion exponent with perfect csit grows unbounded as the ratio between the channel and source bandwidth increases while the exponent achieved with any feedback link of fixed finite resolution is bounded above by a polynomial of the product between the number of transmit and number of receive antennas the resolution of the feedback link should grow with the bandwidth ratio to make the distortion exponent scale as fast as that in the perfect csit case we show that in order to achieve the optimal scaling the csit feedback resolution must grow logarithmically with the bandwidth ratio for mimo channels and faster than linear for the single input single output channel the achievable distortion exponent of some hybrid schemes with heavily quantized feedback is also derived the results demonstrate that dramatic performance improvement over the case of no csit can be achieved by combining simple schemes with a very coarse csit feedback

design and analysis of mimo spatial multiplexing systems with quantized feedback this paper investigates the problem of transmit beamforming in multiple antenna spatial multiplexing sm systems employing a finite rate feedback channel assuming a fixed number of spatial channels and equal power allocation we propose a new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel using the criterion we develop an iterative design algorithm that converges to a locally optimum codebook under the independent identically distributed channel and high signal to noise ratio snr assumption the effect on channel capacity of the finite bit representation of the beamforming matrix is analyzed central to this analysis is the complex multivariate beta distribution and tractable approximations to the voronoi regions associated with the code points furthermore to compensate for the degradation due to the equal power allocation assumption we propose a multimode sm transmission strategy wherein the number of data streams is determined based on the average snr this approach is shown to allow for effective utilization of the feedback bits resulting in a practical and efficient multiple input multiple output system design

analysis on nilpotent groups soit g un groupe de lie nilpotent reel simplement connexe et soit l son algebre de lie soient l 1 l et l k 1 l k l k 1 2 soit d d g d l k 1 kdim r l k l k 1 d est la dimension de dirichlet de g soit h un groupe nilpotent discret finiment genere on demontre des theoremes d analyse pour g

on the distortion snr exponent of hybrid digital analog space time coding we consider the transmission of a real independent and identically distributed i i d analog source over a quasi static m input n output multiple input multiple output mimo block fading channel the relevant performance criterion is end to end average quadratic distortion d versus channel signal to noise ratio snr for given spectral efficiency eta defined as the ratio of the source bandwidth over the channel bandwidth in the limit of high snr we define the distortion snr exponent a eta as the largest a such that d esdot snr a over all possible source channel coding schemes of spectral efficiency eta we find a simple upper bound on a eta an achievable lower bound asep eta achievable by separated tandem source channel coding and a tighter lower bound ahybrid eta achievable by new hybrid digital analog space time coding schemes as a corollary we have that a eta is completely determined for the scalar case m n 1 and for the bandwidth compression case eta ges 2 min m n expiicit and simple construction of hybrid space time codes achieving ahybrid eta are also given

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

linear speed up for cellular automata synchronizers and applications abstract simple cellular automata can be used as language recognizers or function calculators there exist several proofs of the linear speed up theorem in strong form for recognizers 7 6 11 but not for calculators in this paper we design a linear speed up method for a special kind of calculators namely the synchronizers which are different from recognizers as a consequence we extend a result from j mazoyer by proving that any polynomial with rational coefficients of a synchronization time is also a synchronization time provided that it be greater than a certain minimal time