a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

mean field theory of avalanches in self organized critical states abstract a new mean field approximation is proposed for the sandpile model of bak tang and wiesenfeld and the distribution of heights in the self organized critical state is calculated we treat several series of successive topples to approximate various avalanches in contrast to the previous mean field theory given by tang and bak which assumes the stationary condition among topples in an avalanche out theory takes into account long term behavior of the system the results are in good agreement with the values estimated by computer simulations even in low dimensions d 2 and 3 higher approximations obtained by including local correlations or by imposing a reducibility condition which is used in the cluster variation method are also shown

a t 1 theorem for singular radon transforms we prove an analogue for singular radon transforms to the t 1 theorem of david and journe

continuously varying critical exponents in a sandpile model with internal disorder a sandpile model with an internal disorder is presented the updating of critical sites is done according to a stochastic rule with a probabilistic toppling q using a unified mean field theory and numerical simulations we have shown that the criticality is ensured for any value of q the static critical exponents have been calculated and found to be the same as those obtained for the deterministic sandpile model which is a particular case of the stochastic model they have a universal q independent behavior in the limit of slow driving we have developed a relation between our model and the branching process in order to compute the size exponent tau it presents a continuous variation with the parameter of toppling q

a physicist s sandbox we discuss some recent results suggesting that certain spatially extended dynamical systems naturally evolve toward a state characterized by domains of all length scales the analogy with second order phase transitions has prompted the name self organized criticality specific results are available for cellular automaton models which can be thought of as caricatures of a sandpile undergoing avalances the potential generality of the results stems from the very simple nonlinear diffusion dynamics governing the system

asymptotic bep and sep of quadratic diversity combining receivers in correlated ricean fading non gaussian noise and interference in this paper we study the asymptotic behavior of the bit error probability bep and the symbol error probability sep of quadratic diversity combining schemes such as coherent maximum ratio combining mrc differential equal gain combining egc and noncoherent combining nc in correlated ricean fading and non gaussian noise which in our definition also includes interference we provide simple and easy to evaluate asymptotic bep and sep expressions which show that at high signal to noise ratios snrs the performance of the considered combining schemes depends on certain moments of the noise and interference impairing the transmission we derive general rules for calculation of these moments and we provide closed form expressions for the moments of several practically important types of noise such as spatially dependent and spatially independent gaussian mixture noise correlated synchronous and asynchronous co channel interference and correlated gaussian interference from our asymptotic results we conclude that a the asymptotic performance loss of binary frequency shift keying bfsk with nc compared to binary phase shift keying bpsk with mrc is always 6 db independent of the type of noise and the number of diversity branches b the asymptotic performance loss of differential egc compared to mrc is always 3 db for additive white gaussian noise but depends on the number of diversity branches and may be larger or smaller than 3 db for other types of noise and c not only fading correlation but also noise correlation negatively affects the performance of quadratic diversity combiners

tight error bounds for space time orthogonal block codes under slow rayleigh flat fading the performance of space time orthogonal block stob codes over slow rayleigh fading channels and maximum likelihood ml decoding is investigated two bonferroni type bounds one upper bound and one lower bound for the symbol error rate ser and bit error rate ber of the system are obtained the bounds are expressed in terms of the pairwise error probabilities peps and the two dimensional pairwise error probabilities 2 d peps of the transmitted symbols furthermore the bounds can be efficiently evaluated and they hold for arbitrary nonstandard signaling schemes and mappings numerical results demonstrate that the bounds are very accurate in estimating the performance of stob codes in particular the upper and lower bounds often coincide even at low channel signal to noise ratios large constellation sizes and large diversity orders

a characterization of hajlasz sobolev and triebel lizorkin spaces via grand littlewood paley functions abstract in this paper we establish the equivalence between the hajlasz sobolev spaces or classical triebel lizorkin spaces and a class of grand triebel lizorkin spaces on euclidean spaces and also on metric spaces that are both doubling and reverse doubling in particular when p n n 1 we give a new characterization of the hajlasz sobolev spaces m 1 p r n via a grand littlewood paley function

construction of higher level 3 d signal constellations and their accurate symbol error probabilities in awgn a simple and straightforward method of constructing higher level three dimensional 3 d signal constellations for a reliable digital communication system is proposed in this paper the new method expands basic 8 ary constellation into 3 d signal space systematically so that it produces lattice configurations we also derive accurate closed form symbol error probability sep of cross lattice constellations in additive white gaussian noise awgn it is verified that the theoretical seps are almost the same as simulation results minimum euclidean distance med of the higher level 3 d constellations is increased at least 49 in comparison with quadrature amplitude modulation qam when the number of symbols is 256 the 3 d constellation has around 105 longer med than the 2 d qam due to increase in med the 3 d constellations have much improved error performance compared to the qam configurations it is therefore considered that the higher level 3 d constellations are appropriate for high quality digital communications

optimum detection of fading signals in impulsive noise this paper deals with the synthesis and the analysis of optimum receivers to detect one out of m equally likely equi energy fading signals in impulsive noise modelled as a compound gaussian possibly correlated process we show that the conventional coherent and incoherent detectors are still optimum independent of the noise as well as the fading probability density functions the performance analysis has been carried on with reference to the general case of arbitrarily distributed disturbance in order to simplify the analysis asymptotical expressions have been developed for high signal to noise ratios as well as high signal space dimensionality interestingly enough this allows separating the effect of the noise spikyness from that of the fading law results indicate that for deep fading the noise marginal distribution does not dramatically affect the error probability nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions for non fluctuating signals instead the noise distribution plays a primary role spiky noise usually produces performance impairment moreover the limit performance in impulsive disturbance may exhibit marked deviations from the well known stepwise shape which is typical of gaussian channels

asymptotical performance of m ary and binary signals over multipath multichannel rayleigh and rician fading this paper presents a general framework for computing the asymptotic error probability i e at high average snrs of m ary and binary signaling schemes over rician and rayleigh fading diversity channels a general theorem theorem 1 relates the asymptotic error rate of multipath and multichannel receivers over awgn isi free channels to the multidimensional integral of the conditional error probability two other theorems are presented for the particular cases where the conditional error probability is a function of the sum of received snrs theorem 2 or received amplitudes theorem 3 theorems 2 and 3 are related for linear coherent systems and closed form expressions are obtained for equal gain combining systems detection structures for typical diversity schemes coherent noncoherent maximal ratio and equal gain combining and quadratic noncoherent combining are considered we analyze the asymptotic error rates of some m ary signaling schemes mpsk mpam with kth order diversity and orthogonal signals with k 1 and with coherent and noncoherent detection binary signaling is also considered in our study

exact method for the error probability calculation of three dimensional signal constellations the contribution of this letter is the computation of exact symbol error probability sep of three dimensional 3 d signal constellations over an additive white gaussian noise awgn channel the originality of the proposed method is that it can be applied to any arbitrary 3 d constellation whose decision regions may not meet at right angles we express the sep in a triple integral form which is further simplified the simplified form requires a single integral evaluation of standard erf function using the derived exact sep formula we plot sep for a number of selected 3 d constellations the sep obtained using the proposed formula is validated by simulation results it is also compared with the union bound approximation an upper bound for sep

log concavity property of the error probability with application to local bounds for wireless communications a clear understanding of the behavior of error probability ep as a function of signal to noise ratio snr and other system parameters is fundamental for assessing the design of digital wireless communication systems we propose an analytical framework based on the log concavity property of the ep which we prove for a wide family of multidimensional modulation formats in the presence of gaussian disturbances and fading based on this property we construct a class of local bounds for the ep that improve known generic bounds in a given region of the snr and are invertible as well as easily tractable for further analysis this concept is motivated by the fact that communication systems often operate with performance in a certain region of interest roi and thus it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all snrs we present a possible application of these local bounds but their relevance is beyond the example made in this paper

critical exponents of the sand pile models in two dimensions abstract we study three sand pile automaton models namely the critical height critical slope and the critical laplacian models in two dimensions in which the stability criterion of the sand columns depend on the zeroth first and the second derivatives of the sand height function we carried out simulations on system sizes up to 2048 2048 and up to 108 avalanches were generated the exponents of the critical height model were calculated by taking into account the strong corrections to scaling in order to determine the exponents of the critical laplacian model accurately we introduced a height restriction in the toppling criterion that maintains universality but accelerates convergence to the steady state by orders of magnitude we see clear scaling in the critical height and the critical laplacian models and find that they belong to different universality classes however we do not find any scaling in the critical slope model

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

error probabilities of two dimensional m ary signaling in fading a new exact method for computing the average symbol error probability of two dimensional m ary signaling in slow fading is presented the method is generally applicable to polygonal decision regions the exact average symbol error rate of coherent 16 star qam is obtained and compared to that of 16 rectangular qam new results for optimum ring ratios of 16 star qam in additive white gaussian noise awgn and in slow fading are also given

boundedness of singular radon transforms on l p spaces under a finite type condition in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger are proven 1 introduction in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger in 3 are proved singular radon transforms are a type of singular integral operator a prototype for which is the hilbert transform along curves let 1 1 r n be a curve with 0 0 and let f be a schwarz function on r n 1

the square_ b heat equation and multipliers via the wave equation recently nagel and stein studied the square b heat equation where square b is the kohn laplacian on the boundary of a weakly pseudoconvex domain of finite type in mathbb c 2 they showed that the schwartz kernel of e t square b satisfies good off diagonal estimates while that of e t square b pi satisfies good on diagonal estimates where denotes the szego projection we offer a simple proof of these results which easily generalizes to other similar situations our methods involve adapting the well known relationship between the heat equation and the finite propagation speed of the wave equation to this situation in addition we apply these methods to study multipliers of the form m square b in particular we show that m square b is an nis operator where m satisfies an appropriate mihlin hormander condition

singular and maximal radon transforms analysis and geometry part 2 geometric theory 8 curvature introduction 8 1 three notions of curvature 8 2 theorems 8 3 examples 9 curvature some details 9 1 the exponential representation 9 2 diffeomorphism invariance 9 3 curvature condition cy 9 4 two lemmas 9 5 double fibration formulation 10 equivalence of curvature conditions 10 1 invariant submanifolds and deficient lie algebras 10 2 vanishing jacobians 10 3 construction of invariant submanifolds

uncoded and coded performance of mfsk and dpsk in nakagami fading channels the author presents uncoded and coded performance results for noncoherent m ary frequency shift keying mfsk and differentially coherent binary phase shift keying dpsk in a slow nonselective nakagami m 1960 fading channel he gives simple expressions for the asymptotic slopes of probability of bit error for large signal to noise ratio and shows that the effective order of diversity compared to an uncoded rayleigh channel is the product of two parameters one for the channel and one for the code he also compares the uncoded nakagami m results to those of the rician channel in order to show performance differences between these two generalized fading channel models

new analytical probability of error expressions for classes of orthogonal signals in rayleigh fading new exact expressions for the symbol error rate and bit error rate of coherent 3 ary and 4 ary orthogonal and transorthogonal signaling in slowly fading rayleigh channels are derived new exact error probability expressions for coherent 6 ary and 8 ary biorthogonal signaling in slow rayleigh fading are also presented the use of these exact expressions as accurate approximations for the error rates of m ary orthogonal biorthogonal and transorthogonal signaling with arbitrary m is illustrated

generalized abelian sandpile model abstract a sufficient condition for which the particle addition operations commute in the eventual phase space of a class of sandpile models with either integral or real local heights are obtained in case the local heights take on real numbers the volume of the eventual phase space is found to be det under the usual lebesgue measure which extends the earlier result by dhar for the integral case the geometrical aspect of the results including the effect on the avalanche size distribution are also discussed

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

signaling constellations for fading channels the performance of various coherent 8 ary and 16 ary modulations in additive white gaussian noise awgn and slowly fading channels are analyzed new expressions for the exact symbol error rates ser in fading with diversity combining are derived for any two dimensional signaling format having polygonal decision boundaries maximal ratio combining equal gain combining and selection combining are considered the ser formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine which constellation has the lowest probability of error for example a star constellation such as that specified in the ccitt v 29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0 63 db power in awgn without sacrificing the phase error tolerance while maintaining the same error rate the sensitivity of each constellation to phase error is presented and comparisons are made six 8 ary signal sets and 11 16 ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

scaling behavior of a directed sandpile automata with random defects in a recent paper b tadic u nowak k d usadel r ramaswamy and s padlewski phys rev a 45 8536 1992 the directed two dimensional sandpile is modified to include a concentration ital p of randomly placed holes for ital p gt 0 they observe a characteristic cutoff size for the duration and mass of avalanches this breaks the formal power law behavior that is a signature of self organized criticality the scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law and the exponents are numerically determined in this brief report it is shown that a previously described mean field approximation can account for the observed exponents

performance of bicm sc and bicm ofdm systems with diversity reception in non gaussian noise and interference in this paper we present a general mathematical framework for performance analysis of single carrier sc and orthogonal frequency division multiplexing ofdm systems employing popular bit interleaved coded modulation bicm and multiple receive antennas the proposed analysis is applicable to bicm systems impaired by general types of fading including rayleigh ricean nakagami m nakagami q and weibull fading and general types of noise and interference with finite moments such as additive white gaussian noise awgn additive correlated gaussian noise gaussian mixture noise co channel interference narrowband interference and ultra wideband interference we present an approximate upper bound for the bit error rate ber and an accurate closed form approximation for the asymptotic ber at high signal to noise ratios for viterbi decoding with the standard euclidean distance branch metric for the standard rate 1 2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at bers of 10 6 and 10 12 respectively however if the code is punctured to higher rates e g 2 3 or 3 4 the asymptotic approximation also becomes tight at a ber of 10 6 exploiting the asymptotic ber approximation we show that the diversity gain of bicm systems only depends on the free distance of the code the type of fading and the number of receive antennas but not on the type of noise in contrast their coding gain strongly depends on the noise moments our asymptotic analysis shows that as long as the standard euclidean distance branch metric is used for viterbi decoding bicm systems optimized for awgn are also optimum for any other type of noise and interference with finite moments

mean field theory for ordinary and hot sandpiles a mean field theory is discussed for a sandpile model a cellular automaton prototype of systems showing self organized criticality the previous formulation of the mean field does not take into account the dissipation effects that take place on boundaries this gives rise to some inconsistencies that are eliminated by carefully considering the boundaries effects as it is shown in this paper we present here a revised version of the mf equations the main result is that criticality arises in the thermodynamic limit for sandpile systems confirming numerical observations on the behavior of the order parameter the mean field approach is also generalized by applying it to the more general case of sandpiles in thermal equilibrium where a temperature like parameter t is introduced in this case we show that criticality is not destroyed at t 0

radon transforms and finite type conditions the purpose of this paper is to study averaging operators of radon transform type we shall formulate suitable finite type conditions and prove lp sobolev and lplq estimates the results will be essentially sharp for operators associated with families of curves in the plane let xc and t be smooth manifolds dimx3 nl dim2 nr and let m be a submanifold in xc x t with conormal bundle n m we denote by t the codimension of m we shall always assume that the projections lry m x and 7rt m 42 are surjective with rank dirx nl rank dr9 nr this in particular implies that n m c t x o x t o where 0 refers to the zero sections in t x and t 2 respectively this is the usual assumption for the canonical relation associated with lagrangian distributions arising as kernels of fourier integral operators the assumptions on dirx d7rt imply that for fixed x e x y e 2 the sets amx y e t x y e mi m x ye2x x y em i

on the inverse symbol error probability for diversity reception this paper addresses the problem of finding the inverse symbol error probability sep expression for coherent detection of m ary phase shift keying with multichannel reception and maximal ratio combining in rayleigh fading to this aim we derive upper and lower bounds on sep that are simply invertible and uniformly tight for all values of signal to noise ratio this enables us to obtain tight bounds on the inverse sep and on the symbol error outage seo i e sep based outage probability as an example of application to digital mobile radio the seo in a log normal shadowing environment is analyzed

asymptotic performance of m ary orthogonal signals in worst case partial band interference and rayleigh fading it is shown that for worst case partial band jamming the error probability performance for fixed e sub b n sub i becomes worse with increasing m for m 16 the asymptotic probability of error is not zero for any e sub b n sub i ln 2 but decreases inverse linearly with respect to it in the fading case the error probability performance for fixed e sub b n sub 0 improves with m for noncoherent detection but worsens with m for coherent detection for large e sub b n sub 0 the performance of the rayleigh fading channel asymptotically approaches the same limit as the worst case partial band jammed channel however for values of m at least up to 4096 the partial band jammed channel does better while it is unlikely that an m ary orthogonal signal set with m 1024 will be used in a practical situation these results suggest an important theoretical problem namely what signal set achieves reliable communication

how self organized criticality works a unified mean field picture we present a unified dynamical mean field theory based on the single site approximation to the master equation for stochastic self organized critical models in particular we analyze in detail the properties of sandpile and forest fire ff models in analogy with other nonequilibrium critical phenomena we identify an order parameter with the density of active sites and control parameters with the driving rates depending on the values of the control parameters the system is shown to reach a subcritical absorbing or supercritical active stationary state criticality is analyzed in terms of the singularities of the zero field susceptibility in the limit of vanishing control parameters the stationary state displays scaling characteristics of self organized criticality soc we show that this limit corresponds to the breakdown of space time locality in the dynamical rules of the models we define a complete set of critical exponents describing the scaling of order parameter response functions susceptibility and correlation length in the subcritical and supercritical states in the subcritical state the response of the system to small perturbations takes place in avalanches we analyze their scaling behavior in relation with branching processes in sandpile models because of conservation laws a critical exponents subset displays mean field values ensuremath nu frac 1 2 and ensuremath gamma 1 in any dimensions we treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects we present numerical simulations that confirm our results in the case of the forest fire model our approach can distinguish between different regimes soc ff and deterministic ff studied in the literature and determine the full spectrum of critical exponents

sandpile models with and without an underlying spatial structure we present a simple mean field model for the sandpile model introduced by bak tang and wiesenfeld btw phys rev lett 59 381 1987 in the mean field model we are able to pinpoint the process of self organization as well as the emerging scale invariance displayed as a power law distribution of avalanche sizes we discuss the btw sandpile model on a lattice and show that the dynamical behavior can be expressed as a transport problem this implies that the average avalanche size scales with the system size and additional heuristic arguments related to the transport properties more than indicate the origin of the power law behavior we review recent work in which scaling relations and additional constraints between the various critical exponents are addressed we demonstrate that some of the proposed relations are inconsistent we present a coherent theory in which the scaling relations along with additional constraints leave only one exponent unknown

coding for frequency hopped spread spectrum communication with partial band interference part i capacity and cutoff rate the performance of optimal codes on frequency hopped channels with partial band interference is investigated the performance measures considered are channel capacity and cutoff rate worst case partial band gaussian noise interference is assumed with the interference independent of the transmitted signal the capacity and cutoff rate are calculated as a function of the signal to noise ratio we consider soft decision receivers and hard decision receivers with and without side information optimal code rates are found for each of the above cases the required signal to noise ratio for reliable communication when codes are used is determined as a function of the code rate

dimension of branching processes and self organized criticality branching processes and their application as a model of self organized criticality are briefly reviewed the critical dimension for this model is calculated the differences between our result and similar ones on polymers and percolation are explained we discuss semiquantitatively why the critical dimension of a model of self organized criticality that includes the oscillation of the sandpile around its critical value would be different perhaps even infinite finally we conjecture that our mathematical results are more general than they seem

asymptotic error analysis of diversity schemes on arbitrarily correlated rayleigh channels asymptotic error rate expressions are derived for multi branch equal gain combining and selection combining operating on arbitrarily correlated rayleigh fading channels these closed form solutions are used to provide rapid and accurate estimation of the error rates in large signal to noise ratio regions more importantly they reveal additional insights into the transmission characteristics of linear diversity combining schemes operating on correlated rayleigh fading channels it is shown that the asymptotic error rates over correlated branches can be obtained by scaling the asymptotic error rates over independent branches with a factor det m where det m is the determinant of the normalized channel correlation matrix this relationship is valid for both coherent and noncoherent signalings a similar relationship is also established for the outage probabilities of fading wireless systems employing multi branch diversity reception

exact solutions for a mean field abelian sandpile we introduce a model for a sandpile with n sites critical height n and each site connected to every other site it is thus a mean field model in the spin glass sense we find an exact solution for the steady state probability distribution of avalanche sizes and discuss its asymptotics for large n

unified asymptotic analysis of linearly modulated signals in fading non gaussian noise and interference in this paper we present a unified asymptotic symbol error rate ser analysis of linearly modulated signals impaired by fading and possibly non gaussian noise which in our definition also includes interference the derived asymptotic closed form results are valid for a large class of fading and noise processes our analysis also encompasses diversity reception with equal gain and selection combining and is extended to binary orthogonal modulation we show that for high signal to noise ratios snrs the ser of linearly modulated signals depends on the mellin transform of the probability density function pdf of the noise since the mellin transform can be readily obtained for all commonly encountered noise pdfs the provided ser expressions are easy and fast to evaluate furthermore we show that the diversity gain only depends on the fading statistic and the number of diversity branches whereas the combining gain depends on the modulation format the type of fading the number of diversity branches and the type of noise an exception are systems with a diversity gain of one since their combining gain and asymptotic ser are independent of the type of noise however in general in a log log scale for high snr the ser curves for different types of noise are parallel but not identical and their relative shift depends on the mellin transforms of the noise pdfs

performance limits of m fsk with reed solomon coding and diversity combining this paper examines the asymptotic m spl rarr spl infin performance of m ary frequency shift keying m fsk in multi channels or multiple frequency nonselective slowly fading channels with coding side information and diversity reception in particular reed solomon rs coding is considered in conjunction with the ratio threshold test rtt which generates side information regarding the reliability of received symbols the asymptotic performance of orthogonal signaling in multichannels with maximal ratio combining mrc postdetection equal gain combining egc hybrid selection combining h sc and selection combining sc is derived for an arbitrary statistical fading model and diversity order the derivations reveal that coherent and noncoherent implementations of diversity combining schemes yield the same performance asymptotically in addition the asymptotic results are evaluated assuming a nakagami m fading model and the effect of fading severity diversity order code rate and side information upon the performance of the various diversity combiners is investigated the minimum signal to noise ratio snr required to achieve arbitrarily reliable or error free communication as well as the associated optimal rs code rate are determined for various cases

adaptive orthogonal signaling with diversity in a frequency nonselective rayleigh fading channel power and rate adaptations with diversity are considered for m ary orthogonal signals in a frequency nonselective rayleigh fading channel we derived the minimum required e sub b n sub 0 for a given probability of error the maximum average data rate and the outage probability when maximal ratio combining is performed with an imperfect channel estimation we analyzed the effects of channel estimation errors on the required e sub b n sub 0 and outage probability as a function of diversity order and adaptation methods the relative benefits of rate and power control techniques are further presented in terms of channel estimation error diversity order and outage probability the minimum required e sub b n sub 0 with reed solomon codes is also presented for comparison purposes

self organized branching processes avalanche models with dissipation we explore in the mean field approximation robustness with respect to dissipation of self organized criticality in sandpile models to this end we generalize a recently introduced self organized branching process and show that the model self organizes not into a critical state but rather into a subcritical state when dissipation is present the dynamical fixed point does not coincide with the critical point thus the level of dissipation acts as a relevant parameter in the renormalization group sense we study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs s1063 651x 96 08009 9

scaling properties of a rice pile model inertia and friction effects we present a rice pile cellular automaton model that includes inertial and friction effects this model is studied in one dimension where the updating of metastable sites is done according to a stochastic dynamics governed by a probabilistic toppling parameter p that depends on the accumulated energy of moving grains we investigate the scaling properties of the model using finite size scaling analysis the avalanche size the lifetime and the residence time distributions exhibit a power law behavior their corresponding critical exponents respectively ensuremath tau y and y r are not universal they present continuous variation versus the parameters of the system the maximal value of the critical exponent ensuremath tau that our model gives is very close to the experimental one ensuremath tau 2 02 frette et al nature london 379 49 1996 and the probability distribution of the residence time is in good agreement with the experimental results we note that the critical behavior is observed only in a certain range of parameter values of the system which correspond to low inertia and high friction

performance limits of reed solomon coded cdma with orthogonal signaling in a rayleigh fading channel the asymptotic performance of reed solomon rs coded m ary orthogonal signaling with ratio threshold test rtt type demodulation in a rayleigh fading channel is considered we show that the minimum e sub b n sub 0 needed for error free communication is eln2 2 75 db with rtt and 4 79 6 8 db with hard decisions the optimum code rate that minimizes the required e sub b n sub 0 is e sup 1 with rtt and 0 46 with hard decision and the optimum ratio threshold approaches 1 for large m next we investigate the fundamental limit in a direct sequence spread spectrum multiple access ds ssma system employing an m ary orthogonal code of length n mm which is obtained by spreading every row of an m spl times m hadamard matrix with a user specific random sequence of length n we derive the minimum e sub b n sub 0 for error free communication as a function of the number of users the optimum code rate that minimizes e sub b n sub 0 and the maximum limit on the total information transmission rate then we consider a multirate ds ssma system where a population of users simultaneously transmit at different power levels a variety of traffic types of different information rates we derive the minimum required e sub b n sub 0 and the optimum code rate for each traffic type

asymptotic performance of m ary orthogonal modulation in generalized fading channels the asymptotic m to infinity probability of symbol error p sub e sub m for m ary orthogonal modulation in a nakagami m fading channel is given by the incomplete gamma function p m mx where x in 2 e sub b n sub 0 and e sub b is the average energy per bit for large signal to noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of e sub b n sub 0 these channels exist for all m or 1 2 the special case of m 1 corresponds to rayleigh fading an inverse linear channel

structure of two dimensional sandpile i height probabilities the height probabilities of the two dimensional abelian sandpile model are the fractionial numbers of lattice sites having heights 1 2 3 4 a combinatorial method for evaluation of these quantities is proposed the method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice exact analytical expressions for all probabilities are obtained

universality in sandpiles we perform extensive numerical simulations of different versions of the sandpile model we find that previous claims about universality classes are unfounded since the method previously employed to analyze the data suffered from a systematic bias we identify the correct scaling behavior and provide evidences suggesting that sandpiles with stochastic and deterministic toppling rules belong to the same universality class

universality classes for rice pile models we investigate sandpile models where the updating of unstable columns is done according to a stochastic rule we examine the effect of introducing nonlocal relaxation mechanisms we find that the models self organize into critical states that belong to three different universality classes the models with local relaxation rules belong to a known universality class that is characterized by an avalanche exponent ensuremath tau ensuremath approx 1 55 whereas the models with nonlocal relaxation rules belong to new universality classes characterized by exponents ensuremath tau ensuremath approx 1 35 and ensuremath tau ensuremath approx 1 63 we discuss the values of the exponents in terms of scaling relations and a mapping of the sandpile models to interface models

innovations based map detection for time varying frequency selective channels by using the innovations process this paper provides a unification and extension of the existing maximum a posteriori map detectors mapds the practically important topics of linear modulations time varying frequency selective channels differential phase detection and fractional sampling are accounted for the mapds are derived under different conditions of optimality and a priori knowledge as follows when the map criterion is applied to the constellation mapper s input bits or output symbols when all observations or only a fixed number of future observations i e fixed lag mapds from a transmission are available when the time varying channel impulse response is perfectly known and when only the gaussian distributed channel s mean and autocovariance and the noise variance are known as these quantities are actually unknown their estimation in the context of map detection is also discussed the mapds are characterized through simulation and a novel unified analysis although mapds are less suited to hardware implementation than the traditional maximum likelihood sequence detectors the mapds can accept nonuniform a priori bit or symbol probabilities and provide soft outputs in this way the mapds are well suited to iterative decoding and so they will become increasingly integral to high performance receiver designs

disorder induced phase transition in a one dimensional model of rice pile abstract we propose a one dimensional rice pile model which connects the 1d btw sandpile model phys rev a 38 1988 364 and the oslo rice pile model phys rev lett 77 1997 107 in a continuous manner we found that for a sufficiently large system there is a sharp transition between the trivial critical behaviour of the 1d btw model and the self organized critical soc behaviour when there is soc the model belongs to a known universality class with the avalanche exponent 1 53