a novel decomposition analysis of nonlinear distortion in ofdm transmitter systems in orthogonal frequency division multiplexing ofdm transmitter systems nonlinear distortion is a major impairment caused by power amplifier pa the distortion is constituted by numerous noise like inter modulation products imps although the overall behavior of nonlinear imp distortion has been well studied in large multi carrier contexts such as in ofdm the knowledge of individual imps and their quantitative interrelationships together with the derivation of behavioural knowledge and the predictability of consequences arising from such interrelationships is a fairly unexplored topic this is the subject of this paper the powers of the very numerous individual imps generated are analytically derived based on a bessel fourier pa behavioural model and it is proven that these powers have only a small number of distinct powers proven also is that the ratios of these power values are constants and that these constants are invariant with the particular pa s nonlinearity characteristics or operating point further it is proven that specific types of imps dominate nonlinear distortion effects finally it is shown that imp power spectra can be derived from a simple product of two polynomials which are quadrature functions of frequency and pa operating point respectively application possibilities for findings presented in this paper such as their potential to contribute efficiency improvements in ofdm system modulation fidelity calculations over 1100 times faster than conventional methods are also outlined in the conclusions

generation and monitoring of discrete stable random processes using multiple immigration population models some properties of classical population processes that comprise births deaths and multiple immigrations are investigated the rates at which the immigrants arrive can be tailored to produce a population whose steady state fluctuations are described by a pre selected distribution attention is focused on the class of distributions with a discrete stable law which have power law tails and whose moments and autocorrelation function do not exist the separate problem of monitoring and characterizing the fluctuations is studied analysing the statistics of individuals that leave the population the fluctuations in the size of the population are transferred to the times between emigrants that form an intermittent time series of events the emigrants are counted with a detector of finite dynamic range and response time this is modelled through clipping the time series or saturating it at an arbitrary but finite level whereupon its moments and correlation properties become finite distributions for the time to the first counted event and for the time between events exhibit power law regimes that are characteristic of the fluctuations in population size the processes provide analytical models with which properties of complex discrete random phenomena can be explored and in addition provide generic means by which random time series encompassing a wide range of intermittent and other discrete random behaviour may be generated

existence of primitive divisors of lucas and lehmer numbers we prove that for n 30 every n th lucas and lehmer number has a primitive divisor this allows us to list all lucas and lehmer numbers without a primitive divisor

cryptanalysis of large rsa exponent by using the lll algorithm the study of paper cryptanalysis of rsa with private key d less than n 0 2 9 2 ieee trans information theory 46 2000 1339 which boneh and durfee published in ieee transactions on information theory in july 2000 supported that when d

faster recursions in sphere decoding most of the calculations in standard sphere decoders are redundant in the sense that they either calculate quantities that are never used or calculate some quantities more than once a new method which is applicable to lattices as well as finite constellations is proposed to avoid these redundant calculations while still returning the same result pseudocode is given to facilitate immediate implementation simulations show that the speed gain with the proposed method increases linearly with the lattice dimension at dimension 60 the new algorithms avoid about 75 of all floating point operations

the optimal lll algorithm is still polynomial in fixed dimension in this paper we consider the open problem of the complexity of the lll algorithm in the case when the approximation parameter of the algorithm has as its extreme value 1 this case is of interest because the output is then the strongest lovasz reduced basis experiments reported by lagarias and odlyzko j acm 32 1 1985 229 seem to show that the algorithm remains polynomial in average however no bound better than a naive exponential order one is established for the worst case complexity of the optimal lll algorithm even for fixed small dimension higher than 2 here we prove that for any fixed dimension n the number of iterations of the lll algorithm is linear with respect to the size of the input it is easy to deduce from vallee j algorithms 12 1991 556 that the linear order is optimal moreover in 3 dimensions we give a tight bound for the maximum number of iterations and we characterize precisely the output basis our bound also improves the known one for the usual non optimal lll algorithm

constrained and preconditioned stochastic gradient method we consider stochastic approximations that arise from such applications as data communications and image processing we demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be incorporated into a preconditioning technique to derive the preconditioned stochastic gradient method psgm we perform convergence analysis to show that the psgm converges to the theoretical best approximation under some simple assumptions on the preconditioner and on the independence of samples drawn from a stochastic process simulation results are presented to demonstrate the effectiveness of the constrained and preconditioned stochastic gradient method

the smoluchowski coagulation equations with continuous injection we study a system of equations which models the formation of clusters by coagulation with particles of unit size being injected at a time dependent rate we observe that the criteria under which gelation occurs are the same as for the constant mass and constant monomer cases which have been studied previously we identify a variety of types of behaviour in the large time limit depending on the coagulation kernel and on the rate at which monomer is introduced into the system the results are obtained by means of exact generating function techniques matched asymptotic expansions and numerical simulations

arithmetic multivariate descartes rule let inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i be any number field or p adic field and consider f f 1 f k where f 1 f k inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i x 1 x n and no more than distinct exponent vectors occur in the monomial term expansions of the f i we prove that f has no more than 1 c n n 3 log n n geometrically isolated roots in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i n where c is an explicit and effectively computable constant depending only on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i this gives a significantly sharper arithmetic analogue of khovanski s theorem on real fewnomials and a higher dimensional generalization of an earlier result of hendrik w lenstra jr for the special case of a single univariate polynomial we also present some further refinements of our new bounds and a higher dimensional generalization of a bound of lipshitz on p adic complex roots connections to non archimedean amoebae and computational complexity including additive complexity and solving for the geometrically isolated rational roots are discussed along the way we thus provide the foundations for an effective arithmetic analogue of fewnomial theory

solving a system of linear diophantine equations with lower and upper bounds on the variables we develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables the algorithm is based on lattice basis reduction it first finds a short vector satisfying the system of diophantine equations and a set of vectors belonging to the nullspace of the constraint matrix due to basis reduction all these vectors are relatively short the next step is to branch on linear combinations of the null space vectors which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists the research was motivated by the need for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing our algorithm is tested with good results on real life data and on instances from the literature

fast multiple antenna differential decoding we present an algorithm based on lattice reduction for the fast decoding of diagonal differential modulation across multiple antenna while the complexity of the maximum likelihood ml algorithm is exponential both in the number of antenna and the rate the complexity of our approximate lattice algorithm is polynomial in the number of antennas and the rate we show that the error performance of our lattice algorithm is very close to the ml algorithm

accuracy analysis of measurements on a stable power law distributed series of events we investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined the model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events this leads to a scale free discrete random process where customary measures such as mean value and variance do not exist however converting the number of events occurring in fixed time intervals to a 1 bit clipped process allows the construction of well behaved statistics that still retain vestiges of the original power law and fluctuation properties these statistics include the clipped mean and correlation function from measurements of which both the power law index of the distribution of events and the time constant of its fluctuations can be deduced we report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process this indicates that for a fixed experiment time the error on measurements of the sample mean is minimized by an optimum choice of the number of samples it is shown furthermore that this choice is sensitive to the power law index and that the approach to poisson statistics is dominated by rare events or outliers our results are supported by numerical simulation

a lattice based public key cryptosystem ajtai recently found a random class of lattices of integer points for which he could prove the following worst case average case equivalence result if there is a probabilistic polynomial time algorithm which finds a short vector in a random lattice from the class then there is also a probabilistic polynomial time algorithm which solves several problems related to the shortest lattice vector problem svp in any n dimensional lattice ajtai and dwork then designed a public key cryptosystem which is provably secure unless the worst case of a version of the svp can be solved in probabilistic polynomial time however their cryptosystem suffers from massive data expansion because it encrypts data bit by bit here we present a public key cryptosystem based on similar ideas but with much less data expansion

on p adic absolute cm periods i the second author defined the absolute cm period symbol using the multiple gamma function this symbol is conjectured to give the same value as shimura s period symbol up to multiplication by algebraic numbers in this paper we define a p adic analogue of the absolute cm period symbol using the p adic multiple gamma function studied by the first author in the completely split case we present a conjecture which predicts the exact value of this symbol as well as supporting evidences

hardness of approximating the shortest vector problem in lattices let p 1 be any fixed real we show that assuming np n rp there is no polynomial time algorithm that approximates the shortest vector problem svp in e p norm within a constant factor under the stronger assumption np n rtime 2poly log n we show that there is no polynomial time algorithm with approximation ratio 2 log n 1 2 e where n is the dimension of the lattice and e 0 is an arbitrarily small constant we first give a new randomized reduction from closest vector problem cvp to svp that achieves some constant factor hardness the reduction is based on bch codes its advantage is that the svp instances produced by the reduction behave well under the augmented tensor product a new variant of tensor product that we introduce this enables us to boost the hardness factor to 2 log n 1 2 e

digital predistortion for power amplifiers using separable functions this paper is concerned with digital predistortion for linearization of rf high power amplifiers hpas it has two objectives first we establish a theoretical framework for a generic predistorter system and show that if a postdistorter exists then it is also a predistorter and therefore the predistorter and postdistorter are equivalent this justifies the indirect learning methods for a large class of hpas second we establish a systematic and general structure for a predistorter that is capable of compensating nonlinearity for a large variety of hpas this systematic structure is derived using approximation by separable functions and avoids selection of predistorters based on the assumption of hpa models traditionally done in the literature

fluctuations in a coupled population model we investigate a discrete markov process in which the immigration of individuals into one population is controlled by the fluctuations in another we examine the effect of coupling back the second population to the first through a similar mechanism and derive exact solutions for the generating functions of the population statistics we show that a stationary state exists over a certain parameter range and obtain expressions for moments and correlation functions in this regime when more than two populations are coupled cyclically transient oscillations and periodic behaviour of correlation functions are predicted we demonstrate that if the initial distribution of either population is stable or more generally has a power law tail that falls off like n 1 0 1 then for certain parameter values there exists a stationary state that is also power law but not stable this stationary state cannot be accessed from a single multiple immigrant population model but arises solely from the nonlinear interaction of the coupled system

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

distinguishing population processes by external monitoring we investigate the statistical and correlation properties of two stochastic population models that give rise to identical first order probability densities we assume that the processes are monitored indirectly through measurement of the rate at which individuals emigrate from the population formulae characterizing the integrated statistics of these counting processes are derived and it is shown how they may be used to distinguish the population models

code construction and decoding algorithms for semi quantitative group testing with nonuniform thresholds we analyze a new group testing scheme termed semi quantitative group testing which may be viewed as a concatenation of an adder channel and a discrete quantizer our focus is on non uniform quantizers with arbitrary thresholds for the most general semi quantitative group testing model we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds the sequences represent extensions and generalizations of b h and certain types of super increasing and lexicographically ordered sequences and they lead to code structures amenable for efficient recursive decoding we describe the decoding methods and provide an accompanying computational complexity and performance analysis

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

newman polynomials with prescribed vanishing and integer sets with distinct subset sums we study the problem of determining the minimal degree d m of a polynomial that has all coefficients in 0 1 and a zero of multiplicity m at 1 we show that a greedy solution is optimal precisely when m 5 mirroring a result of boyd on polynomials with 1 coefficients we then examine polynomials of the form e e xe 1 where e is a set of m positive odd integers with distinct subset sums and we develop algorithms to determine the minimal degree of such a polynomial we determine that d m satisfies inequalities of the form 2m c1m d m 103 96 2m c2 last we consider the related problem of finding a set of m positive integers with distinct subset sums and minimal largest element and show that the conway guy sequence yields the optimal solution for m 9 extending some computations of lunnon

generation and monitoring of a discrete stable random process a discrete stochastic process with stationary power law distribution is obtained from a death multiple immigration population model emigrations from the population form a random series of events which are monitored by a counting process with finite dynamic range and response time it is shown that the power law behaviour of the population is manifested in the intermittent behaviour of the series of events

reduce and split cuts improving the performance of mixed integer gomory cuts mixed integer gomory cuts have become an integral part of state of the art software for solving mixed integer linear programming problems therefore improvements in the performance of these cutting planes can be of great practical value in this paper we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed integer gomory cuts this is motivated by the fact that in a mixed integer gomory cut the coefficient of an integer variable lies between 0 and 1 whereas for a continuous variable there is no upper bound the heuristic tries to reduce the coefficients of the continuous variables we call the resulting cuts reduce and split cuts we found that on several test problems reduce and split cuts can substantially enhance the performance of a branch and bound algorithm

on lattices learning with errors random linear codes and cryptography our main result is a reduction from worst case lattice problems such as gapsvp and sivp to a certain learning problem this learning problem is a natural extension of the learning from parity with error problem to higher moduli it can also be viewed as the problem of decoding from a random linear code this we believe gives a strong indication that these problems are hard our reduction however is quantum hence an efficient solution to the learning problem implies a quantum algorithm for gapsvp and sivp a main open question is whether this reduction can be made classical i e nonquantum we also present a classical public key cryptosystem whose security is based on the hardness of the learning problem by the main result its security is also based on the worst case quantum hardness of gapsvp and sivp the new cryptosystem is much more efficient than previous lattice based cryptosystems the public key is of size o n2 and encrypting a message increases its size by a factor of o n in previous cryptosystems these values are o n4 and o n2 respectively in fact under the assumption that all parties share a random bit string of length o n2 the size of the public key can be reduced to o n

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

improved rounding for spline coefficients and knots when representing the coefficients and knots of a spline using only small integers independently rounding each infinite precision value is not the best strategy we show how to build an affine model for the error expanded about the optimal full precision free knot or parameterized spline then use the lovasz basis reduction algorithm to select a better rounding the technique could be used for other situations in which a quadratic error model can be computed

the iterated mod problem abstract the iterated mod problem is this given a b1 b2 bn all integers or all polynomials in q x is a mod b1 mod b2 mod bn 0 when the inputs are integers we prove the problem p complete with respect to log space reductions whereas in the polynomial case we prove the problem is in nc the significance of these results lies primarily in the similarity between the iterated mod problem and the euclidean algorithm we also show that the superincreasing knapsack problem is p complete using a very similar proof

integer sets with distinct subset sums in section 1 we introduce the problem of finding minimal height sets of n natural numbers with distinct subset sums ssd and in section 2 review the well known conway guy sequence u conjectured to yield a minimal ssd set for every n we go on section 3 to prove that u certainly cannot be improved upon by any greedy sequence to verify numerically section 4 that it does yield ssd sets for n 80 and section 5 by direct search to show that these are minimal for n s 8 there is a brief interlude section 6 on the problem of decoding the subset from its sum in section 7 generalizations of u are constructed which are asymptotically smaller defining the limit ratio of a sequence w to be a 1imn wn 2l the atkinson negro santoro sequence v known to give ssd sets has a 0 6334 conwayguy conjectured to has a 0 4703 and our best generalization has a 0 4419 we also section 8 discuss when such sequences have the same a and section 9 how a may efficiently be computed to high accuracy 1 the distinct subset sum problem a well known problem in combinatorial number theory 2 pp 64 65 involves the construction for given n of a set p pi i 1 n of natural numbers possessing the property we shall call subset sum distinctness or ssd for short that is l l f pi p e pi s t c l n i s i t or distinct subsets of p have distinct sums evidently choosing pi 21 satisfies 1 1 the interest lies in how much the maximum element pn can be reduced below 2n 1 in order to explore the ssd property it is convenient to consider a more general concept we say that x has a representation by p with length k and signature 1 when for some s and t as before 1 2 x e pe po ies iet where s n t 0 si it k isi iti 1 that is x is the difference of two disjoint subset sums of which the first has 1 terms more than the second and the two together have k terms alternatively n 1 3 x eip i l received june 23 1986 revised october 20 1986 1980 mathematics subject classification 1985 revision primary 11b13 05 04 05a99 11j13 94a60 65b05

on the structure of reduced kernel lattice bases lattice based reformulation techniques have been used successfully both theoretically and computationally one such reformulation is obtained from the kernel lattice associated with an input matrix some of the hard instances in the literature that have been successfully tackled by lattice based techniques have randomly generated input since the considered instances are very hard even in low dimension less experience is available for larger instances recently we have studied larger instances and observed that the lll reduced basis of the kernel lattice has a specific sparse structure in particular this translates into a map in which some of the original variables get a rich translation into a new variable space whereas some variables are only substituted in the new space if an original variable is important in the sense of branching or cutting planes this variable should be translated in a nontrivial way in this paper we partially explain through a probabilistic analysis the obtained struct

predicting spectral regrowth of nonlinear power amplifiers power amplifiers pas are important elements in communications systems and they are inherently nonlinear nonlinearity generates spectral regrowth i e spectral broadening in digitally modulated signals which causes adjacent channel interference in this paper we present a closed form expression for the auto covariance function of the pa output whose fourier transform yields the output power spectral density psd the pa input does not need to be gaussian and the psd calculation can be carried out using common pa descriptions such as the am am and am pm characteristics we assume that the input is narrow band thus pa memory effects on the order of a symbol period are not present the analytical results allow us to predict spectral regrowth without running expensive or time consuming time domain simulations they also lead to a variety of optimization possibilities in transmitter design that includes the pas

effective hilbert irreducibility in this paper we prove by entirely elementary means a very effective version of the hilbert irreducibility theorem we then apply our theorem to construct a probabilistic irreducibility test for sparse multivariate polynomials over arbitrary perfect fields for the usual coefficient fields the test runs in polynomial time in the input size

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

sentences over integral domains and their computational complexities letrbe a hilbertian domain and letkbe its fraction field let x1 xn y be a quantifier free arithmetical formula overr we may also take x1 xn y to be an arithmetical formula overkx1 xn and write it as y in this paper we show that ifrhas enough non units and x1 xn y x1 xn y called an n sentence is true inr then y y is true inkx1 xn also ifr kt wherekis an infinite integral domain and x1 xn y x1 xn y is true inr then y y is true inrx1 xn these results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences some of the results are 1 the decision problem of sentences and diophantine equations with parameters over the ring of integers of a global field are co np complete 2 the decision problem of sentences over the ring of integers of a global field is np complete 3 letkbe an infinite domain the time complexities of the decision problems of equations with parameters and sentences over the polynomial ringkt are polynomial time reducible to factoring polynomials overk 4 the decision problem of sentences over all algebraic integer rings is in p 5 the decision problem of sentences over all integral domains with characteristic 0 is in p 6 the time complexity of the decision problem of sentences over all integral domains is polynomial time reducible to factoring integers overzand factoring polynomials over finite fields

period computations for covers of elliptic curves in this article we construct algebraic equations for a curve c and a map f to an elliptic curve e with pre specified branching data we do this by determining certain relations that the periods of c and e must satisfy and use these relations to approximate the coefficients to high precision we then conjecture which algebraic numbers the coefficients are and then we prove this conjecture to be correct

a note on gao s algorithm for polynomial factorization shuhong gao 2003 6 has proposed an efficient algorithm to factor a bivariate polynomial f over a field f this algorithm is based on a simple partial differential equation and depends on a crucial fact the dimension of the polynomial solution space g associated with this differential equation is equal to the number r of absolutely irreducible factors of f however this holds only when the characteristic of f is either zero or sufficiently large in terms of the degree of f in this paper we characterize a vector subspace of g for which the dimension is r regardless of the characteristic of f and the properties of gao s construction hold moreover we identify a second vector subspace of g that leads to an analogous theory for the rational factorization of f

the gomory chvatal closure of a nonrational polytope is a rational polytope the question as to whether the gomory chvatal closure of a nonrational polytope is a polytope has been a longstanding open problem in integer programming in this paper we answer this question in the affirmative by combining ideas from polyhedral theory and the geometry of numbers

a stochastic conjugate gradient method for the approximation of functions a stochastic conjugate gradient method for the approximation of a function is proposed the proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution in addition the method performs the conjugate gradient steps by using an inner product that is based on stochastic sampling theoretical analysis shows that the method is convergent in probability the method has applications in such fields as predistortion for the linearization of power amplifiers

dual rsa and its security analysis we present new variants of an rsa whose key generation algorithms output two distinct rsa key pairs having the same public and private exponents this family of variants called dual rsa can be used in scenarios that require two instances of rsa with the advantage of reducing the storage requirements for the keys two applications for dual rsa blind signatures and authentication secrecy are proposed in addition we also provide the security analysis of dual rsa compared to normal rsa the security boundary should be raised when applying dual rsa to the types of small d small e and rebalanced rsa

orthogonal polynomials for complex gaussian processes power amplifiers are the major source of nonlinearity in communications systems such nonlinearity causes spectral regrowth as well as in band distortion which leads to adjacent channel interference and increased bit error rate polynomials are often used to model the nonlinear power amplifier or its predistortion linearizer in this paper we present a novel set of orthogonal polynomials for baseband gaussian input to replace the conventional polynomials and show how they alleviate the numerical instability problem associated with the conventional polynomials the orthogonal polynomials also provide an intuitive means of spectral regrowth analysis

power law distributed level crossings define fractal behavior a relationship is established between the autocorrelation function of continuous gaussian and non gaussian stochastic processes and the discrete process that describes their zero or level crossings random fractals occur when the distribution for the number of crossings is described by a class of markov processes whose singlefold statistics are the discrete analog of the levy stable continuous probability densities

a multidimensional continued fraction based on a high order recurrence relation the paper describes and studies an iterative algorithm for finding of a set of linear forms over vectors of integers the algorithm small values of a set of linear forms over vectors of integers the algorithm uses a linear recurrence relation to generate a vector sequence the basic idea being to choose the integral coefficients in the recurrence relation in such a way that the linear forms take small values subject to the requirement that the integers should not become too large the problem of choosing good coefficients for the recurrence relation is thus related to the problem of finding a good approximation of a given vector by a vector in a certain one parameter family of lattices the novel feature of our approach is that practical formulae for the coefficients are obtained by considering the limit as the parameter tends to zero the paper discusses two rounding procedures to solve the underlying inhomogeneous diophantine approximation problem the first which we call naive rounding leads to a multidimensional continued fraction algorithm with suboptimal asymptotic convergence properties in particular when it is applied to the familiar problem of simultaneous rational approximation the algorithm reduces to the classical jacobi perron algorithm the second rounding procedure is babai s nearest plane procedure we compare the two rounding procedures numerically our experiments suggest that the multidimensional continued fraction corresponding to nearest plane rounding converges at an optimal asymptotic rate

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

levy random walks with fluctuating step number and multiscale behavior random walks with step number fluctuations are examined in n dimensions for when step lengths comprising the walk are governed by stable distributions or by random variables having power law tails when the number of steps taken in the walk is large and uncorrelated the conditions of the levy gnedenko generalization of the central limit theorem obtain when the number of steps is correlated infinitely divisible limiting distributions result that can have levy like behavior in their tails but can exhibit a different power law at small scales for the special case of individual steps in the walk being gaussian distributed the infinitely divisible class of k distributions result the convergence to limiting distributions is investigated and shown to be ultraslow random walks formed from a finite number of steps modify the behavior and naturally produce an inner scale the single class of distributions derived have as special cases k distributions stable distributions distributions with power law tails and those characteristic of high and low frequency cascades the results are compared with cellular automata simulations that are claimed to be paradigmatic of self organized critical systems

tile invariants new horizons let t be a finite set of tiles the group of invariants g t introduced by pak trans ams 352 2000 5525 is a group of linear relations between the number of copies of tiles in tilings of the same region we survey known results about g the height function approach the local move property various applications and special cases

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

a primal all integer algorithm based on irreducible solutions this paper introduces an exact primal augmentation algorithm for solving general linear integer programs the algorithm iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities we prove that various versions of our algorithm are finite it is a major concern in this paper to show how the subproblem of replacing a column can be accomplished effectively an implementation of the presented algorithms is given computational results for a number of hard 0 1 integer programs from the miplib demonstrate the practical power of the method

fast lll type lattice reduction we modify the concept of lll reduction of lattice bases in the sense of lenstra lenstra lovasz factoring polynomials with rational coefficients math ann 261 1982 515 534 towards a faster reduction algorithm we organize lll reduction in segments of the basis our slll bases approximate the successive minima of the lattice in nearly the same way as lll bases for integer lattices of dimension n given by a basis of length 2 o n slll reduction runs in o n 5 e bit operations for every e 0 compared to o n 7 e for the original lll and to o n 6 e for the lll algorithms of schnorr a more efficient algorithm for lattice reduction journal of algorithm 9 1988 47 62 and storjohann faster algorithms for integer lattice basis reduction tr 249 swiss federal institute of technology eth zurich department of computer science zurich switzerland july 1996 we present an even faster algorithm for slll reduction via iterated subsegments running in o n 3log n arithmetic steps householder reflections are shown to provide better accuracy than gram schmidt for orthogonalizing lll bases in floating point arithmetic

hard equality constrained integer knapsacks we consider the following integer feasibility problem given positive integer numbersa0 a1 a n with gcd a1 a n 1 anda a1 a n does there exist a vectorx z n 0satisfyinga x a0 we prove that if the coefficientsa1 a nhave a certain decomposable structure then the frobenius number associated witha1 a n i e the largest value ofa0 for whicha x a0 does not have a nonnegative integer solution is close to a known upper bound in the instances we consider we takea0 to be the frobenius number furthermore we show that the decomposable structure ofa1 a nmakes the solution of a lattice reformulation of our problem almost trivial since the number of lattice hyperplanes that intersect the polytope resulting from the reformulation in the direction of the last coordinate is going to be very small for branch and bound such instances are difficult to solve since they are infeasible and have large values ofa0 a i 1 i n we illustrate our results by some computational examples

a deterministic version of pollard s p 1 algorithm in this article we present applications of smooth numbers to the unconditional derandomization of some well known integer factoring algorithms we begin with pollard s p 1 algorithm which finds in random polynomial time the prime divisors p of an integer n such that p 1 is smooth we show that these prime factors can be recovered in deterministic polynomial time we further generalize this result to give a partial derandomization of the k th cyclotomic method of factoring k 2 devised by bach and shallit we also investigate reductions of factoring to computing euler s totient function we point out some explicit sets of integers n that are completely factorable in deterministic polynomial time given n these sets consist roughly speaking of products of primes p satisfying with the exception of at most two certain conditions somewhat weaker than the smoothness of p 1 finally we prove that o ln n oracle queries for values of are sufficient to completely factor any integer n in less than exp 1 o 1 ln n 1 3 ln ln n 2 3 deterministic time

an efficient low complexity detector for spatially multiplexed mc cdm we propose a novel suboptimum detection method for spatially multiplexed multicarrier code division multiplexing sm mc cdm communications compared to the spatially multiplexed ofdm sm ofdm the frequency domain spreading in sm mc cdm systems results in an additional diversity gain to take advantage of diversity and multiplexing while mitigating interference we design a low complexity efficient detector called unified successive interference cancellation sic detector for sm mc cdm communications further performance improvement is achieved by adopting in conjunction with the unified sic the iterative subcarrier reconstruction detection algorithm originally proposed for single antenna systems the results demonstrate significant performance improvement over other existing methods of comparable complexity a close approximation for the probability density function pdf of the proposed detector s output signal to interference plus noise ratio sinr is found and used to obtain error bounds for the bit error rate ber performance of the coded sm mc cdm transmission is also discussed in the paper

on the computation of totally real quartic fields of small discriminant all totally real quartic fields of discriminant less than 106 are computed the method used to generate the fields is derived from delone and faddeev with corrections and improvements a new method for deciding field i8omorphism is used to eliminate redundant examples integral bases and galois groups are given for each field 1 introduction in 3 pp 184 200 delone and faddeev give a number geometric method for computing generating equations for all totally real quartic fields of discriminant not exceeding a fixed upper bound l e r 0 this method is well suited for implementation on a computer unfortunately the original paper contains many mistakes and the proofs are sometimes hard to understand in the present paper we give a corrected version of the delone faddeev algorithm we describe its implementation and we give a table of all totally real quartic fields of discriminant less than 1 000 000 including their integral bases and the galois groups of their normal closures a different method for computing totally real quartic fields was given by god win 6 and for general algorithms for computing fields of small discriminants see martinet 8 and pohst 9 10

hidden number problem with hidden multipliers timed release crypto and noisy exponentiation we consider a generalisation of the hidden number problem recently introduced by boneh and venkatesan the initial problem can be stated as follows recover a number a fp such that for many known random t fp approximations to the values of at p are known here we study a version of the problem where the multipliers t are not known but rather certain approximations to them are given we present a probabilistic polynomial time solution when the error is small enough and we show that the problem cannot be solved if the error is sufficiently large we apply the result to the bit security of timed release crypto introduced by rivest shamir and wagner to noisy exponentiation black boxes and to the bit security of the inverse exponentiation we also show that it implies a certain bit security result for weil pairing on elliptic curves