dynamic phase transition for decoding algorithms the state of the art error correcting codes are based on large random constructions random graphs random permutations etc and are decoded by linear time iterative algorithms because of these features they are remarkable examples of diluted mean field spin glasses both from the static and dynamic points of view we analyze the behavior of decoding algorithms by mapping them onto statistical physics models this allows us to understand the intrinsic i e algorithm independent features of this behavior

group codes outperform binary coset codes on nonbinary symmetric memoryless channels typical minimum distances and error exponents are analyzed on the 8 psk gaussian channel for two capacity achieving code ensembles with different algebraic structure it is proved that the typical group code over the cyclic group of order eight achieves both the gilbert varshamov bound and the expurgated error exponent on the other hand the typical binary coset codes under any labeling is shown to be bounded away both from the gilbert varshamov bound at any rate and the expurgated exponent at low rates the reason for this phenomenon is shown to rely on the symmetry structure of the 8 psk constellation which is known to match the cyclic group of order eight but not the direct product of three copies of the binary group the presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical code performance than designing codes whose algebraic structure does not match the channel this contrasts the well known fact that the average binary coset code achieves both the capacity and the random coding error exponent of any discrete memoryless channel

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

continuation theorems for periodic perturbations of autonomous systems it is first shown in this paper that whenever it exists the coincidence degree of the left hand member of an autonomous differential equation x g x 0 in the space of periodic functions with fixed period omega can be computed in terms of the brouwer degree of g this result provides efficient continuation theorems specially for omega periodic perturbations of autonomous systems extensions to differential equations in flow invariant enr s are also given

average and reliability error exponents in low density parity check codes we present a theoretical method for a direct evaluation of the average and reliability error exponents in low density parity check error correcting codes using methods of statistical physics results for the binary symmetric channel are presented for codes of both finite and infinite connectivity

existence of coexistence states a generic property for cyclic 3 dimensional competitive systems abstract in this paper we consider the class c t of all dissipative 3 dimensional t periodic kolmogorov competitive and cyclic systems such that the trivial solution is a source and we prove that almost every such system possesses a coexistence state more precisely we characterize an open and dense subset u of c t with respect to the topology of the uniform convergence in compact sets such that each member of u has a coexistence state

a logarithmic upper bound on the minimum distance of turbo codes we derive new upper bounds on the minimum distance which turbo codes can maximally attain with the optimum interleaver of a given length the new bounds grow approximately logarithmically with the interleaver length and they are tighter than all previously derived bounds for medium length and long interleavers an extensive discussion highlights the impacts of the new bounds in the context of interleaver design and provides some new design guidelines

homeomorphisms of the disk with trivial dynamics and extinction of competitive systems let h be a homeomorphism of a closed two dimensional disk d and let fix h denote the set of fixed points of h we say that h has trivial dynamics if the omega limit set of every orbit h p n z p d is included in fix h in general the dynamics of a homeomorphism of the disk can be very intricate and one cannot expect this simple behavior unless additional assumptions are imposed in this paper we shall assume that h is orientation preserving and that all fixed points are on the boundary that is

low rate repeat zigzag hadamard codes in this paper we propose a new class of low rate error correction codes called repeat zigzag hadamard rzh codes featuring simple encoder and decoder structures and flexible coding rate rzh codes are serially concatenated turbo like codes where the outer code is a repetition code and the inner code is a punctured zigzag hadamard zh code by analyzing the code structure of rzh codes we prove that both systematic and nonsystematic rzh codes are good codes in the sense that for an rzh code ensemble there exists a positive number gamma0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than the average block error probability of maximum likelihood ml decoding approaches zero two decoding algorithms serial and parallel decoders for rzh codes are proposed we then employ the extrinsic information transfer exit chart technique to design irregular rzh codes results show that the optimized irregular rzh codes exhibit a performance that is very close to capacity in the low rate regime

the minimum distance of turbo like codes worst case upper bounds are derived on the minimum distance of parallel concatenated turbo codes serially concatenated convolutional codes repeat accumulate codes repeat convolute codes and generalizations of these codes obtained by allowing nonlinear and large memory constituent codes it is shown that parallel concatenated turbo codes and repeat convolute codes with sub linear memory are asymptotically bad it is also shown that depth two serially concatenated codes with constant memory outer codes and sublinear memory inner codes are asymptotically bad most of these upper bounds hold even when the convolutional encoders are replaced by general finite state automata encoders in contrast it is proven that depth three serially concatenated codes obtained by concatenating a repetition code with two accumulator codes through random permutations can be asymptotically good

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

the performance of serial turbo codes does not concentrate minimum distances and maximum likelihood error probabilities of serial turbo codes with uniform interleaver are analyzed it is shown that for a fraction of interleavers approaching one as the block length grows large the minimum distance of serial turbo codes grows as a positive power of their block length while their error probability decreases exponentially fast in some positive power of their block length on sufficiently good memoryless channels such a typical code behavior contrasts the performance of the average serial turbo code whose error probability is dominated by an asymptotically negligible fraction of poorly performing interleavers and decays only as a negative power of the block length the analysis proposed in this paper relies on precise bounds of the minimum distance of the typical serial turbo code whose scaling law is shown to depend both on the free distance of its outer constituent encoder which determines the exponent of its sub linear growth in the block length and on the effective free distance of its inner constituent encoder the latter is defined as the smallest weight of codewords obtained when the input word of the inner encoder has weight two and appears as a linear scaling factor for the minimum distance of the typical serial turbo code hence despite the lack of concentration of the maximum likelihood error probability around its expected value the main design parameters suggested by the average code analysis turn out to characterize also the performance of the typical serial turbo code by showing for the first time that the typical serial turbo code s minimum distance scales linearly in the effective free distance of the inner constituent encoder the presented results generalize and improve upon the probabilistic bounds of kahale and urbanke as well as the deterministic upper bound of bazzi mahdian and spielman where only the dependence on the outer encoder s free distance was proved

global positive periodic solutions of periodic n species competition systems abstract in this paper an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n species lotka volterra type and gilpin ayala type competition systems is obtained it improves a series of the well known sufficiency theorems in the literature about the problems mentioned above the method is based on a well known fixed point theorem in a cone of banach space this approach can be applied to more general competition systems

existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls abstract sufficient conditions are obtained for the existence and global stability of a positive periodic solution in some periodic integrodifferential systems with feedback controls by using the technique of coincidence degree and lyapunov functional

accumulate repeat accumulate codes in this paper we propose an innovative channel coding scheme called accumulate repeat accumulate ara codes this class of codes can be viewed as serial turbo like codes or as a subclass of low density parity check ldpc codes and they have a projected graph or protograph representation this allows for high speed iterative decoding implementation using belief propagation an ara code can be viewed as precoded repeat accumulate ra code with puncturing or as precoded irregular repeat accumulate ira code where simply an accumulator is chosen as the precoder the amount of performance improvement due to the precoder will be called precoding gain using density evolution on their associated protographs we find some rate 1 2 ara codes with a maximum variable node degree of 5 for which a minimum bit snr as low as 0 08 db from channel capacity threshold is achieved as the block size goes to infinity such a low threshold cannot be achieved by ra ira or unstructured irregular ldpc codes with the same constraint on the maximum variable node degree furthermore by puncturing the inner accumulator we can construct families of higher rate ara codes with thresholds that stay close to their respective channel capacity thresholds uniformly iterative decoding simulation results are provided and compared with turbo codes in addition to iterative decoding analysis we analyzed the performance of ara codes with maximum likelihood ml decoding by obtaining the weight distribution of these codes and through existing tightest bounds we have shown that the ml snr threshold of ara codes also approaches very closely to that of random codes these codes have better interleaving gain than turbo codes

coexistence states for periodic competitive kolmogorov systems abstract we prove the existence of positive periodic solutions for a class of nonautonomous competitive periodic kolmogorov systems which generalize the may leonard model a necessary and sufficient condition is also obtained

on the asymptotic weight and stopping set distribution of regular ldpc ensembles in this correspondence we estimate the variance of weight and stopping set distribution of regular low density parity check ldpc ensembles using this estimate and the second moment method we obtain bounds on the probability that a randomly chosen code from regular ldpc ensemble has its weight distribution and stopping set distribution close to respective ensemble averages we are able to show that a large fraction of total number of codes have their weight and stopping set distribution close to the average

applications of robust distances for regression the dd plot introduced by rousseeuw and van driessen 1999 is a plot of classical vs robust mahalanobis distances mdi vs rdi the dd plot can be used as a diagnostic for multivariate normality and elliptical symmetry and to assess the success of numerical transformations towards elliptical symmetry in the regression context many procedures can be adversely aected if strong nonlinearities are present in the predictors even if strong nonlinearities are present the robust distances can be used to help visualize important regression models such as generalized linear models

performance of parallel concatenated coding schemes in this paper ensembles of parallel concatenated codes are studied and rigorous results on their asymptotic performance under the assumption of maximum likelihood ml decoding are presented in particular it is proven that in any parallel concatenation scheme with k branches where all k encoders are recursive and the bhattacharyya parameter of the channel is sufficiently small the bit error rate ber and the word error rate go to 0 exactly like n 1 k and n 2 k respectively different types of ensembles by changing the subgroup of permutations used to interconnect the various encoders are considered

an exclusion principle for periodic competitive systems in three dimensions an exclusion principle for periodic competitive systems in three dimensionst rafael ortega and antonio tineo departamento de matemzitica aplicada universidad de granada 18071 granada spain and departmento de matem iticas facultad de ciencias universidad de los andes 5101 m6rida venezuela received 29 february 1996 received in revised form 25 september 1996 received for publication 18 february 1997 key words and phrases logistic equation competing species problem periodic solutions exclusion principle 0 introduction in this paper we consider the following three dimensional periodic system u uifi t ul u2 u u i 0 1 0 and uif t u is locally lipschitz continuous in u we shall assume that the system is strongly competitive and dissipative and prove the following exclusion principle theorem 0 1 suppose that a f t ul 2

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance