conservative arrays multidimensional modulation codes for holographic recording in holographic storage two dimensional arrays of binary data is optically recorded in a medium via an interference process to ensure optimum operation of a holographic recording system it is desirable that the patterns of 1s light and 0s no light in the recorded array satisfy the following modulation constraint in each row and column of the array there are at least t transitions of the type 1 spl rarr 0 or 0 spl rarr 1 for a prescribed integer t a two dimensional array with this property is said to be a conservative array of strength t in general an n dimensional conservative array of strength t is a binary array having at least t transitions in each column extending in any of the n dimensions of the array we present an algorithm for encoding unconstrained binary data into an n dimensional conservative array of strength t the algorithm employs differential coding and error correcting codes using n binary codes one per dimension with minimum hamming distance d spl ges 2t 3 we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code

new mds self dual codes from generalized reed solomon codes both maximum distance separable and euclidean self dual codes have theoretical and practical importance and the study of mds self dual codes has attracted lots of attention in recent years in particular determining the existence of q ary mds self dual codes for various lengths has been investigated extensively the problem is completely solved for the case where q is even this paper focuses on the case where q is odd we construct a few classes of new mds self dual codes through generalized reed solomon codes more precisely we show that for any given even length n we have a q ary mds code as long as q equiv 1 bmod 4 and q is sufficiently large say q ge 4 n times n 2 furthermore we prove that there exists a q ary mds self dual code of length n if q r 2 and n satisfies one of the three conditions 1 n le r and n is even 2 q is odd and n 1 is an odd divisor of q 1 and 3 r equiv 3 mod 4 and n 2tr for any t le r 1 2

multiple burst correcting array codes two families of binary linear multiple burst correcting array codes are presented the codes consist of all possible n sub 1 n sub 2 arrays over gf 2 where the columns have even parity and the rows belong to any given code of length n sub 2 and minimum distance 2t it is shown that if the bits are read out diagonally instead of horizontally each diagonal followed by the preceding one viewed cyclically then the code can correct up to t bursts of length or tn sub 1 1 if each diagonal is followed by the next one the code can correct up to t bursts of length or 2t n 2 1 for t 1 some of these results are already known decoding algorithms are presented and the case t 1 is discussed in more detail

on helson matrices moment problems non negativity boundedness and finite rank we study helson matrices also known as multiplicative hankel matrices that is infinite matrices of the form m nm n m 1m nm n m 1 where is a sequence of complex numbers helson matrices are considered as linear operators on l2 n l2 n by interpreting helson matrices as hankel matrices in countably many variables we use the theory of multivariate moment problems to show that m is non negative if and only if is the moment sequence of a measure on r assuming that does not grow too fast we then characterize the non negative bounded helson matrices m as those where the corresponding moment measures are carleson measures for the hardy space of countably many variables finally we give a complete description of the helson matrices of finite rank in parallel with the classical kronecker theorem on hankel matrices

shift register synthesis modulo m the berlekamp algorithm takes a sequence of elements from a field and finds the shortest linear recurrence or linear feedback shift register that can generate the sequence we present an algorithm which generalizes berlekamp s to the case when the elements of the sequence are integers modulo m where m is an arbitrary but known integer details will be published elsewhere

shortening array codes and the perfect 1 factorization conjecture the existence of a perfect 1 factorization of the complete graph with n nodes namely kn for arbitrary even number n is a 40 year old open problem in graph theory so far two infinite families of perfect 1 factorizations have been shown to exist namely the factorizations of kp 1 and k2 p where p is an arbitrary prime number p 2 it was shown in previous work that finding a perfect 1 factorization of kn is related to a problem in coding specifically it can be reduced to constructing an mds minimum distance separable lowest density array code in this paper a new method for shortening arbitrary array codes is introduced it is then used to derive the kp 1 family of perfect 1 factorization from the k2p family namely techniques from coding theory are used to prove a new result in graph theory that the two factorization families are related

new array codes for multiple phased burst correction an optimal family of array codes over gf q for correcting multiple phased burst errors and erasures where each phased burst corresponds to an erroneous or erased column in a code array is introduced as for erasures these array codes have an efficient decoding algorithm which avoids multiplications or divisions over extension fields replacing these operations with cyclic shifts of vectors over gf q the erasure decoding algorithm can be adapted easily to handle single column errors as well the codes are characterized geometrically by means of parity constraints along certain diagonal lines in each code array thus generalizing a previously known construction for the special case of two erasures algebraically they can be interpreted as reed solomon codes when q is primitive in gf q the resulting codes become conventional reed solomon codes of length p over gf q sup p 1 in which case the new erasure decoding technique can be incorporated into the berlekamp massey algorithm yielding a faster way to compute the values of any prescribed number of errors

mds array codes for correcting a single criss cross error we present a family of maximum distance separable mds array codes of size p 1 spl times p 1 p a prime number and minimum criss cross distance 3 i e the code is capable of correcting any row or column in error without a priori knowledge of what type of error occurred the complexity of the encoding and decoding algorithms is lower than that of known codes with the same error correcting power since our algorithms are based on exclusive or operations over lines of different slopes as opposed to algebraic operations over a finite field we also provide efficient encoding and decoding algorithms for errors and erasures

a new design of binary mds array codes with asymptotically weak optimal repair binary maximum distance separable mds array codes are a special class of erasure codes for distributed storage that not only provides fault tolerance with minimum storage redundancy but also achieves low computational complexity they are constructed by encoding k information columns into r parity columns in which each element in a column is a bit such that any k out of the k r columns suffice to recover all information bits in addition to providing fault tolerance it is critical to improve repair performance in practical applications specifically if a single column fails then our goal is to minimize the repair bandwidth by downloading the least amount of bits from d healthy columns where k leq d leq k r 1 if one column of an mds code is failed it is known that we need to download at least 1 d k 1 fraction of the data stored in each of the d healthy columns if this lower bound is achieved for the repair of the failure column from accessing arbitrary d healthy columns we say that the mds code has optimal repair however if such lower bound is only achieved by d specific healthy columns then we say the mds code has weak optimal repair in this paper we propose two explicit constructions of binary mds array codes with more parity columns i e r geq 3 that achieve asymptotically weak optimal repair where k 1 leq d leq k lfloor r 1 2 rfloor and asymptotic means that the repair bandwidth achieves the minimum value asymptotically in d codes in the first construction have odd number of parity columns and asymptotically weak optimal repair for anyone information failure while codes in the second construction have even number of parity columns and asymptotically weak optimal repair for any one column failure

codes with local regeneration and erasure correction regenerating codes and codes with locality are two coding schemes that have recently been proposed which in addition to ensuring data collection and reliability also enable efficient node repair in a situation where one is attempting to repair a failed node regenerating codes seek to minimize the amount of data downloaded for node repair while codes with locality attempt to minimize the number of helper nodes accessed this paper presents results in two directions in one this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures by employing local codes having minimum distance 2 an upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed the second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes these codes termed here as codes with local regeneration are codes with locality over a vector alphabet in which the local codes themselves are regenerating codes we derive an upper bound on the minimum distance of vector alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property this property is possessed by both minimum storage regeneration msr and minimum bandwidth regeneration mbr codes we provide several constructions of codes with local regeneration which achieve this bound where the local codes are either msr or mbr codes also included in this paper is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance

x code mds array codes with optimal encoding we present a new class of mds maximum distance separable array codes of size n spl times n n a prime number called x code the x codes are of minimum column distance 3 namely they can correct either one column error or two column erasures the key novelty in x code is that it has a simple geometrical construction which achieves encoding update optimal complexity i e a change of any single information bit affects exactly two parity bits the key idea in our constructions is that all parity symbols are placed in rows rather than columns

banach spaces of general dirichlet series abstract we study when the spaces of general dirichlet series bounded on a half plane are banach spaces and show that some of those classes are isometrically isomorphic between themselves in a precise way let n be a strictly increasing sequence of positive real numbers such that lim n n we denote by h n the complex normed space of all dirichlet series d s n b n n s which are convergent and bounded on the half plane re s 0 endowed with the norm d sup re s 0 d s if there exists q 0 such that inf n n 1 q n q 0 then h n is a banach space further if there exists a strictly increasing sequence r n of positive numbers such that the sequence log r n is q linearly independent n r for n p and n is the increasing rearrangement of the sequence n then h n is isometrically isomorphic to h b c 0 with this condition we explain more explicitly the optimal cases of the difference among the abscissas c b u and a

zeros of functions in hilbert spaces of dirichlet series the dirichlet hardy space fancyscript h 2 consists of those dirichlet series sum n a n n s for which sum n a n 2 1 2 is a necessary and sufficient condition for the existence of a nontrivial function f in fancyscript h 2 vanishing on a given bounded sequence the proof implies in fact a stronger result every function in the hardy space h 2 of the half plane text re s 1 2 can be interpolated by a function in fancyscript h 2 on such a blaschke sequence analogous results are proved for the hilbert space fancyscript d alpha of dirichlet series sum n a n n s for which sum n a n 2 d n alpha 1 2 partial results are then obtained for the zeros of functions in fancyscript h p l p analogues of fancyscript h 2 for 2 p infty based on certain contractive embeddings of fancyscript d alpha in fancyscript h p

norms of composition operators on the h2 space of dirichlet series abstract we consider composition operators c on the hardy space of dirichlet series h 2 generated by dirichlet series symbols we prove two different subordination principles for such operators one concerns affine symbols only and is based on an arithmetical condition on the coefficients of the other concerns general symbols and is based on a geometrical condition on the boundary values of both principles are strict in the sense that they characterize the composition operators of maximal norm generated by symbols having given mapping properties in particular we generalize a result of j h shapiro on the norm of composition operators on the classical hardy space of the unit disc based on our techniques we also improve the recently established upper and lower norm bounds in the special case that s c r 2 s a number of other examples are given

the multiplicative hilbert matrix abstract it is observed that the infinite matrix with entries m n log m n 1 for m n 2 appears as the matrix of the integral operator h f s 1 2 f w w s 1 d w with respect to the basis n s n 2 here s is the riemann zeta function and h is defined on the hilbert space h 0 2 of dirichlet series vanishing at and with square summable coefficients this infinite matrix defines a multiplicative hankel operator according to helson s terminology or alternatively it can be viewed as a bona fide small hankel operator on the infinite dimensional torus t by analogy with the standard integral representation of the classical hilbert matrix this matrix is referred to as the multiplicative hilbert matrix it is shown that its norm equals and that it has a purely continuous spectrum which is the interval 0 these results are in agreement with known facts about the classical hilbert matrix it is shown that the matrix m 1 p n p 1 p log m n 1 has norm sin p when acting on l p for 1 p however the multiplicative hilbert matrix fails to define a bounded operator on h 0 p for p 2 where h 0 p are h p spaces of dirichlet series it remains an interesting problem to decide whether the analytic symbol n 2 log n 1 n s 1 2 of the multiplicative hilbert matrix arises as the riesz projection of a bounded function on the infinite dimensional torus t

volterra operators on hardy spaces of dirichlet series for a dirichlet series symbol g s n 1bnn s the associated volterra operator tg acting on a dirichlet series f s n 1ann s is defined by the integral f sf w g w dw we show that tg is a bounded operator on the hardy space hp of dirichlet series with 0 0 whenever tg is bounded in particular such g belong to hp for every p we relate the boundedness of tg to several other bmo type spaces bmoa in half planes the dual of h1 and the space of symbols of bounded hankel forms moreover we study symbols whose coefficients enjoy a multiplicative structure and obtain coefficient estimates for m homogeneous symbols as well as for general symbols finally we consider the action of tg on reproducing kernels for appropriate sequences of subspaces of h2 our proofs employ function and operator theoretic techniques in one and several variables a variety of number theoretic arguments are used throughout the paper in our study of special classes of symbols g

braided block codes a new class of binary iteratively decodable codes with good decoding performance is presented these codes called braided block codes bbcs operate on continuous data streams and are constructed by interconnection of two component block codes bbcs can be considered as convolutional or sliding version of either elias product codes or expander codes in this paper we define bbcs describe methods of their construction analyze code properties and study asymptotic iterative decoding performance

acoustic boundary condition for unsteady one dimensional flow calculations abstract a new calculation method is presented that allows the use of the acoustic characteristics of a given singularity as a boundary condition for a non linear one dimensional flow calculation the method is based on the one hand on the non linear decomposition of the pressure perturbation into forward and backward components and on the other hand on the possibility of representing a certain singularity by means of its reflection and transmission coefficients the response of the singularity to the incident pressure components is calculated in the frequency domain and imposed as a boundary condition for the time domain calculation in the rest of the duct the procedure being iterative in this way the calculation takes into account both the acoustic behaviour of the singularity and its interaction with the acoustic source and the rest of the system considered the method is applied to the computation of the flow in the exhaust pipe of a four cylinder spark ignition engine when a complex commercial silencer is used and the results show good agreement with experimental measurements both for in duct pressure and for radiated noise

on the stopping distance of array code parity check matrices for q an odd prime and 1 les m les q we study two binary qm times q2 parity check matrices for binary array codes for both parity check matrices we determine the stopping distance and the minimum distance of the associated code for 2 les m les 3 and for m q 4 5 in the case m q 4 7 the stopping distance and the related minimum distance are also determined for one of the given parity check matrices moreover we give a lower bound on the stopping distances for m 3 and q 3

cross parity check convolutional codes a class of convolutional codes called cross parity check cpc codes which are useful for the protection of data stored on magnetic tape is described and analyzed cpc codes are first explained geometrically their construction is described in terms of constraining data written onto a tape in such a way that when lines of varying slope are drawn across the tape the bits falling on those lines sum to zero modulo two this geometric interpretation is then formalized by the construction of canonical parity check matrices and systematic generator matrices for cpc codes and by computing their constraint lengths the distance properties of cpc codes are analyzed and it is shown that these codes are maximum distance separable convolutional codes in addition examples are given of both error and erasure decoding algorithms that take advantage of the geometric regularity of cpc codes the technique of parity check matrix reduction which is useful for reducing the inherent decoding delay of cpc codes is described the technique consists of dividing each term of the parity check matrix by some polynomial and retaining only the remainder a class of polynomials that are particularly attractive for this purpose if identified

composition operators and embedding theorems for some function spaces of dirichlet series we observe that local embedding problems for certain hardy and bergman spaces of dirichlet series are equivalent to boundedness of a class of composition operators following this we perform a careful study of such composition operators generated by polynomial symbols varphi on a scale of bergman type hilbert spaces mathscr d alpha we investigate the optimal beta such that the composition operator mathscr c varphi maps mathscr d alpha boundedly into mathscr d beta we also prove a new embedding theorem for the non hilbertian hardy space mathscr h p into a bergman space in the half plane and use it to consider composition operators generated by polynomial symbols on mathscr h p finding the first non trivial results of this type the embedding also yields a new result for the functional associated to the multiplicative hilbert matrix

a hybrid boundary for the prediction of intake wave dynamics in ic engines abstract this paper concerns the calculation of wave dynamics in the intake systems of naturally aspirated internal combustion ic engines in particular it presents a method for improving the boundary conditions required to solve the one dimensional euler equations that are commonly used to describe the wave dynamics in time and space a number of conclusions are reached in this work the first relates to the quasi steady state inflow boundary specified in terms of ingoing and outgoing characteristics that is commonly adopted for engine simulation this is correctly specified by using the pair of primitive variables pressure p and density but will be unrealistic at frequencies above a hemholtz number of 0 1 as only stagnation values po o are used for the case of ic engine intake simulations this sets a maximum frequency of around 300 hz above that frequency the results obtained will become increasingly unrealistic secondly a hybrid time and frequency domain boundary has been developed and tested against linear acoustic theory this agrees well with results obtained using a quasi steady state boundary at low frequencies helmholtz number less than 0 1 and should remain realistic at higher frequencies in the range of helmholtz number 0 1 1 84 thirdly the cyclic nature of the operation of the ic engine has been exploited to make use of the inverse fourier transform to develop an analytical hybrid boundary that functions for non sinusoidal waves in ducts the method is self starting does not rely on iterations over complete cycles and is entirely analytical and therefore is an improvement over earlier hybrid boundaries

time domain computation of muffler frequency response comparison of different numerical schemes abstract a comparative study of the performance of different schemes used to solve one dimensional gas flow equations when applied to the computation of the frequency response of exhaust mufflers is presented simple but representative systems with well known acoustic behaviour were considered apart from the classical lax wendroff and maccormack schemes the total variation diminishing schemes flux corrected transport techniques or the innovative space time conservation element and solution element method were considered the results provide guidelines for a proper choice of the numerical scheme taking into account the mesh spacing

an encoding algorithm of triply extended reed solomon codes with asymptotically optimal complexities in this paper we devise a fast encoding algorithm for triply extended reed solomon codes the proposed approach requires approximately two xors per bit which improves the prior result of three xors per bit established by certain maximum distance separable mds array codes we also prove that for mds codes with two and three parities the scheduling algorithms require at least two xors per bit to the best of our knowledge this is the first provable scheduling algorithm for the triple parity mds codes to approach the theoretical lower bounds the implementation with simd instructions is provided the simulations show that the proposed approach is competitive as compared with other cutting edge implementations

a non linear quasi 3d model with flux corrected transport for engine gas exchange modelling modelling has proven to be an important tool in the design of manifolds and silencers for internal combustion engines although simple 1d models are generally sufficiently precise in the case of manifold models they would usually fail to predict the high frequency behaviour of modern compact manifold designs and of course of a complex shaped silencing system complete 3d models are able to account for transversal modes and other non 1d phenomena but at a high computational cost a suitable alternative is provided by time domain non linear quasi 3d models whose computational cost is relatively low but still providing an accurate description of the high frequency behaviour of certain elements in this paper a quasi 3d model which makes use of a non linear second order time and space discretization based on finite volumes is presented as an alternative for avoiding overshoots at discontinuities a flux corrected transport technique has been adapted to the quasi 3d method in order to achieve convergence and avoid numerical dispersion it is shown that the combination of dissipation via damping together with the phoenical form of the anti diffusion term provides satisfactory results

addendum to a hilbert space of dirichlet series and systems of dilated functions in l 2 0 1 addendum to a hilbert space of dirichlet series and systems of dilated functions in l 2 0 1

formulation and validation of boundary conditions at a branched junction for nonlinear waves abstract a numerical model is presented for the calculation of nonlinear waves through the branched junctions in a gas transmission pipe system in the one dimensional time domain analysis of the wave dynamics the behaviour of the nonlinear waves is determined by quasi steady boundary conditions at junctions in a pipe system the quasi steady treatment through the junction yields a system of nonlinear balance equations the iterative solution procedure of the system of nonlinear equations causes the problems of divergence and multiple solutions in order to overcome the difficulties a new set of quasi linear balance equations is formulated without a sacrifice of accuracy the present model therefore requires a non iterative solution procedure that results in a unique solution and a smaller computational effort thompson s boundary condition is used at each pipe a new time derivative form of balance equations based thompson boundary condition gives a set of linear algebraic equations for the balance equations when implementing the new time derivative form of the balance equations corrected terms are added numerically the present numerical model is implemented and tested for the calculation of behaviour of nonlinear waves in a branched pipe and the calculation of sound attenuation of a helmholtz resonator and the prediction of radiated orifice noise of an internal combustion engine calculation results show good agreements with previous iterative calculations and measurement data

application of maccormack schemes to i c engine exhaust noise prediction non linear flow calculations are a usual tool for describing the flow inside intake and exhaust systems of internal combustion engines therefore they may also be used to estimate the noise radiated by these systems most of the work reported in this field is related to the use of the method of characteristics and some references to the use of the lax wendroff finite differences scheme are also found in this paper maccormack predictor corrector schemes are shown to be less dispersive and slightly faster than the lax wendroff scheme and are used to solve the one dimensional flow equations in the case of the exhaust system of a single cylinder engine a modification of the treatment of the source terms is proposed which results in a considerable reduction in the computation time without any loss of information an iterative procedure has been devised that allows the use with this finite differences scheme of boundary conditions developed to be used with the method of characteristics comparison with experimental results is given for the case of an exhaust duct without muffler and with an expansion chamber showing fair agreement in both cases

constructions of high rate minimum storage regenerating codes over small fields a novel technique for construction of minimum storage regenerating msr codes is presented based on this technique three explicit constructions of msr codes are given the first two constructions provide access optimal msr codes with two and three parities respectively which attain the sub packetization bound for access optimal codes the third construction provides longer msr codes with three parities i e codes with larger number of systematic nodes this improvement is achieved at the expense of the access optimality and the field size in addition to a minimum storage in a node all three constructions allow the entire data to be recovered from a minimal number of storage nodes that is given storage ell in each node the entire stored data can be recovered from any 2 log 2 ell for two parity nodes and either 3 log 3 ell or 4 log 3 ell for three parities second in the first two constructions a helper node accesses the minimum number of its symbols for repair of a failed node access optimality the goal of this paper is to provide a construction of such optimal codes over the smallest possible finite fields the generator matrix of these codes is based on perfect matchings of complete graphs and hypergraphs and on a rational canonical form of matrices for two parities the field size is reduced by a factor of two for access optimal codes compared to previous constructions for three parities in the first construction a field size of at least 6 log 3 ell 1 or 3 log 3 ell 1 for fields with characteristic 2 is sufficient and in the second construction the field size is larger yet linear in log 3 ell both constructions with three parities provide a significant improvement over previous works due to either decreased field size or lower subpacketization

error correcting regenerating and locally repairable codes via rank metric codes this paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings one being storage using existing regenerating codes and the second being storage using locally repairable codes the concatenated coding scheme brings together a maximum rank distance code as an outer code and either a globally regenerating or a locally repairable code as an inner code in addition error resilience for combination of locally repairable codes with regenerating codes is considered this concatenated coding system is designed to handle two different types of adversarial errors the first type includes an adversary that can replace the content of an affected node only once while the second type studies an adversary that is capable of polluting data an unbounded number of times the paper establishes an upper bound on the resilience capacity for a locally repairable code this paper also proves that the proposed concatenated coding approach attains the upper bound on the resilience capacity in the presence of the first type of adversary for both minimum storage regenerating codes and locally repairable codes further this paper presents mechanisms that combine the presented concatenated coding scheme with subspace signatures to achieve error resilience for the second type of errors

contractive inequalities for bergman spaces and multiplicative hankel forms we consider sharp inequalities for bergman spaces of the unit disc establishing analogues of the inequality in carleman s proof of the isoperimetric inequality and of weissler s inequality for dilations by contractivity and a standard tensorization procedure the unit disc inequalities yield corresponding inequalities for the bergman spaces of dirichlet series we use these results to study weighted multiplicative hankel forms associated with the bergman spaces of dirichlet series reproducing most of the known results on multiplicative hankel forms associated with the hardy spaces of dirichlet series in addition we find a direct relationship between the two type of forms which does not exist in lower dimensions finally we produce some counter examples concerning carleson measures on the infinite polydisc

block markov superposition transmission construction of big convolutional codes from short codes a construction of big convolutional codes from short codes called block markov superposition transmission bmst is proposed the bmst is very similar to superposition block markov encoding sbme which has been widely used to prove multiuser coding theorems the bmst codes can also be viewed as a class of spatially coupled codes where the generator matrices of the involved short codes referred to as basic codes are coupled the encoding process of bmst can be as fast as that of the basic code while the decoding process can be implemented as an iterative sliding window decoding algorithm with a tunable delay more importantly the performance of bmst can be simply lower bounded in terms of the transmission memory given that the performance of the short code is available numerical results show that 1 the lower bounds can be matched with a moderate decoding delay in the low bit error rate ber region implying that the iterative sliding window decoding algorithm is near optimal 2 bmst with repetition codes and single parity check codes can approach the shannon limit within 0 5 db at the ber of 10 5 for a wide range of code rates and 3 bmst can also be applied to nonlinear codes

local properties of hilbert spaces of dirichlet series we show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the hilbert space of dirichlet series defined using these as weights this extends results recently obtained describing the local behavior of dirichlet series with square summable coefficients in terms of local integrability boundary behavior carleson measures and interpolating sequences as these spaces can be identified with functions spaces on the infinite dimensional polydisk this gives new results on the dirichlet and bergman spaces on the infinite dimensional polydisk as well as the scale of besov sobolev spaces containing the drury arveson space on the infinite dimensional unit ball we use both techniques from the theory of sampling in paley wiener spaces and classical results from analytic number theory c 2011 elsevier inc all rights reserved less

design of network codes for multiple user multiple relay wireless networks we investigate the design of network codes for multiple user multiple relay mumr wireless networks with slow fading quasi static channels in these networks m users have independent information to be transmitted to a common base station bs with the help of n relays where m 2 and n 1 are arbitrary integers we investigate such networks in terms of diversity order to measure asymptotic performance for networks with orthogonal channels we show that network codes based on maximum distance separable mds codes can achieve the maximum diversity order of n 1 we further show that the mds coding construction of network codes is also necessary to obtain full diversity for linear finite field network coding ffnc then we compare the performance of the ffnc approach with superposition coding sc at the relays the results show that the ffnc based on mds codes has better performance than sc in both the high rate and the high snr regime further we discuss networks without direct source to bs channels for n m we show that the proposed ffnc can obtain the diversity order n m 1 which is equivalent to achieving the singleton bound for network error correction codes finally we study the network with nonorthogonal channels and show our codes can still achieve a diversity order of n 1 which cannot be achieved by a scheme based on sc

prediction of the acoustical performances of muffling pipe systems by the method of characteristics abstract a numerical model is presented for the calculation of sound attenuation of flow duct systems in the frequency domain the method of characteristics is used to solve the non linear hyperbolic problem of plane wave motion in ducts the basic conservation equations are not linearized to achieve a comparison between linear model and gas dynamic model predictions boundary conditions providing acoustic excitation of the duct system are explained and details are given about the calculation of the transfer functions of muffling pipe systems including some numerical algorithms to achieve satisfactory predictions by the method of characteristics end corrections have been introduced to take account of phase shifts in the wave reflection at open terminations as well as at abrupt area changes a comparison between experimental attenuation curves measured in a semi anechoic room and calculated ones is displayed for some simple geometries including helmholtz resonators and expansion chambers and shows a fairly good agreement

low complexity array codes for random and clustered 4 erasures a new family of low complexity array codes is proposed for correcting 4 column erasures the new codes are tailored for the new error model of clustered column erasures that captures the properties of high order failure combinations in storage arrays the model of clustered column erasures considers the number of erased columns together with the number of clusters into which they fall without pre defining the sizes of the clusters this model addresses the problem of correlated device failures in storage arrays whereby each failure event may affect multiple devices in a single cluster the new codes correct essentially all combinations of clustered 4 erasures i e those combinations that fall into three or less clusters the new codes are significantly more efficient in all relevant complexity measures than the best known 4 erasure correcting codes these measures include encoding complexity decoding complexity and update complexity

on lowest density mds codes let f sub q denote the finite field gf q and let h be a positive integer mds maximum distance separable codes over the symbol alphabet f sub q sup b are considered that are linear over f sub q and have sparse low density parity check and generator matrices over f sub q that are systematic over f sub q sup b lower bounds are presented on the number of nonzero elements in any systematic parity check or generator matrix of an f sub q linear mds code over f sub q sup b along with upper bounds on the length of any mds code that attains those lower bounds a construction is presented that achieves those bounds for certain redundancy values the building block of the construction is a set of sparse nonsingular matrices over f sub q whose pairwise differences are also nonsingular bounds and constructions are presented also for the case where the systematic condition on the parity check and generator matrices is relaxed to be over f sub q rather than over f sub q sup b

maximizing burst erasure correction capability of mds codes in general an n k maximum distance separable mds code over gf pm can not correct all burst erasures of length n k m over gf p in this letter we constructively show that such a linear mds code over gf pm can be modified to correct all burst erasures of length up to n k m over gf p while maintaining its mds property over gf pm

algebraic characterization of mds group codes over cyclic groups an n k group code over a group g is a subset of g sup n which forms a group under componentwise group operation and can be defined in terms of n k homomorphisms from g sup k to g the set of homomorphisms which define maximum distance separable mds group codes defined over cyclic groups are characterized each defining homomorphism can be specified by a set of k endomorphisms of g a matrix is associated with the k n k defining endomorphisms of the code and necessary and sufficient conditions for this matrix to define an mds code over cyclic groups is proved using this matrix characterization it is proved that over a cyclic group with m elements where m p sub 1 sup d 1 p sub 2 sup d 2 spl middot spl middot spl middot p sub m sup d m k s k mds group codes for all s k spl ges 2 do not exist if max s k spl ges min p sub 1 p sub 2 spl middot spl middot p sub m finally it is shown that the dual code of an mds group code over c sub m a cyclic group with m elements is also an mds group code

experimental validation of a new semi implicit ce se scheme for the calculation of unsteady one dimensional flow in tapered ducts this paper presents an improvement in the conservation element solution element ce se scheme for calculating one dimensional flow through tapered ducts this new ce se scheme has been validated against experiments in tapered ducts with non steady flow using pressure impulses this validation analyses scheme s ability to reproduce instantaneous pressure in time and frequency domains mass conservation when the section of the duct changes which was the main drawback of the original ce se scheme and finally computational time in order to quantify the improvement of the scheme the calculations have been compared with experimental data and with the results provided by other schemes such as the original ce se or total variation diminishing schemes this comparison shows important improvements in mass conservation in relation to the original ce se and not significant penalties in computational time copyright 2007 john wiley sons ltd

two dimensional half rate codes using two dimensional finite field filter banks this correspondence introduces two dimensional 2 d filter bank codes tdfbcs the synthesis bank of a two channel two dimensional filter bank over a finite field is used to design the 2 d code and the corresponding analysis bank is used to generate the syndrome of the code first we study the encoder of half rate tdfbcs and show that these linear codes are lattice cyclic it is proven that any 2 d lattice cyclic code can also be generated by a 2 d filter bank second we introduce a methodology to design tdfbcs over binary erasure channels these codes have a simple and efficient maximum likelihood ml decoding algorithm for burst erasures we show that half rate tdfbcs of dimensions n1 x n2 can recover burst erasures of size up to n1 x n2 2 and n1 2 x n2 using the proposed decoding technique finally we present examples of tdfbcs that satisfy the reiger bound with equality i e they are capable of correcting any burst of size n1 x n2 2

new efficient mds array codes for raid part ii rabin like codes for tolerating multiple spl ges 4 disk failures for pt 1 see ibid vol 54 no 9 p 1071 1080 2005 a new class of binary maximum distance separable mds array codes which are based on circular permutation matrices are introduced in this paper these array codes are used for tolerating multiple spl ges 4 disk failures in redundant arrays of inexpensive disks raid architecture the size of the information part is m spl times n where n is the number of information disks and m 1 is a prime integer the size of the parity check part is m spl times r the minimum distance is r 1 and the number of parity check disks is r in practical applications m can be very large and n ranges from 20 to 50 the code rate is r n n r these codes can be used for tolerating up to r disk failures with very fast encoding and decoding the complexities of encoding and decoding algorithms are o rmn and o m sup 3 r sup 4 respectively when r 4 there need to be 9mn xor operations for encoding and 9n 95 m 1 xor operations for decoding

a class of burst error correcting array codes corresp the usual k 2 1 times k 1 1 array code in which the last row and the last column contain redundant bits can correct any single error however if the bits are read diagonally instead of horizontally the code can correct bursts of errors it is shown that the k 2 1 times k 1 1 array code with diagonal readout can correct any burst of length up to k 1 if and only if k 2 geq 2 k 1 1

ldpc codes for 2d arrays binary codes over 2d arrays are very useful in data storage where each array column represents a storage device or unit that may suffer failure in this paper we propose a new framework for probabilistic construction of codes on 2d arrays instead of a pure combinatorial erasure model used in traditional array codes we propose a mixed combinatorial probabilistic model of limiting the number of column failures and assuming a binary erasure channel in each failing column for this model we give code constructions and detailed analysis that allow sustaining a large number of column failures with graceful degradation in the fraction of erasures correctable in failing columns another advantage of the new framework is that it uses low complexity iterative decoding the key component in the analysis of the new codes is to analyze the decoding graphs induced by the failed columns and infer the decoding performance as a function of the code design parameters as well as the array size and failure parameters a particularly interesting class of codes called probabilistically maximum distance separable mds array codes gives fault tolerance that is equivalent to traditional mds array codes the results also include a proof that the 2d codes outperform standard 1d low density parity check codes

nearly optimal constructions of pir and batch codes in this paper we study two families of codes with availability namely private information retrieval pir codes and batch codes while the former requires that every information symbol has k mutually disjoint recovering sets the latter imposes this property for each multiset request of k information symbols the main problem under this paradigm is to minimize the number of redundancy symbols we denote this value by r p n k and r b n k for pir codes and batch codes respectively where n is the number of information symbols previous results showed that for any constant k r p n k theta sqrt n and r b n k mathcal o sqrt n log n in this paper we study the asymptotic behavior of these codes for non constant k and specifically for k theta n epsilon we also study the largest value of k such that the rate of the codes approaches 1 and show that for all epsilon r p n n epsilon o n and r b n n epsilon o n furthermore several more results are proved for the case of fixed k

new efficient mds array codes for raid part i reed solomon like codes for tolerating three disk failures this paper presents a class of binary maximum distance separable mds array codes for tolerating disk failures in redundant arrays of inexpensive disks raid architecture based on circular permutation matrices the size of the information part is m spl times n the size of the parity check part is m spl times 3 and the minimum distance is 4 where n is the number of information disks the number of parity check disks is 3 and m 1 is a prime integer in practical applications m can be very large and n is from 20 to 50 the code rate is r n n 3 these codes can be used for tolerating three disk failures the encoding and decoding of the reed solomon like codes are very fast there need to be 3mn xor operations for encoding and 3mn 9 m 1 xor operations for decoding

on the hamming distance properties of group codes under certain mild conditions the minimum hamming distance d of an n k d group code c over a non abelian group g is bounded by d n 2 consequently there exists no n k n k 1 group code c over an non abelian group g if 1

more on the stopping and minimum distances of array codes for q an odd prime and 1 m q two specific binary qm q2 parity check matrices denoted by hp m q and hi m q are considered the corresponding binary codes cp m q and ci m q respectively are called proper and improper array codes with parameters m and q given a parity check matrix h representing a binary code c let s h denote the stopping distance of h and d c be the minimum hamming distance of c it is known that that s hi m q s hp m q d ci m q d cp m q for m 3 in this paper we show that these equalities do not hold for all values of m and q in particular although s hp 4 7 d cp 4 7 8 we have s hi 4 7 9 and d ci 4 7 10 it is also shown that s hp 5 1 dcp 5 11 10 while s hi 5 11 11 and d ci 5 11 12 this suggests that in many cases the improper array codes would perform better than the proper array codes over the awgn and binary erasure channels performance results are given which confirm this claim the combinatorial structure of the eight element stopping sets for h m 4 q 5 is also determined

modifications to the lax wendroff scheme for hyperbolic systems with source terms for wave phenomena in one spatial dimension governed by hyperbolic partial differential equations with source terms the standard lax wendroff scheme leads to oscillations at discontinuous wavefronts even if the courant friedrich lewy cfl number is set equal to unity we modify the lax wendroff scheme for hyperbolic systems with source terms based on characteristic analysis to preserve the wave profile correctly when the cfl number is set equal to 1 the new scheme can be used as easily as the original lax wendroff scheme since the calculation of the characteristics is not introduced in the new scheme thus additional computations of characteristics are not necessary we also extend our method for higher spatial dimensions and illustrate our approach by numerical examples copyright 1999 john wiley sons ltd

xi code a family of practical lowest density mds array codes of distance 4 designing the lowest density maximum distance separable mds array codes has gained much attention in recent years due to the optimal redundancy and minimum update penalty lowest density of such codes however the existing lowest density mds array codes of distance 4 have extremely strict constraints on the code length which makes them impractical in particular most of them require the code length to be p or p 1 where p is a prime that satisfies i 3 p 1 and ii 2 is primitive in mathrm gf p in this paper we propose a new family of the lowest density mds array codes of distance 4 called xi code it has the properties of 1 being capable of correcting both triple erasures and a single error combined with one erasure 2 having code length of either p or p 1 with p being an odd prime number 3 achieving optimality in encoding and update and 4 achieving optimality in erasure decoding for certain erasure patterns and near optimality for other erasure patterns it is worth mentioning that xi code is the first discovered family of the lowest density mds array codes of distance 4 that supports the code length of p or p 1 with p being an odd prime

a class of array codes correcting multiple column erasures a family of binary array codes of size p 1 spl times n with p a prime correcting multiple column erasures is proposed the codes coincide with a subclass of shortened reed solomon codes and achieve the maximum possible correcting capability complexity of encoding and decoding is proportional to rnp where r is the number of correctable erasures i e is simpler than the forney decoding algorithm the length n of the codes is at most 2p 1 that is twice as big as the length of the blaum roth codes having comparable decoding complexity

flux corrected transport this paper describes a class of explicit eulerian finite difference algorithms for solving the continuity equation which are built around a technique called flux correction these flux corrected transport fct algorithms are of indeterminate order but yield realistic accurate results in addition to the mass conserving property of most conventional algorithms the fct algorithms strictly maintain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well this first paper concentrates on a simple one dimensional version of fct utilizing shasta a new transport algorithm for the continuity equation which is described in detail

cyclic lowest density mds array codes three new families of lowest density maximum distance separable mds array codes are constructed which are cyclic or quasi cyclic in addition to their optimal redundancy mds and optimal update complexity lowest density the symmetry offered by the new codes can be utilized for simplified implementation in storage applications the proof of the code properties has an indirect structure first mds codes that are not cyclic are constructed and then transformed to cyclic codes by a minimum distance preserving transformation

hilbert spaces of dirichlet series and their multipliers we consider various hilbert spaces of dirichlet series whose norms are given by weighted 2 norms of the dirichlet coefficients we describe the multiplier algebras of these spaces the functions in the multiplier algebra may or may not extend to be analytic on a larger half plane than the functions in the hilbert space

phased burst error correcting array codes various aspects of single phased burst error correcting array codes are explored these codes are composed of two dimensional arrays with row and column parities with a diagonally cyclic readout order they are capable of correcting a single burst error along one diagonal optimal codeword sizes are found to have dimensions n sub 1 n sub 2 such that n sub 2 is the smallest prime number larger than n sub 1 these codes are capable of reaching the singleton bound a new type of error approximate errors is defined in q ary applications these errors cause data to be slightly corrupted and therefore still close to the true data level phased burst array codes can be tailored to correct these codes with even higher rates than before

codes correcting phased burst erasures we introduce a family of binary array codes of size t spl times n correcting multiple phased burst erasures of size t the codes achieve maximal correcting capability i e being considered as codes over gf 2 sup t they are mds the length of the codes is n spl sigma sub l 1 sup l sub l sup t where l is a constant or is slowly growing in t the complexity of encoding and decoding is proportional to rnml where r is the number of correctable erasures and m is the smallest number such that 2 sup t 1 modulo m this compares favorably with the complexity of decoding codes obtained from the shortened reed solomon codes having the same parameters

on the minimum distance of array codes as ldpc codes for a prime q and an integer j spl les q the code c q j is a class of low density parity check ldpc codes from array codes which has a nice algebraic structure in this correspondence we investigate the minimum distance d q j of the code in an algebraic way we first prove that the code is invariant under a doubly transitive group of affine permutations then we show that d 5 4 8 d 7 4 8 and d q 4 spl ges 10 for any prime q 7 in addition we also analyze the codewords of weight 6 in the case of j 3 and the codewords of weight 8 in c 5 4 and c 7 4

access versus bandwidth in codes for storage maximum distance separable mds codes are widely used in storage systems to protect against disk node failures a node is said to have capacity l over some field f if it can store that amount of symbols of the field an n k l mds code uses n nodes of capacity l to store k information nodes the mds property guarantees the resiliency to any n k node failures an optimal bandwidth respectively optimal access mds code communicates respectively accesses the minimum amount of data during the repair process of a single failed node it was shown that this amount equals a fraction of 1 n k of data stored in each node in previous optimal bandwidth constructions l scaled polynomially with k in codes when the asymptotic rate is less than 1 moreover in constructions with a constant number of parities i e when the rate approaches 1 l is scaled exponentially with k in this paper we focus on the case of linear codes with linear repair operations and constant number of parities n k r and ask the following question given the capacity of a node l what is the largest number of information disks k in an optimal bandwidth respectively access k r k l mds code we give an upper bound for the general case and two tight bounds in the special cases of two important families of codes the first is a family of codes with optimal update property and the second is a family with optimal access property moreover the bounds show that in some cases optimal bandwidth codes have larger k than optimal access codes and therefore these two measures are not equivalent

analysis of acoustic networks including cavities by means of a linear finite volume method abstract a procedure allowing for the analysis of complex acoustic networks including three dimensional cavities described in terms of zero dimensional equivalent elements is presented and validated the procedure is based on the linearization of the finite volume method often used in gas dynamics which is translated into an acoustic network comprising multi ports accounting for mass exchanges between the finite volumes and equivalent 2 ports describing momentum exchange across the volume surfaces the application of the concept to a one dimensional case shows that it actually converges to the exact analytical solution when a sufficiently large number of volumes are considered this has allowed the formulation of an objective criterion for the choice of a mesh providing results with a prefixed error up to a certain helmholtz number which has been generalized to three dimensional cases the procedure is then applied to simple but relevant three dimensional geometries in the absence of a mean flow showing good agreement with experimental and other computational results