estimates for a family of multi linear forms abstract we consider a special class of the multi linear forms studied by brascamp and lieb 1976 7 for these forms we give a characterization of the l p spaces for which the form is bounded this characterization appears in earlier work of barthe 1998 1 we use this characterization to study a non linear map that arises in scattering theory

an optimal two transmit antenna space time code and its stacked extensions a space time code is proposed that exhibits the highest coding gain among competing full rate full transmit diversity space time codes for the two transmit and receive antenna coherent quasi static fading channel the proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation qam information symbols in two dimensions the existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations an analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code moreover the coding gain of the proposed code is independent of its rate this implies that the proposed code achieves the optimal diversity multiplexing tradeoff curve for the two transmit antenna system a stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas performance enhancement in several scenarios is verified through simulations

trace orthonormal full diversity cyclotomic space time codes in this paper we consider the design of full diversity space time codes for a coherent multiple input multiple output mimo communication system starting from both the information theoretic and detection error viewpoints we first establish that a desirable property for general linear dispersion ld codes is to have an interunitary as well as an intraunitary structure a structure we call trace orthonormality by imposing the trace orthonormal structure on an ld code and applying cyclotomic number theory we establish for an arbitrary number of transmitter and receiver antennas a systematic and simple method to jointly design a unitary cyclotomic matrix the diophantine number and the corresponding constellation for an ld code as a result this enables us to construct full diversity rectangular cyclotomic ld codes with any symbol transmission rate less than or equal to the number of transmitter antennas in addition for the case when the number of transmitter antennas is greater than the number of receiver antennas by taking advantage of the delay we also arrive at the design of a special trace orthonormal full diversity cyclotomic space time block code which for the number of transmitter antenna being equal to 2m can be proved to minimize the worst case pairwise error probability of a maximum likelihood ml detector for a q ary quadrature amplitude modulation qam signal constellation and therefore achieves optimal coding gain computer simulations show that these codes have bit error performance advantages over currently available codes

some designs and normalized diversity product upper bounds for lattice based diagonal and full rate space time block codes in this paper we first present two tight upper bounds for the normalized diversity products or product distances of 2ntn2 diagonal space time block codes from quadratic extensions on bbq i and bbq mmbzeta6 where i radic 1 and mmbzeta6 exp i 2pi 6 two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products we present two new diagonal space time block codes from higher order algebraic extensions on bbq i and bbq mmbzeta6 for three and four transmit antennas we also present a nontight upper bound for normalized diversity products of 2ntn2 diagonal space time block codes with qam information symbols i e in bbz i from general 2ntn2 complex valued generating matrices we then present an nntnn diagonal space time code design method directly from 2n real integers based on extended complex lattices of generating matrix size nntn2n that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do we finally use the optimal 2ntn2 diagonal space time codes from the optimal quadratic extensions to construct two 2ntn2 full rate space time block codes and find that both of them have better normalized diversity products than the golden code does

design of spherical lattice space time codes in this paper we propose a systematic procedure for designing spherical lattice space time codes by employing stochastic optimization techniques we design lattice codes which are well matched to the fading statistics as well as to the decoder used at the receiver the decoders we consider here include the optimal albeit of highest decoding complexity maximum likelihood ml decoder the suboptimal lattice decoders as well as the suboptimal lattice reduction aided lra decoders having the lowest decoding complexity for each decoder our design methodology can be tailored to obtain low error rate lattice codes for arbitrary fading statistics and signal to noise ratios snrs of interest further we obtain fundamental lower bounds on the error probabilities yielded by lattice and lra decoders and characterize their asymptotic behavior

multiple critical points of invariant functionals and applications abstract this paper deals with some multiplicity results of periodic orbits of hamiltonian systems and for solution of a non linear dirichlet problem these results follow from an abstract theorem of lusternik schnirelman type as applied to an invariant equation of the form lu delta f u 0 in a hilbert space x l sub 2 omega r sub n where l is an unbounded self adjoint operator and f is a c sub 1 strictly convex function author

mmse analysis of certain large isometric random precoded systems linear precoding consists in multiplying by an n spl times k matrix a k dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted in this paper new tools borrowed from the so called free probability theory are introduced for the purpose of analyzing the performance of minimum mean square error mmse receivers for certain large random isometric precoded systems on fading channels the isometric condition represents the case of precoding matrices with orthonormal columns it is shown in this contribution that the signal to interference plus noise ratio sinr at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when n spl rarr spl infin and k n spl rarr spl alpha spl les 1 these asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding while preserving a simple mmse equalization scheme at the receiver

analysis and optimization of diagonally layered lattice schemes for mimo fading channels embodiments of the diagonal bell laboratories layered space time d blast architecture for multiple input multiple output mimo communication are developed wherein information symbol vectors are encoded using codewords from a lattice code called a diagonally layered lattice dll code which are formatted onto the diagonals of a space time frame decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing zf or minimum mean square error mmse filtering and decision feedback these operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is gaussian in the zf filtering case and non gaussian in the mmse filtering case the so called full modulation diversity fmd property is nevertheless shown to yield the maximum achievable diversity orders over the mimo channel for both the zf and the mmse filtering based decoders respectively for any arbitrary fading distribution in the case of the independent identically distributed i i d rayleigh fading mimo channel with k transmit and n receive antennas with ngesk these diversity orders are nk k k 1 2 and nk for zf and mmse filtering based decoding respectively the error probability analysis also yields a design criterion for optimizing transmit power allocations several lattice design methods are proposed for the effective parallel channel models two methods are proposed to achieve high coding gain in the rayleigh fading mimo channel a third method is proposed that minimizes the exact symbol error probability sep and can be tailored for any given fading distribution a novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback the salient feature of the proposed dll schemes is that they have nearly full rate and full or high diversity order and yet a much lower decoding complexity than other existing full rate full diversity space time block codes stbcs the frame error probability fep performance of the optimized dll schemes for moderate to high spectral efficiencies and a wide range of signal to noise ratios snrs can be quite close to the performance of the best performing but more complex to decode stbcs moreover the proposed dll schemes significantly outperform other existing mimo systems of comparable decoding complexity

multiple solutions of semilinear elliptic problems in a ball in this paper lower bounds for the number of solutions of semilinear elliptic problems in a ball of rn are given its hypotheses are only related to the behavior of the nonlinearities at and at 0 global assumptions are never made for example oddness is never required for the proof of multiplicity results

joint multiuser detection of multidimensional constellations over fading channels we investigate the error performance of multidimensional constellations in the multiple access and broadcast channels more specifically we provide closed form expressions for the pairwise error probability pep of the joint maximum likelihood detection for multiuser signaling in the presence of additive white gaussian noise and rayleigh fading arbitrary numbers of users and multidimensional signal sets are assumed while the provided formula for the pep is a function of the dimension wise distances of the multidimensional constellation furthermore a useful upper bound on the average symbol error probability is also obtained through the union bound the analysis is applied to the sparse code multiple access systems the analytical results are validated successfully through simulations and show their importance in the multidimensional constellation design

action of a scattering map on weighted sobolev spaces in the plane abstract we consider a scattering map that arises in the approach to the scattering theory for the davey stewartson ii equation and show that the map is an invertible map between certain weighted l 2 sobolev spaces

algebraic tools to build modulation schemes for fading channels a unified framework is presented in order to build lattice constellations matched to both the rayleigh fading channel and the gaussian channel the method encompasses the situations where the interleaving is done on the real components or on two dimensional signals in the latter case a simple construction of lattices congruent to the densest binary lattices with respect to the euclidean distance is proposed it generalizes in a sense to be clarified later the structural construction proposed by forney 1991 these constellations are next combined with coset codes the partitioning rules and the gain formula are similar to those used for the gaussian channel

diagonal lattice space time codes from number fields and asymptotic bounds in this paper we reformulate some constructions of real and complex diagonal lattice space time codes from number fields which have been given explicitly or implicitly by other researchers these constructions establish a connection between good diagonal lattice space time codes and number fields with small absolute values of discriminants we present two tables for diversity products of some lattice space time codes from these constructions the maximal rank of diagonal lattice space time codes with positive diversity product is determined we also discuss the asymptotic problem of lattice space time codes by using an infinite tower of hilbert class field and a tamely ramified class field tower we obtain asymptotically good sequences of lattice space time codes some asymptotic upper bounds are given in the paper as well

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

perfect space time codes for any number of antennas in a recent paper perfect n times n space time codes were introduced as the class of linear dispersion space time st codes having full rate nonvanishing determinant a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted energy per antenna consequence of these conditions include optimality of perfect codes with respect to the zheng tse diversity multiplexing gain tradeoff dmt as well as excellent low signal to noise ratio snr performance yet perfect space time codes have been constructed only for two three four and six transmit antennas in this paper we construct perfect codes for all channel dimensions present some additional attributes of this class of st codes and extend the notion of a perfect code to the rectangular case

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

good lattice constellations for both rayleigh fading and gaussian channels recent work on lattices matched to the rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency we present a new family of lattice constellations based on complex algebraic number fields which have good performance on rayleigh fading channels some of these lattices also present a reasonable packing density and thus may be used at the same time over a gaussian channel conversely we show that particular versions of the best lattice packings d sub 4 e sub 6 e sub 8 k sub 12 spl lambda sub 16 spl lambda sub 24 constructed from totally complex algebraic cyclotomic fields present better performance over the rayleigh fading channel the practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results

error performance of multidimensional lattice constellations part i a parallelotope geometry based approach for the awgn channel multidimensional lattice constellations which present signal space diversity ssd have been extensively studied for single antenna transmission over fading channels with focus on their optimal design for achieving high diversity gain in this two part series of papers we present a novel combinatorial geometrical approach based on parallelotope geometry for the performance evaluation of multidimensional finite lattice constellations with arbitrary structure dimension and rank in part i we present an analytical expression for the exact symbol error probability sep of multidimensional signal sets and two novel closed form bounds named multiple sphere lower bound mlsb and multiple sphere upper bound msub part ii extends the analysis to the transmission over fading channels where multidimensional signal sets are commonly used to combat fading degradation numerical and simulation results show that the proposed geometrical approach leads to bounds that can be used for the performance evaluation and the design of multidimensional lattice constellations both in additive white gaussian noise awgn and fading channels

simple iterative methods to exploit the signal space diversity signal space diversity is a power and bandwidth efficient diversity technique to exploit the signal space diversity joint maximum likelihood ml detection at the receiver is usually needed where the complexity grows exponentially with the dimension of the lattice in this letter we propose a serial concatenated scheme and two simple iterative methods to exploit the signal space diversity the simple iterative methods are based on the idea of soft interference cancellation the first iterative method is based on a vector gaussian approximation while the second one is based on a scalar gaussian approximation the complexity of the first iterative method grows cubically with the dimension of the lattice and the simulations show that its performance approaches that of the optimal maximum a posteriori detection method the complexity of the second iterative method grows linearly with the dimension of the lattice and the simulations show that when the dimension of the lattice n 32 at bit error rate 10 sup 5 the performance gap between the rayleigh fading channel and the gaussian channel is only 0 3 db

on a reverse form of the brascamp lieb inequality we prove a reverse form of the multidimensional brascamp lieb inequality our method also gives a new way to derive the brascamp lieb inequality and is rather convenient for the study of equality cases

lattice decoding for joint detection in direct sequence cdma systems a new joint detection method based on sphere packing lattice decoding is presented in this paper the algorithm is suitable for both synchronous and asynchronous multiple access direct sequence code division multiple access ds cdma systems and it may jointly detect up to 64 users with a reasonable complexity the detection complexity is independent of the modulation size and large m pam or m qam constellations can be used furthermore a theoretical gain analysis is performed in which the multiple access system performance is derived from the lattice parameters

trellis coded modulation on time selective fading channels a general analysis of trellis coded modulation tcm on time selective fading channels with correlated signal samples is presented gaussian quadratic forms are used to evaluate the pairwise sequence error probability the effect of interleaving is studied and it is shown that moderate interleaving with respect to the doppler frequency of the channel suffices to achieve good performance the analysis is then extended to treat non ideal estimation of the complex channel gain in the coherent case using a general linear channel estimator it is shown that differential phase shift keying dpsk and differential trellis coded modulation dtcm on correlated fading channels call be treated analytically and that the error probability of dtcm like of coherent tcm depends only on the euclidean distance of the error sequences results show that dtcm suffers a degradation of up to 3 db with respect to coherent tcm on slow fading channels but performs better on fast fading channels error floor curves are presented for dtcm for different interleaving depths the event error probability p sub e and the bit error probability p sub b of tcm approximated by truncated averaged union bounds are calculated for the codes used a comparison of the approximations of p sub b with simulation results show that the union bound is relatively loose for fading channels

on the restriction of the fourier transform to curves endpoint results and the degenerate case for smooth curves f in rn with certain curvature properties it is shown that the composition of the fourier transform in rn followed by restriction to r defines a bounded operator from lp rn to lq f for certain p q the curvature hypotheses are the weakest under which this could hold and p is optimal for a range of q in the proofs the problem is reduced to the estimation of certain multilinear operators generalizing fractional integrals and they are treated by means of rearrangement inequalities and interpolation between simple endpoint estimates

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

encoding and decoding binary product lattices a binary product lattice is generated from two binary component lattices of lower dimensions by employing the kronecker product this work focuses on codes carved from binary product lattices defined as such an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points a novel approach is disclosed yielding an explicit connection between source bits and lattice points decoding methods typically used for binary product codes do not apply for product lattices several alternative decoding approaches are discussed in particular a provably bounded distance decoder is presented it relies on the fact that a product lattice code point may be regarded as a two dimensional array whose rows and columns are points in the component lattices the obtained results are compared with classical lattices known in the art

trellis complexity and minimal trellis diagrams of lattices this paper presents results on trellis complexity and low complexity trellis diagrams of lattices we establish constructive upper bounds on the trellis complexity of lattices these bounds both improve and generalize the similar results of tarokh and vardy see ibid vol 43 p 1294 1300 1997 we also construct trellis diagrams with minimum number of paths for some important lattices such trellises are called minimal the constructed trellises which are novel in many cases can be employed to efficiently decode the lattices via the viterbi algorithm in particular a general structure for minimal trellis diagrams of d sub n lattices is obtained this structure corresponds to a new code formula for d sub n moreover we develop some important duality results which are used in both deriving the upper bounds and finding the minimal trellises all the discussions are based on a universal approach to the construction and analysis of trellis diagrams of lattices using their bases

multiple solutions of semilinear dirichlet problems on a domain withs1 group actions abstract let be a bounded domain with a smooth boundary such that there exists an s 1 group of isometric linear transformations on in the present paper we consider the multiple existence of solutions of the problem formula where g c 1 r and h l 2

algebraic lattice constellations bounds on performance in this work we give a bound on performance of any full diversity lattice constellation constructed from algebraic number fields we show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain furthermore we discuss constructions minimum product distance and bounds for full diversity complex rotated z i sup n lattices for any dimension n which avoid the need of component interleaving

symbol mapping diversity design for multiple packet transmissions in this paper we present a simple but effective method of enhancing and exploiting diversity from multiple packet transmissions in systems that employ nonbinary linear modulations such as phase shift keying psk and quadrature amplitude modulation qam this diversity improvement results from redesigning the symbol mapping for each packet transmission by developing a general framework for evaluating the upper bound of the bit error rate ber with multiple transmissions a criterion to obtain optimal symbol mappings is attained the optimal adaptation scheme reduces to solutions of the well known quadratic assignment problem qap symbol mapping adaptation only requires a small increase in receiver complexity but provides very substantial ber gains when applied to additive white gaussian noise awgn and flat fading channels

stability of the inverse conductivity problem in the plane for less regular conductivities abstract the dirichlet to neumann map or voltage to current map takes dirichlet data u f to the conormal derivatives u at the boundary where u is a solution to the elliptic equation div u 0 on a plane lipchitz domain r2 we consider the inverse conductivity problem that consists of the recovery of in the interior of from the knowledge of we prove stability for this inverse map assuming an isotropic conductivity c1 e we reduce the equation div u 0 to an equivalent system and use the scattering transform this approach relaxes the number of derivatives of required in former works

an inverse scattering transform for the davey stewartson ii equations ii the rigorous treatment of the direct and inverse problems is carried out for an inverse scattering transform that can be used to solve the davey stewartson ii equations

existence of nontrivial solutions of semilinear elliptic equations soit cr n un domaine borne a frontiere lisse et g r r une application continue telle que g 0 0 on etudie l existence des solutions non triviales du probleme aux valeurs limites de la forme u g u dans u 0

an inverse scattering transform for the davey stewartson ii equations iii abstract the cauchy problem of the davey stewartson ii equations is solved by the method of an inverse scattering transform results of existence and uniqueness of global solutions regularity spatial and long time decay are obtained

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

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

a noncommutative analogue of the odlyzko bounds and bounds on performance for space time lattice codes this paper considers space time coding over several independently rayleigh faded blocks in particular we will concentrate on giving upper bounds for the coding gain of lattice space time codes as the number of blocks grow this problem was previously considered in the single antenna case by bayer fluckiger et al in 2006 crucial to their work was odlyzko s bound on the discriminant of an algebraic number field as this provides an upper bound for the normalized coding gain of number field codes in the mimo context natural codes are constructed from division algebras defined over number fields and the coding gain is measured by the discriminant of the corresponding noncommutative algebra in this paper we will develop analogues of the odlyzko bounds in this context and show how these bounds limit the normalized coding gain of a very general family of division algebra based space time codes these bounds can also be used as benchmarks in practical code design and as tools to analyze asymptotic bounds of performance as the number of independently faded blocks increases

a nonlinear plancherel theorem with applications to global well posedness for the defocusing davey stewartson equation and to the inverse boundary value problem of calderon author s nachman adrian i regev idan tataru daniel i abstract we prove a plancherel theorem for a nonlinear fourier transform in two dimensions arising in the inverse scattering method for the defocusing davey stewartson ii equation we then use it to prove global well posedness and scattering in l 2 for defocusing dsii this plancherel theorem also implies global uniqueness in the inverse boundary value problem of calder x27 on in dimension 2 for conductivities sigmag0 with log sigma in dot h 1 the proof of the nonlinear plancherel theorem includes new estimates on classical fractional integrals as well as a new result on l 2 boundedness of pseudo differential operators with non smooth symbols valid in all dimensions

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free