universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

optimal and lattice codes in a mimo system with complete feedback space time coding for a multiple input multiple output mimo system with complete feedback and maximum likelihood ml decoding is considered first a criterion for designing an optimal codebook with complete feedback in the case of high signal to noise ratio snr is given it turns out that designing an optimal codebook with complete feedback in the case of high snr is equivalent to efficiently packing a finite number of points into a dynamic ellipsoid in a finite dimensional real euclidean space second based on this design criterion an optimal tradeoff between diversity and multiplexing is then derived finally practical design using lattice codes is addressed and surprisingly it is shown that the lattice codes can achieve the optimal tradeoff it is also demonstrated that it is not necessary for an optimal lattice code to use all the subchannels generated by the system this is in striking contrast with a general optimal code which generally utilizes all the subchannels

optimal throughput diversity delay tradeoff in mimo arq block fading channels in this paper we consider an automatic repeat request arq retransmission protocol signaling over a block fading multiple input multiple output mimo channel unlike previous work we allow for multiple fading blocks within each transmission arq round and we constrain the transmitter to fixed rate codes constructed over complex signal constellations in particular we examine the general case of average input power constrained con stellations with a fixed signaling alphabet of finite cardinality this scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing ofdm techniques over a mimo arq channel two cases of fading dynamics are considered namely short term static fading where channel fading gains change randomly for each arq round and long term static fading where channel fading gains remain constant over all arq rounds pertaining to a given message as our main result we prove that for the block fading mimo arq channel with a fixed signaling alphabet satisfying a short term power constraint the optimal signal to noise ratio snr exponent is given by a modified singleton bound relating all the system parameters to demonstrate the practical significance of the theoretical analysis we present numerical results showing that practical singleton bound achieving maximum distance separable codes achieve the optimal snr exponent

quadratic forms and space time block codes from generalized quaternion and biquaternion algebras in the context of space time block codes stbcs the theory of generalized quaternion and biquaternion algebras i e tensor products of two quaternion algebras over arbitrary base fields is presented as well as quadratic form theoretic criteria to check if such algebras are division algebras for base fields relevant to stbcs these criteria are exploited via springer s theorem to construct several explicit infinite families of bi quaternion division algebras these are used to obtain new 2 2 and 4 4 stbcs

on space time code design with a conditional pic group decoding space time code designs based on a partial interference cancellation pic group decoding have been recently proposed the pic group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ml decoding complexity the symbol rate for a space time code achieving full diversity with the pic group decoding is also between those for the linear receivers and the ml decoding in this paper we propose a new decoding called conditional pic group decoding that is between the pic group decoding and the ml decoding with the proposed new decoding we obtain a new design criterion for space time codes to achieve full diversity which is also between the one with the pic group decoding and the one with the ml decoding we then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the pic group decoding

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

fast decodable asymmetric space time codes from division algebras multiple input double output mido codes are important in the near future wireless communications where the portable end user device is physically small and will typically contain at most two receive antennas especially tempting is the 4 2 channel due to its immediate applicability in the digital video broadcasting dvb such channels optimally employ rate two space time st codes consisting of 4 4 matrices unfortunately such codes are in general very complex to decode hence setting forth a call for constructions with reduced complexity recently some reduced complexity constructions have been proposed but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes in this paper it will be shown that a family of division algebra based mido codes will always result in at least 37 5 worst case complexity reduction while maintaining full diversity and for the first time the nonvanishing determinant nvd property the reduction follows from the fact that similarly to the alamouti code the codes will be subsets of matrix rings of the hamiltonian quaternions hence allowing simplified decoding at the moment such reductions are among the best known for rate two mido codes 5 6 several explicit constructions are presented and shown to have excellent performance through computer simulations simulations

constructions of multiblock space time coding schemes that achieve the diversity multiplexing tradeoff constructions of multiblock space time coding schemes that are optimal with respect to diversity multiplexing d m tradeoff when coding is applied over any number of fading blocks are presented in this correspondence the constructions are based on a left regular representation of elements in some cyclic division algebra in particular the main construction applies to the case when the quasi static fading interval equals the number of transmit antennas hence the resulting scheme is termed a minimal delay multiblock space time coding scheme constructions corresponding to the cases of nonminimal delay are also provided as the number of coded blocks approaches infinity coding schemes derived from the proposed constructions can be used to provide a reliable multiple input multiple output mimo communication with vanishing error probability

optimal selection of reduced rank estimators of high dimensional matrices we introduce a new criterion the rank selection criterion rsc for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models the corresponding rsc estimator minimizes the frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model the rank of the rsc estimator provides a consistent estimator of the rank of the coefficient matrix in general the rank of our estimator is a consistent estimate of the effective rank which we define to be the number of singular values of the target matrix that are appropriately large the consistency results are valid not only in the classic asymptotic regime when n the number of responses and p the number of predictors stay bounded and m the number of observations grows but also when either or both n and p grow possibly much faster than m we establish minimax optimal bounds on the mean squared errors of our estimators our finite sample performance bounds for the rsc estimator show that it achieves the optimal balance between the approximation error and the penalty term furthermore our procedure has very low computational complexity linear in the number of candidate models making it particularly appealing for large scale problems we contrast our estimator with the nuclear norm penalized least squares nnp estimator which has an inherently higher computational complexity than rsc for multivariate regression models we show that nnp has estimation properties similar to those of rsc albeit under stronger conditions however it is not as parsimonious as rsc we offer a simple correction of the nnp estimator which leads to consistent rank estimation we verify and illustrate our theoretical findings via an extensive simulation study

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

an introduction to some statistical aspects of pac learning theory in this paper a brief introduction is given to some statistical aspects of pac probably approximately correct learning theory it is shown that there is a close connection between the principal results in pac learning theory and those in empirical process theory the latter being a well established branch of probability theory the main results in each area are summarized without proofs and the reader is directed to appropriate sources in the literature

a construction of a space time code based on number theory we construct a full data rate space time st block code over m 2 transmit antennas and t 2 symbol periods and we prove that it achieves a transmit diversity of 2 over all constellations carved from z i sup 4 further we optimize the coding gain of the proposed code and then compare it to the alamouti code it is shown that the new code outperforms the alamouti see ieee j select areas commun vol 16 p 1451 58 1998 code at low and high signal to noise ratio snr when the number of receive antennas n 1 the performance improvement is further enhanced when n or the size of the constellation increases we relate the problem of st diversity gain to algebraic number theory and the coding gain optimization to the theory of simultaneous diophantine approximation in the geometry of numbers we find that the coding gain optimization is equivalent to finding irrational numbers the furthest from any simultaneous rational approximations

cyclic algebras for noncoherent differential space time coding we investigate cyclic algebras for coding over the differential noncoherent channel cyclic algebras are an algebraic object that became popular for coherent space time coding since it naturally yields linear families of matrices with full diversity coding for the differential noncoherent channel has a similar flavor in the sense that it asks for matrices that achieve full diversity except that these matrices furthermore have to be unitary in this work we give a systematic way to find infinitely many unitary matrices inside cyclic algebras which holds for all dimensions we show how cyclic algebras generalize previous families of unitary matrices obtained using the representation of fixed point free groups as an application of our technique we present families of codes for three and four antennas that achieve high coding gain

quadratic extension field codes for free space optical intensity communications in this paper we propose a space time code construction with a symbol rate of two for free space optical multiple input multiple output fso mimo communication systems unlike the radio frequency space time coding design that deals with complex symbols holding phase and magnitude information the phase detection in wireless optical communications remains very challenging this restricts optical mimo codes to carry positive magnitude information belonging to a finite range to meet these requirements we propose to design the fso mimo codes considering first the whole real space mathbb r followed by a bipolar to unipolar conversion to fit in the intensity margin we consider the mimo configurations with two or four transmitters lasers we base our shape preserving construction on quadratic extension fields that linearly combine the real symbols to form a full diversity space time code with a symbol rate equal to two for each configuration we show how to optimize the choice of the algebraic field numbers to jointly optimize the non vanishing code determinant and the bipolar to unipolar attenuation factor

on the densest mimo lattices from cyclic division algebras it is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index the number of tx rx antennas is derived also numerous examples of division algebras achieving the bound are given for example a matrix lattice with quadrature amplitude modulation qam coefficients that has 2 5 times as many codewords as the celebrated golden code of the same minimum determinant is constructed also a general algorithm due to ivanyos and ronyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

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

decoding by sampling a randomized lattice algorithm for bounded distance decoding despite its reduced complexity lattice reduction aided decoding exhibits a widening gap to maximum likelihood ml performance as the dimension increases to improve its performance this paper presents randomized lattice decoding based on klein s sampling technique which is a randomized version of babai s nearest plane algorithm i e successive interference cancelation sic and samples lattice points from a gaussian like distribution over the lattice to find the closest lattice point klein s algorithm is used to sample some lattice points and the closest among those samples is chosen lattice reduction increases the probability of finding the closest lattice point and only needs to be run once during preprocessing further the sampling can operate very efficiently in parallel the technical contribution of this paper is twofold we analyze and optimize the decoding radius of sampling decoding resulting in better error performance than klein s original algorithm and propose a very efficient implementation of random rounding of particular interest is that a fixed gain in the decoding radius compared to babai s decoding can be achieved at polynomial complexity the proposed decoder is useful for moderate dimensions where sphere decoding becomes computationally intensive while lattice reduction aided decoding starts to suffer considerable loss simulation results demonstrate near ml performance is achieved by a moderate number of samples even if the dimension is as high as 32

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

penalized least squares regression methods and applications to neuroimaging the goals of this paper are to review the most popular methods of predictor selection in regression models to explain why some fail when the number p of explanatory variables exceeds the number n of participants and to discuss alternative statistical methods that can be employed in this case we focus on penalized least squares methods in regression models and discuss in detail two such methods that are well established in the statistical literature the lasso and elastic net we introduce bootstrap enhancements of these methods the be lasso and be enet that allow the user to attach a measure of uncertainty to each variable selected our work is motivated by a multimodal neuroimaging dataset that consists of morphometric measures volumes at several anatomical regions of interest white matter integrity measures from diffusion weighted data fractional anisotropy mean diffusivity axial diffusivity and radial diffusivity and clinical and demographic variables age education alcohol and drug history in this dataset the number p of explanatory variables exceeds the number n of participants we use the be lasso and be enet to provide the first statistical analysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging and clinical predictors including their interactions the major novelty of this analysis is that biomarker selection and dimension reduction are accomplished with a view towards obtaining good predictions for the outcome of interest i e the neurocognitive indices unlike principal component analysis that are performed only on the predictors space independently of the outcome of interest

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

regularization of wavelet approximations in this paper we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced the approach can apply readily to many other statistical contexts various new penalty functions are proposed the hard thresholding and soft thresholding estimators of donoho and johnstone are specific members of nonlinear regularized wavelet estimators they correspond to the lower and upper envelopes of a class of the penalized least squares estimators necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions the sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax to efficiently solve penalized least squares problems nonlinear regularized sobolev interpolators nrsi are proposed as initial estimators wh

multiple beamforming with perfect coding perfect space time block codes pstbcs achieve full diversity full rate nonvanishing constant minimum determinant uniform average transmitted energy per antenna and good shaping however the high decoding complexity is a critical issue for practice when the channel state information csi is available at both the transmitter and the receiver singular value decomposition svd is commonly applied for a multiple input multiple output mimo system to enhance the throughput or the performance in this paper two novel techniques perfect coded multiple beamforming pcmb and bit interleaved coded multiple beamforming with perfect coding bicmb pc are proposed employing both pstbcs and svd with and without channel coding respectively with csi at the transmitter csit the decoding complexity of pcmb is substantially reduced compared to a mimo system employing pstbc providing a new prospect of csit especially because of the special property of the generation matrices pcmb provides much lower decoding complexity than the state of the art svd based uncoded technique in dimensions 2 and 4 similarly the decoding complexity of bicmb pc is much lower than the state of the art svd based coded technique in these two dimensions and the complexity gain is greater than the uncoded case moreover these aforementioned complexity reductions are achieved with only negligible or modest loss in performance

joint unitary triangularization for gaussian multi user mimo networks the problem of transmitting a common message to multiple users over the gaussian multiple input multiple output broadcast channel is considered where each user is equipped with an arbitrary number of antennas a closed loop scenario is assumed for which a practical capacity approaching scheme is developed by applying judiciously chosen unitary operations at the transmit and receive nodes the channel matrices are triangularized so that the resulting matrices have equal diagonals up to a possible multiplicative scalar factor this along with the utilization of successive interference cancellation reduces the coding and decoding tasks to those of coding and decoding over the single antenna additive white gaussian noise channel over the resulting effective channel any off the shelf code may be used for the two user case it was recently shown that such joint unitary triangularization is always possible in this paper it is shown that for more than two users it is necessary to carry out the unitary linear processing jointly over multiple channel uses i e space time processing is employed it is further shown that exact triangularization where all resulting diagonals are equal is still not always possible and appropriate conditions for the existence of such are established for certain cases when exact triangularization is not possible an asymptotic construction is proposed that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small at the price of processing a sufficiently large number of channel uses together

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

application of perfect space time codes pep bounds and some practical insights the design of perfect space time codes constructed from cyclic division algebra cda on the quasi static mimo channel has received lots of attention in industry over the last few years however the recent standards that use multiple antennas terminals such as ieee 802 11n ieee 802 16e or lte are based on more realistic assumptions involving the use of outer codes and multi taps channels in this paper the question regarding the utility of using a high dimensional modulation schemes such as space time codes in a standard context is addressed for this we evaluate the performance of the perfect space time codes in term of an upper bound on the pairwise error probability and we compare it to the one of simple spatial division multiplexing sdm schemes finally simulation results considered in the context of ieee 802 11n show that the 2 2 mimo perfect code i e the golden code performs relatively similarly as the sdm scheme in the presence of a good outer code

extended bayesian information criteria for model selection with large model spaces summary the ordinary bayesian information criterion is too liberal for model selection when the model space is large in this paper we re examine the bayesian paradigm for model selection and propose an extended family of bayesian information criteria which take into account both the number of unknown parameters and the complexity of the model space their consistency is established in particular allowing the number of covariates to increase to infinity with the sample size their performance in various situations is evaluated by simulation studies it is demonstrated that the extended bayesian information criteria incur a small loss in the positive selection rate but tightly control the false discovery rate a desirable property in many applications the extended bayesian information criteria are extremely useful for variable selection in problems with a moderate sample size but with a huge number of covariates especially in genome wide association studies which are now an active area in genetics research

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

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

spatially modulated orthogonal space time block codes with non vanishing determinants this paper proposes a multiple input multiple output mimo transmission scheme for m ary modulations called spatially modulated orthogonal space time block coding sm ostbc based on the concept of spatial constellation sc codewords introduced by le at el in the proposed scheme transmit codeword matrices are generated by multiplying sc matrices with codewords constructed from orthogonal space time block codes o stbc the maximum spectral efficiency of the proposed scheme is equal to n t 2 log 2 m bpcu where n t is the number of transmit antennas and m is the modulation order the sc matrices provide a means of carrying information bits together with the o stbc codewords and allow the sm ostbc scheme to achieve second order transmit diversity by satisfying the non vanishing determinant property a systematic method to design the sc codewords for an even number of transmit antennas greater than 3 is presented a single stream maximum likelihood ml decoder which requires a low computational complexity thanks to the structure of the sm ostbc codewords and to the orthogonality of the o stbcs and a sphere decoder with further reduced signal processing complexity are developed the bit error rate ber performance of the proposed scheme is studied by using both theoretical union bound analysis and computer simulations finally simulation results are presented in order to compare ber performance energy efficiency and decoding complexity of the proposed scheme with those of several existing mimo transmission schemes

achieving the optimal diversity versus multiplexing tradeoff for mimo flat channels with qam space time spreading and dfe equalization the use of multiple transmit tx and receive rx antennas allows to transmit multiple signal streams in parallel and hence to increase communication capacity we have previously introduced simple convolutive linear precoding schemes that spread transmitted symbols in time and space involving spatial spreading delay diversity and possibly temporal spreading in this paper we show that the use of the classical multiple input multiple output mimo decision feedback equalizer dfe but with joint detection for this system allows to achieve the optimal diversity versus multiplexing tradeoff introduced in zheng and tse diversity and multiplexing a fundamental tradeoff in multiple antenna channels ieee trans inf theory may 2003 when a minimum mean squared error mmse design is used one of the major contributions of this work is the diversity analysis of a mmse equalizer without the gaussian approximation furthermore the tradeoff is discussed for an arbitrary number of transmit and receive antennas we also show the tradeoff obtained for a mmse zero forcing zf design so another originality of this paper is to show that the mimo optimal tradeoff can be attained with a suboptimal receiver in this case a dfe as opposed to optimal maximum likelihood sequence estimation mlse

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

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

space time block code designs based on quadratic field extension for two transmitter antennas space time block code designs based on algebraic field extension for full rate large diversity product and nonvanishing minimum determinant of codewords have received great attention there are many different types of codes available for two transmitter antennas such as cyclotomic space time block codes the golden space time block code and rotation based space time block codes in this paper a more general space time block code design scheme which is called quadratic space time block coding is proposed for the two transmitter antennas using quadratic field extension the optimal design of the quadratic space time block codes in terms of a diversity product criterion is also presented it is shown that the optimal quadratic space time block codes designed in this paper do not belong to the existing space time block code family such as the cyclotomic golden and rotation based space time block codes the simulation results demonstrate that the average codeword error rate of the optimal quadratic space time block code attains about 0 5 db signal to noise ratio gain over those of the optimal cyclotomic and golden space time block codes

finite precision analysis for space time decoding low complexity optimal or nearly optimal decoders for space time codes have recently been under intensive investigation for example recent works by sirianunpiboon and others show that the silver code and the golden code can be decoded optimally or nearly optimally with quadratic decoding complexity fast decodability makes them very attractive in practice in implementing these decoders floating point to fixed point conversion ffc needs to be carefully undertaken to minimize hardware cost while retaining decoding performance the process of quantization for fixed point representations is often ignored by research community and lacks investigation and so ffc is often conducted heuristically based on simulations this paper studies the effects of quantization to space time coded systems from an information theoretic perspective it shows the analytical relationship between quantization error and decoding performance deterioration this paper also proposes a general finite precision implementation methodology including two ffc criteria for space time coded systems within an integer optimization framework as a particular example this paper examines the finite precision implementation of the quadratic optimal decoding algorithm of the silver code however our methodology and techniques can be applied to general space time codes

new algebraic constructions of rotated z sup n lattice constellations for the rayleigh fading channel in this correspondence we present various families of full diversity rotated z sup n lattice constellations based on algebraic number theory constructions we are able to give closed form expressions of their minimum product distance using the corresponding algebraic properties

optimal diversity multiplexing tradeoff and code constructions of some constrained asymmetric mimo systems in multiple input multiple output mimo communications the notion of asymmetric channel refers to the situation when the number of transmit antennas is strictly larger than the number of receive antennas such channels can often be found in mimo downlink transmissions while existing cyclic division algebra cda based codes can still be employed to achieve the optimal diversity multiplexing tradeoff dmt at high signal to noise ratio snr regime such codes cannot be directly decoded using for example the pure sphere decoding method although other means of decoding methods such as minimum mean square error generalized decision feedback equalizer mmse gdfe with lattice search and regularized lattice decoding are available an alternative approach is to constrain the number of active transmit antennas in each channel use to be no larger than the number of receive antennas the resulting system is coined constrained asymmetric mimo system two general types of asymmetrical channels are considered in this paper namely 1 when there are two receive antennas and the number of transmit antennas is arbitrary and 2 when the number of transmit antennas is one larger than the number of receive antennas explicit optimal transmission schemes as well as the corresponding code constructions for such constrained asymmetric mimo channels are presented and are shown to achieve the same dmt performance as their unconstrained counterparts

algebraic number precoding for space time block codes we propose a space time block coding framework based on linear precoding the codes for p transmit antennas are formed by transmitting the information vector with p independent information symbols l times where each time it is rotated by a distinct precoding matrix the framework generalizes conventional spatial multiplexing techniques and facilitates tradeoff between rate and diversity we propose a simple construction for precoding matrices whose parameters are chosen to guarantee maximal diversity using algebraic number theory our codes exhibit circular structure which greatly simplifies the performance analysis and facilitates linear decoding theoretical analysis and numerical simulations demonstrated excellent performance of the proposed algebraic precoding framework

diversity analysis and design of space time multiblock codes for mimo systems equipped with linear mmse receivers this paper addresses the problem of designing optimum full symbol rate linear space time block codes stbc for a multi input multi output mimo communication system with m transmitter and n m receiver antennas and a linear minimum mean square error mmse receiver by analyzing the detection error probability expression for the optimized stbc it is shown that for qam signaling the maximum diversity gain for such a system is n m 1 the minimum probability of error stbc design is then extended to systems in which the transmission spans l independent realizations from a block fading channel model and a multiblock linear mmse receiver is employed necessary and sufficient conditions for the optimality of the code are obtained and a systematic design method for generating codes that satisfy these conditions is presented the detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed it is proved that the error probability decreases with l and it is shown numerically that the diversity gain increases with l thus if the corresponding latency can be accommodated for sufficiently large l an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block fading channel and achieve higher diversity gain than that of any single block system of the same symbol rate with a maximum likelihood ml receiver the optimized multiblock linear system achieves this diversity at a substantially lower computational cost in fact the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver

space time codes from structured lattices we present constructions of space time st codes based on lattice coset coding first we focus on st code constructions for the short block length case i e when the block length is equal to or slightly larger than the number of transmit antennas we present constructions based on dense lattice packings and nested lattice voronoi shaping our codes achieve the optimal diversity multiplexing tradeoff dmt of quasi static multiple input multiple output mimo fading channels for any fading statistics and perform very well also at practical moderate values of signal to noise ratios snr then we extend the construction to the case of large block lengths by using trellis coset coding we provide constructions of trellis coded modulation tcm schemes that are endowed with good packing and shaping properties both short block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer mmse gdfe lattice decoding and a combination of this with a viterbi tcm decoder for the tcm case beyond the interesting algebraic structure we exhibit codes whose performance is among the state of the art considering codes with similar encoding decoding complexity

one step sparse estimates in nonconcave penalized likelihood models fan and li propose a family of variable selection methods via penalized likelihood using concave penalty functions the nonconcave penalized likelihood estimators enjoy the oracle properties but maximizing the penalized likelihood function is computationally challenging because the objective function is nondifferentiable and nonconcave in this article we propose a new unified algorithm based on the local linear approximation lla for maximizing the penalized likelihood for a broad class of concave penalty functions convergence and other theoretical properties of the lla algorithm are established a distinguished feature of the lla algorithm is that at each lla step the lla estimator can naturally adopt a sparse representation thus we suggest using the one step lla estimator from the lla algorithm as the final estimates statistically we show that if the regularization parameter is appropriately chosen the one step lla estimates enjoy the oracle properties with good initial estimators computationally the one step lla estimation methods dramatically reduce the computational cost in maximizing the nonconcave penalized likelihood we conduct some monte carlo simulation to assess the finite sample performance of the one step sparse estimation methods the results are very encouraging

sparse regularization techniques provide novel insights into outcome integration processes abstract by exploiting information that is contained in the spatial arrangement of neural activations multivariate pattern analysis mvpa can detect distributed brain activations which are not accessible by standard univariate analysis recent methodological advances in mvpa regularization techniques have made it feasible to produce sparse discriminative whole brain maps with highly specific patterns furthermore the most recent refinement the graph net explicitly takes the 3d structure of fmri data into account here these advanced classification methods were applied to a large fmri sample n 70 in order to gain novel insights into the functional localization of outcome integration processes while the beneficial effect of differential outcomes is well studied in trial and error learning outcome integration in the context of instruction based learning has remained largely unexplored in order to examine neural processes associated with outcome integration in the context of instruction based learning two groups of subjects underwent functional imaging while being presented with either differential or ambiguous outcomes following the execution of varying stimulus response instructions while no significant univariate group differences were found in the resulting fmri dataset l1 regularized sparse classifiers performed significantly above chance and also clearly outperformed the standard l2 regularized dense support vector machine on this whole brain between subject classification task moreover additional l2 regularization via the elastic net and spatial regularization by the graph net improved interpretability of discriminative weight maps but were accompanied by reduced classification accuracies most importantly classification based on sparse regularization facilitated the identification of highly specific regions differentially engaged under ambiguous and differential outcome conditions comprising several prefrontal regions previously associated with probabilistic learning rule integration and reward processing additionally a detailed post hoc analysis of these regions revealed that distinct activation dynamics underlay the processing of ambiguous relative to differential outcomes together these results show that l1 regularization can improve classification performance while simultaneously providing highly specific and interpretable discriminative activation patterns

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

fast decodable mido codes with large coding gain in this paper a new method is proposed to obtain full diversity rate 2 rate of two complex symbols per channel use space time block codes stbcs that are full rate for multiple input double output mido systems using this method rate 2 stbcs for 4 2 6 2 8 2 and 12 2 systems are constructed and these stbcs are fast ml decodable have large coding gains and stbc schemes consisting of these stbcs have a non vanishing determinant nvd so that they are dmt optimal for their respective mido systems it is also shown that the srinath rajan code for the 4 2 system which has the lowest ml decoding complexity among known rate 2 stbcs for the 4 2 mido system with a large coding gain for 4 16 qam has the same algebraic structure as the stbc constructed in this paper for the 4 2 system this also settles in positive a previous conjecture that the stbc scheme that is based on the srinath rajan code has the nvd property and hence is dmt optimal for the 4 2 system

recursive space time trellis codes using differential encoding differential space time modulation dstm has been recently proposed by hughes and hochwald and sweldens when the channel information is not known at the receiver where the demodulation is in fact the same as the coherent demodulation of space time block coding by replacing the channel matrix with the previously received signal matrix on the other hand the dstm also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver which is the interest of this paper this recursive structure of the dstm has been adopted lately by schlegel and grant in joint with a conventional binary code and joint iterative decoding demodulation with a superior performance the number of states of the trellis from the recursive structure depends on both the memory size which is fixed in this case and the unitary space time code ustc when a ustc for the dstm forms a group the number of states is the same as the size of the ustc otherwise the number of the states is the size of the semi group generated by the ustc from all the multiplications of the matrices in the ustc it is well known in the conventional convolutional coding cc or the trellis coded modulation tcm the free hamming or euclidean distance or the performance increases when the number of states increases by adding more memory with a properly designed cc or tcm in this paper we systematically study and design the ustc dstm for the recursive space time trellis modulation and show that the diversity product increases when the number of states increases which is not because of the memory size but because of the different ustc designs that generate different sizes of semi groups we propose a new ustc design criterion to ensure that the trellis structure improves the diversity product over the ustc as a block code based on the new criterion we propose a new class of ustc design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas we then follow schlegel and grant s approach for joint encoding and iterative decoding of a binary coded dstm turbo space time coding and numerically show that our new ustc designs for the recursive space time trellis modulation outperforms the group ustc used by schlegel and grant

sphere decoding complexity exponent for decoding full rate codes over the quasi static mimo channel in the setting of quasi static multiple input multiple output channels we consider the high signal to noise ratio snr asymptotic complexity required by the sphere decoding sd algorithm for decoding a large class of full rate linear space time codes with sd complexity having random fluctuations induced by the random channel noise and codeword realizations the introduced sd complexity exponent manages to concisely describe the computational reserves required by the sd algorithm to achieve arbitrarily close to optimal decoding performance bounds and exact expressions for the sd complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics for the particular example of decoding the recently introduced threaded cyclic division algebra based codes the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff the sd complexity exponent is shown to take a particularly concise form as a non monotonic function of the multiplexing gain to date the sd complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood performance that vanishes in the high snr limit

on space time coding with pulse position and amplitude modulations for time hopping ultra wideband systems in this work we propose novel families of space time st block codes that can be associated with impulse radio ultra wideband ir uwb communication systems the carrier less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes in fact the last generation of complex valued st codes namely the perfect codes cannot be associated with ir uwb systems where the phase reconstitution at the receiver side is practically infeasible on the other hand while the perfect codes were considered mainly with quadrature amplitude modulation qam and hexagonal hex constellations ir uwb systems are often associated with pulse position modulation ppm and hybrid ppm pam pulse amplitude modulation constellations in this paper instead of adopting the classical approach of constructing st codes over infinite fields or for the perfect codes we study the possibility of constructing modulation specific codes that are exclusive to ppm and ppm pam the proposed full rate codes are totally real information lossless and have a uniform average energy per transmit antenna they permit to achieve a full diversity order with any number of transmit antennas in some situations the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real simulations performed over realistic indoor uwb channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras

orthogonal space time block codes with sphere packing orthogonal designs have received considerable attention in the development of efficient modulation and coding methods for future multi antenna wireless communication systems due to their special properties in this paper we propose a class of space time block codes constructed by combining orthogonal designs with sphere packing for an arbitrary number of transmit antennas the structure of the orthogonal designs is exploited to guarantee full diversity and sphere packing is used to improve the coding advantage space time block code construction from block orthogonal designs is also considered the full diversity property is ensured by rotating the sphere packing underlying the code and the optimal rotation angle is determined for a class of sphere packing code design examples are provided for two and four transmit antennas and various transmission rates the simulation results show that by jointly designing the symbols in the orthogonal designs the performance of the block codes can be significantly increased

group decodable space time block codes with code rate 1 high rate space time block codes stbc with code rate 1 in multi input multi output mimo systems are able to provide both spatial multiplexing gain and diversity gain but have high maximum likelihood ml decoding complexity since group decodable quasi orthogonal code structure can reduce the decoding complexity we present in this paper systematic methods to construct group decodable high rate stbc with full symbol wise diversity gain for arbitrary transmit antenna number and code length we show that the proposed group decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number and the slope of this near linear dependence increases with the code length comparisons with existing low rate and high rate codes such as orthogonal stbc and algebraic stbc are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes

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

on the diversity multiplexing tradeoff of unconstrained multiple access channels in this paper the optimal diversity multiplexing tradeoff dmt is investigated for the multiple input multiple output fading multiple access channel with no power constraints infinite constellations for k users k 1 m transmit antennas for each user and n receive antennas infinite constellations in general and lattices in particular are shown to attain the optimal dmt of finite constellations for n ge k 1 m 1 i e user limited regime on the other hand for n it is shown that infinite constellations cannot attain the optimal dmt this is in contrast to the point to point case in which the infinite constellations are dmt optimal for any m and n in general this paper shows that when the network is heavily loaded i e k max left 1 n m 1 m right considering the shaping region in the decoding process plays a crucial role in pursuing the optimal dmt by investigating the cases in which the infinite constellations are optimal and suboptimal this paper also gives a geometrical interpretation to the dmt of infinite constellations in multiple access channels

stbc schemes with nonvanishing determinant for certain number of transmit antennas a space time block code scheme stbc scheme is a family of stbcs c snr indexed by the signal to noise ratio snr such that the rate of each stbc scales with snr an stbc scheme is said to have a nonvanishing determinant if the coding gain of every stbc in the scheme is lower bounded by a fixed nonzero value the nonvanishing determinant property is important from the perspective of the diversity multiplexing gain dm g tradeoff a concept that characterizes the maximum diversity gain achievable by any stbc scheme transmitting at a particular rate this correspondence presents a systematic technique for constructing stbc schemes with nonvanishing determinant based on cyclic division algebras prior constructions of stbc schemes from cyclic division algebra have either used transcendental elements in which case the scheme may have vanishing determinant or is available with nonvanishing determinant only for two three four and six transmit antennas in this correspondence we construct stbc schemes with nonvanishing determinant for the number of transmit antennas of the form 2 sup k 3 spl middot 2 sup k 2 spl middot 3 sup k and q sup k q 1 2 where q is any prime of the form 4s 3 for cyclic division algebra based stbc schemes in a recent work by elia et al the nonvanishing determinant property has been shown to be sufficient for achieving dm g tradeoff in particular it has been shown that the class of stbc schemes constructed in this correspondence achieve the optimal dm g tradeoff moreover the results presented in this correspondence have been used for constructing optimal stbc schemes for arbitrary number of transmit antennas by elia et al

prime fuzzy ideals over noncommutative rings in this paper we introduce prime fuzzy ideals over a noncommutative ring this notion of primeness is equivalent to level cuts being crisp prime ideals it also generalizes the one provided by kumbhojkar and bapat in 1993 which lacks this equivalence in a noncommutative setting semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes this allows us to introduce the fuzzy prime radical and contribute to establish the basis of a fuzzy noncommutative ring theory

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

energy efficient full diversity collaborative unitary space time block code designs via unique factorization of signals in this paper a novel concept called a uniquely factorable constellation pair ufcp is proposed for the systematic design of a noncoherent full diversity collaborative unitary space time block code by normalizing two alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna it is proved that such a unitary ufcp code assures the unique identification of both channel coefficients and transmitted signals in a noise free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case to further improve error performance an optimal unitary ufcp code is designed by appropriately and uniquely factorizing a pair of energy efficient cross quadrature amplitude modulation qam constellations to maximize the coding gain subject to a transmission bit rate constraint after a deep investigation of the fractional coding gain function a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the qam constellations in the denominator of the objective as well as carefully design a constellation triple forming two ufcps with one collaborating with the other two so as to make the accumulated minimum euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time to avoid as many corner points of the qam constellations with the largest energy as possible to achieve the minimum of the numerator in other words the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression computer simulations demonstrate that error performance of the optimal unitary ufcp code presented in this paper outperforms those of the differential code and the signal to noise ratio efficient training code

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

decision theoretic generalizations of the pac model for neural net and other learning applications we describe a generalization of the pac learning model that is based on statistical decision theory in this model the learner receives randomly drawn examples each example consisting of an instance x in x and an outcome y in y and tries to find a hypothesis h x a where h in h that specifies the appropriate action a in a to take for each instance x in order to minimize the expectation of a loss l y a here x y and a are arbitrary sets l is a real valued function and examples are generated according to an arbitrary joint distribution on x times y special cases include the problem of learning a function from x into y the problem of learning the conditional probability distribution on y given x regression and the problem of learning a distribution on x density estimation we give theorems on the uniform convergence of empirical loss estimates to true expected loss rates for certain hypothesis spaces h and show how this implies learnability with bounded sample size disregarding computational complexity as an application we give distribution independent upper bounds on the sample size needed for learning with feedforward neural networks our theorems use a generalized notion of vc dimension that applies to classes of real valued functions adapted from pollard s work and a notion of capacity and metric dimension for classes of functions that map into a bounded metric space supersedes 89 30 and 90 52 also in information and computation vol 100 no 1 september 1992

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

multigroup ml decodable collocated and distributed space time block codes in this paper collocated and distributed space time block codes dstbcs which admit multigroup maximum likelihood ml decoding are studied first the collocated case is considered and the problem of constructing space time block codes stbcs which optimally tradeoff rate and ml decoding complexity is posed recently sufficient conditions for multigroup ml decodability have been provided in the literature and codes meeting these sufficient conditions were called clifford unitary weight cuw stbcs an algebraic framework based on extended clifford algebras ecas is proposed to study cuw stbcs and using this framework the optimal tradeoff between rate and ml decoding complexity of cuw stbcs is obtained for few specific cases code constructions meeting this tradeoff optimally are also provided the paper then focuses on multigroup ml decodable dstbcs for application in synchronous wireless relay networks and three constructions of four group ml decodable dstbcs are provided finally the orthogonal frequency division multiplexing ofdm based alamouti space time coded scheme proposed by li xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays it is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node four group decodable dstbcs applicable in the proposed ofdm based transmission scheme are also given

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

codes over matrix rings for space time coded modulations it is known that for transmission over quasi static mimo fading channels with n transmit antennas diversity can be obtained by using an inner fully diverse space time block code while coding gain derived from the determinant criterion comes from an appropriate outer code when the inner code has a cyclic algebra structure over a number field as for perfect space time codes an outer code can be designed via coset coding more precisely by taking the quotient of the algebra by a two sided ideal which leads to matrices over finite alphabets for the outer code in this paper we show that the determinant criterion induces various metrics on the outer code such as the hamming and bachoc distances when n 2 partitioning the 2 2 golden code by using an ideal above the prime 2 leads to consider codes over either m2 f2 or m2 f2 i both being noncommutative alphabets by identifying them as algebras over a finite field or a finite ring respectively we establish an unexpected connection with classical error correcting codes over f4 and f4 i matrix rings of higher dimension suitable for 3 3 and 4 4 perfect codes give rise to more complex examples

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

high rate full diversity space time frequency codes for broadband mimo block fading channels a systematic design of high rate full diversity space time frequency stf codes is proposed for multiple input multiple output frequency selective block fading channels it is shown that the proposed stf codes can achieve rate mt and full diversity mtmrmbl i e the product of the number of transmit antennas mt receive antennas mr fading blocks mb and channel taps l the proposed stf codes are constructed from a layered algebraic design where each layer of algebraic coded symbols are parsed into different transmit antennas orthogonal frequency division multiplexing tones and fading blocks without rate loss simulation results show that the proposed stf codes achieve higher diversity gain in block fading channels than some typical space frequency codes

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

almost universal codes achieving ergodic mimo capacity within a constant gap this paper addresses the question of achieving capacity with lattice codes in multi antenna block fading channels when the number of fading blocks tends to infinity a design criterion based on the normalized minimum determinant is proposed for division algebra multi block space time codes over fading channels this plays a similar role to the hermite invariant for gaussian channels under maximum likelihood decoding it is shown that this criterion is sufficient to guarantee transmission rates within a constant gap from capacity both for deterministic channels and ergodic fading channels moreover if the number of receive antennas is greater than or equal to the number of transmit antennas the same constant gap is achieved under naive lattice decoding as well in the case of independent identically distributed rayleigh fading the error probability vanishes exponentially fast in contrast to the standard approach in the literature which employs random lattice ensembles the existence results in this paper are derived from the number theory first the gap to capacity is shown to depend on the discriminant of the chosen division algebra then class field theory is applied to build families of algebras with small discriminants the key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants

dmt optimality of lr aided linear decoders for a general class of channels lattice designs and system models this paper identifies the first general explicit and nonrandom mimo encoder decoder structures that guarantee optimality with respect to the diversity multiplexing tradeoff dmt without employing a computationally expensive maximum likelihood ml receiver specifically the work establishes the dmt optimality of a class of regularized lattice decoders and more importantly the dmt optimality of their lattice reduction lr aided linear counterparts the results hold for all channel statistics for all channel dimensions and most interestingly irrespective of the particular lattice code applied as a special case it is established that the lll based lr aided linear implementation of the mmse gdfe lattice decoder facilitates dmt optimal decoding of any lattice code at a worst case complexity that grows at most linearly in the data rate this represents a fundamental reduction in the decoding complexity when compared to ml decoding whose complexity is generally exponential in the rate the results generality lends them applicable to a plethora of pertinent communication scenarios such as quasi static mimo mimo ofdm isi cooperative relaying and mimo arq channels in all of which the dmt optimality of the lr aided linear decoder is guaranteed the adopted approach yields insight and motivates further study into joint transceiver designs with an improved snr gap to ml decoding

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates