filtering image records using wavelets and the zakai equation consider the problem of detecting and localizing a faint object moving in an essentially stationary background using a sequence of 2d low s n ratio images of the scene a natural approach consists of digitizing each snapshot into a discrete set of observations sufficiently perhaps not exactly matched to the object in question then tracking the object using an appropriate stochastic filter the tracking would be expected to make up for the low s n ratio thus allowing one to coherently process successive images in order to beat down the noise and localize the object the problem then becomes one of choosing the appropriate image representation as well as the optimal and necessarily nonlinear filter we propose exact and approximate solutions using wavelets and the zakai equation the smoothness of the wavelets used is required in the derivation of the evolution equation for the conditional density giving the filter and their orthogonality makes it possible to carry out actual computations of the ito and change of gauge terms in the algorithm effectively

evolution equations and levy processes on quantum groups in this chapter we consider stochastic processes on quantum groups that are related to evolution equations of the form partial t u lu with some difference differential operator l for the equations considered in section 7 1 u is an element of a quantum or braided group a we recall that solutions of these equations can be given as appell systems or shifted moments of the associated process and show how these can be calculated explicitly on the q affine group and on a braided analogue of the heisenberg weyl group

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

random walk and the heat equation on superspace and anyspace random walks are used to study diffusion on anyspace anyspace is characterized by coordinate with n 0 and statistics e2 i n between independent copies anyonic integration and anyonic dirac functions are introduced and reduced to familiar results for supersymmetry when n 2 these ingredients are then used to formulate and solve the resulting anyonic diffusion equation

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

unification of boolean monotone anti monotone and tensor independence and levy processes the unification of the boolean and the tensor product of quantum probability spaces given by lenczewski len98 is modified to include the monotone product and its mirror image the anti monotone product and used to reduce the theories of boolean monotone and anti monotone levy processes on dual semi groups to the theory of levy processes on involutive bialgebras this leads to a representation theorem for these processes further applications are a proof of the schoenberg correspondence for boolean monotone and anti monotone convolution semi groups a realization of boolean monotone and anti monotone creation annihilation and conservation operators on boson fock spaces and a discussion of the markov structure of these levy processes

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

quantum random walk for uq su 2 and a new example of quantum noise we derive the quantum version of the central limit theorem for sample sums of q independent q identically distributed quantum variables for q r 1 in particular we consider uq su 2 for which we obtain in the limit a state on the algebra generated by q commuting q oscillators indexed by pairs of real numbers r s where 0 r s giving a new example of non additive quantum noise

quantum levy processes on dual groups we present a theory of quantum non commutative levy processes on dual groups which generalizes the theory of levy processes on bialgebras it follows from a result of n muraki that there exist exactly 5 notions of non commutative positive stochastic independence we show that one can associate a commutative bialgebra with each pair consisting of a dual group and one of the 5 notions of independence this construction is related to a construction of u franz our construction has the advantage that the important case of free independence is included we show that levy processes are given by their generators which are precisely the conditonally positive linear functionals on the dual group

space time block codes achieving full diversity with linear receivers in most of the existing space time code designs achieving full diversity is based on maximum likelihood ml decoding at the receiver that is usually computationally expensive and may not have soft outputs recently zhang liu wong introduced toeplitz codes and showed that toeplitz codes achieve full diversity when a linear receiver zero forcing zf or minimum mean square error mmse receiver is used motivated from zhang liu wong s results on toeplitz codes in this paper we propose a design criterion for space time block codes stbc in which information symbols and their complex conjugates are linearly embedded to achieve full diversity when zf or mmse receiver is used the complex orthogonal stbc ostbc satisfy the criterion as one may expect we also show that the symbol rates of stbc under this criterion are upper bounded by 1 subsequently we propose a novel family of stbc that satisfy the criterion and thus achieve full diversity with zf or mmse receiver our newly proposed stbc are constructed by overlapping the 2times2 alamouti code and hence named overlapped alamouti codes in this paper the new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas simulation results show that overlapped alamouti codes significantly outperform toeplitz codes for all numbers of transmit antennas and also outperform ostbc when the number of transmit antennas is above 4

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

high rate and full diversity space time block codes with low complexity partial interference cancellation group decoding in this letter we propose a systematic design of space time block codes stbc which can achieve high rate and full diversity when the partial interference cancellation pic group decoding is used at receivers the proposed codes can be applied to any number of transmit antennas and admit a low decoding complexity while achieving full diversity for m transmit antennas in each codeword real and imaginary parts of pm complex information symbols are parsed into p diagonal layers and then encoded respectively with pic group decoding it is shown that the decoding complexity can be reduced to a joint decoding of m 2 real symbols in particular for 4 transmit antennas the code has real symbol pairwise i e single complex symbol decoding that achieves full diversity and the code rate is 4 3 simulation results demonstrate that the full diversity is offered by the newly proposed stbc with the pic group decoding

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

renormalized squares of white noise and other non gaussian noises as levy processes on real lie algebras it is shown how the relations of the renormalized squared white noise defined by accardi lu and volovich alv99 can be realized as factorizable current representations or levy processes on the real lie algebra 2 this allows to obtain its ito table which turns out to be infinite dimensional the linear white noise without or with number operator is shown to be a levy process on the heisenberg weyl lie algebra or the oscillator lie algebra furthermore a joint realization of the linear and quadratic white noise relations is constructed but it is proved that no such realizations exist with a vacuum that is an eigenvector of the central element and the annihilator classical levy processes are shown to arise as components of levy processes on real lie algebras and their distributions are characterized in particular the square of white noise analogue of the quantum poisson process is shown to have a 2 probability density and the analogue of the field operators to have a density proportional to where is the usual function and m 0 a real parameter

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

gauss laws in the sense of bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups the goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent first we introduce a braided analogue of the heisenberg weyl group which shall serve as standard example we introduce gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the bernstein property i e that the sum and difference of independent random variables are also independent the corresponding functionals on the braided line braided plane and a braided q heisenberg weyl group are determined section 5 deals with continuous convolution semigroups on nilpotent quantum groups and braided groups we extend recent results proving the uniqueness of the embedding of an infinitely divisible probability law into a continuous convolution semigroup for simply connected nilpotent lie groups to nilpotent quantum groups and braided groups finally in section 6 we give some indications how the semigroup approach of heyer and hazod to the bernstein theorem on groups can be extended to quantum groups and braided groups

the strong markov property for fermion brownian motion abstract a concept of independence of w 2 algebras is developed which is the fermion analogue of independence of von neumann algebras for bosons for a fermion brownian motion process a t a t t r d applebaum fermion stochastic calculus ph d thesis university of nottingham 1984 and a markov time t 0 de it is shown that the process a t t a t a t t a t t r whose components are defined as spectral integrals with operator valued integrands as in r l hudson j funct anal 34 1979 266 constitutes a new fermion brownian motion process such that the pre t and post t w 2 algebras are independent

spatial modulation aided zero padded single carrier transmission for dispersive channels in this paper we consider spatial modulation sm operating in a frequency selective single carrier sc communication scenario and propose zero padding instead of the cyclic prefix considered in the existing literature we show that the zero padded single carrier zp sc sm system offers full multipath diversity under maximum likelihood ml detection unlike the cyclic prefix based sm system furthermore we show that the order of ml detection complexity in our proposed zp sc sm system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver thus we show that the zero padding applied in the sc sm system has two advantages over the cyclic prefix 1 achieves full multipath diversity and 2 imposes a relatively low ml detection complexity furthermore we extend the partial interference cancellation receiver pic r proposed by guo and xia for the detection of space time block codes stbcs in order to convert the zp sc system into a set of narrowband subsystems experiencing flat fading we show that full rank stbc transmissions over these subsystems achieves full transmit receive as well as multipath diversity for the pic r furthermore we show that the zp sc sm system achieves receive and multipath diversity for the pic r at a detection complexity order which is the same as that of the sm system in flat fading scenario our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the zp sc sm system is significantly better than that of the sm in cyclic prefix based orthogonal frequency division multiplexing as well as of the sm in the cyclic prefixed and zero padded single carrier systems relying on zero forcing minimum mean squared error equalizer based receivers

an optimal zero forcing pic group decoding for two user layered alamouti code the decoding complexity of the layered alamouti code with the maximum likelihood ml receiver is high partial interference cancellation pic group decoding is an attractive method to reduce the ml decoding complexity however different grouping schemes for the pic group decoding may have different performances in this letter by fully taking advantage of the alamouti code structure we analytically calculate the power gains of the information symbols after the pic for a grouping scheme where the zero forcing zf operator is used for the pic we then propose an optimal grouping scheme for the pic group decoding by proposing a criterion to choose the grouping schemes adaptively so that the power gains of the information symbols are maximized after the pic

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

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

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

correction to on full diversity space time block codes with partial interference cancellation group decoding oct 09 4366 4385 in this paper a correction is made to the criterion for a linear dispersion space time block code to achieve full diversity with the partial interference cancellation pic group decoding recently published in the above titled paper ibid vol 55 no 10 pp 4366 4385

on the design of minimum ber linear space time block codes for mimo systems equipped with mmse receivers in this paper we consider the design of a full rate linear space time block code for coherent multiple input multiple output mimo communication systems under a quasi static rayleigh flat fading environment our design targets specifically at the use of a linear minimum mean square error mmse receiver that minimizes the asymptotic average bit error rate ber when the transmitted signal is selected from a 4 qam constellation this optimization problem is solved in two main stages 1 a lower bound on the ber is first minimized and 2 how this minimized lower bound can be achieved is then shown by exploiting a rigorous convex optimization technique without any assumption on the code we prove that individual unitary and trace orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average ber with an mmse detector an algorithm is provided for an efficient generation of our codes and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

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

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

toward a preferred 4 x 4 space time block code a performance versus complexity sweet spot with linear filter decoding we develop a new 4 4 hadamard precoded quasi orthogonal space time block code qo stbc that enables highly effective near maximum likelihood near ml reliability based prioritized symbol detection using linear filters approximate block error rate minimization is being used to optimize the code rotation angle detailed computational complexity evaluation of the decoder in terms of real multiplications and additions shows significant complexity reduction for symbol alphabet sizes of interest numerical and simulation studies demonstrate negligible bit error rate degradation compared to the state of the art in bit error rate by ml decoded 4 4 codewords

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

full diversity non coherent alamouti based toeplitz space time block codes recently the liu zhang wong s toeplitz space time block code and the shang xia s alamouti code based overlapped space time block code have been developed to enable coherent full diversity with the linear receivers for a wireless communication system having multiple transmitter antennas and a single receiver antenna in this paper such a noncoherent system is considered in which channel state information is unavailable at both the transmitter and receiver using the alamouti coding scheme and the toeplitz matrix structure a novel noncoherent nonunitary space time block code which is called an alamouti based toeplitz space time block code is proposed by the fundamentals of galois theory and algebraic number theory two important properties on the two alamouti codes generated from a pair of coprime phase shift keying psk constellations i e the uniqueness of factorization itself and the shift invariant uniqueness of factorization are first revealed and rigorously proved then it is further shown that it is these two kinds of unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals as well as noncoherent full diversity with a generalized likelihood ratio test glrt receiver in addition a full diversity unitary code design is also proposed by simply applying the qr decomposition to the full diversity nonunitary alamouti based toeplitz space time block code computer simulations demonstrate that the nonunitary and unitary codes presented in this paper outperform the differential codes and the signal to noise ratio snr efficient training scheme based on the coherent orthogonal space time block codes in the current literature

single symbol maximum likelihood decodable linear stbcs space time block codes stbcs from orthogonal designs ods and coordinate interleaved orthogonal designs ciod have been attracting wider attention due to their amenability for fast single symbol maximum likelihood ml decoding and full rate with full rank over quasi static fading channels however these codes are instances of single symbol decodable codes and it is natural to ask if there exist codes other than stbcs form ods and ciods that allow single symbol decoding in this paper the above question is answered in the affirmative by characterizing all linear stbcs that allow single symbol ml decoding not necessarily full diversity over quasi static fading channels calling them single symbol decodable designs sdd the class sdd includes ods and ciods as proper subclasses further among the sdd a class of those that offer full diversity called full rank sdd fsdd are characterized and classified we then concentrate on square designs and derive the maximal rate for square fsdds using a constructional proof it follows that 1 except for n 2 square complex ods are not maximal rate and 2 a rate one square fsdd exist only for two and four transmit antennas for nonsquare designs generalized coordinate interleaved orthogonal designs a superset of ciods are presented and analyzed finally for rapid fading channels an equivalent matrix channel representation is developed which allows the results of quasi static fading channels to be applied to rapid fading channels using this representation we show that for rapid fading channels the rate of single symbol decodable stbcs are independent of the number of transmit antennas and inversely proportional to the block length of the code significantly the ciod for two transmit antennas is the only stbc that is single symbol decodable over both quasi static and rapid fading channels

space frequency codes for mimo ofdm systems with partial interference cancellation group decoding partial interference cancellation pic group decoding is an attractive decoding alternative for multiple input multiple output mimo wireless communications it can well deal with the tradeoff among rate diversity and decoding complexity of space time block codes in this paper a design criterion of full diversity space frequency codes sfc is proposed for mimo ofdm systems with the pic group decoding based on the criterion a systematic design of full diversity sfc is proposed that can achieve full diversity under the pic group decoding simulation results of the newly proposed codes demonstrate the theory

noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations the notion of a unitary noncommutative stochastic process with independent and stationary increments is introduced and it is proved that such a process under a continuity assumption can be embedded into the solution of a quantum stochastic differential equation in the sense of hudson and parthasarathy 8

fermion ito s formula and stochastic evolutions an ito product formula is proved for stochastic integrals against fermion brownian motion and used to construct unitary processes satisfying stochastic differential equations as in the corresponding boson theory 10 11 these give rise to stochastic dilations of completely positive semigroups

an efficient detector for combined space time coding and layered processing group layered space time architecture glst combines space time block coding and layered space time processing where the transmit stream is partitioned into different groups and in each group space time block coding is applied in the traditional receiver of glst group detection is applied first to suppress the interference from other groups and then decoding is performed for the desired group in this letter a novel detector is proposed in which the entire groups are decoded first and then group detection is performed next theoretical analysis will demonstrate that the new detector can achieve a significant capacity gain compared with the traditional one simulation results will further show that the proposed detector can obtain at least 4 db gain at a frame error rate of 10 sup 2 for instance

improved quasi orthogonal codes through constellation rotation in this letter we show that the performance of recently proposed quasi orthogonal space time codes can be improved by phase shifting the constellations of the symbols constituting the code the optimal rotation of the symbols increases the minimum distance of the corresponding space time codewords leading to substantially improved performance

capacity approaching space time codes for systems employing four transmitter antennas the design of space time codes that are capable of approaching the capacity of multiple input single output miso antenna systems is a challenging problem yet one of high practical importance while a remarkably simple scheme of alamouti 1998 is capable of attaining the channel capacity in the case of two transmitter and one receiver antennas 2 1 no such schemes are known for the case of more than two transmitter antennas we propose a family of space time codes that are especially designed for the case of four transmitter antennas and that are shown to allow the attainment of a significant fraction of the open loop shannon capacity of the 4 1 channel

on the nonexistence of rate one generalized complex orthogonal designs orthogonal space time block coding proposed recently by alamouti 1998 and tarokh et al 1999 is a promising scheme for information transmission over rayleigh fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum likelihood ml decoding algorithm tarokh et al extended the theory of classical orthogonal designs to the theory of generalized real or complex linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space time block codes stbc with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas it has been known that the stbc constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation contrary to this in this correspondence we prove that there does not exist rate one stbc from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation

multigroup decodable stbcs from clifford algebras a space time block code stbc in k symbols variables is called a g group decodable stbc if its maximum likelihood ml decoding metric can be written as a sum of g terms for some positive integer g greater than one such that each term is a function of a subset of the k variables and each variable appears in only one term in this paper we provide a general structure of the weight matrices of multigroup decodable codes using clifford algebras without assuming that the number of variables in each group is the same a method of explicitly constructing the weight matrices of full diversity delay optimal multigroup decodable codes is presented for arbitrary number of antennas for the special case of 2 a number of transmit antennas we construct two subclass of codes 1 a class of 2 a group decodable codes with rate a 2 a 1 which is equivalently a class of single symbol decodable codes and 2 a class of 2a 2 group decodable codes with rate a 1 2 a 2 i e a class of double symbol decodable codes

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

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

infinitely divisible central probability measures on compact lie groups regularity semigroups and transition kernels we introduce a class of central symmetric infinitely divisible probability measures on compact lie groups by lifting the characteristic exponent from the real line via the casimir operator the class includes gauss laplace and stable type measures we find conditions for such a measure to have a smooth density and give examples the hunt semigroup and generator of convolution semigroups of measures are represented as pseudo differential operators for sufficiently regular convolution semigroups the transition kernel has a tractable fourier expansion and the density at the neutral element may be expressed as the trace of the hunt semigroup we compute the short time asymptotics of the density at the neutral element for the cauchy distribution on the d torus on su 2 and on so 3 where we find markedly different behaviour than is the case for the usual heat kernel

quantum stochastic convolution cocycles ii schurmann s theory of quantum levy processes and more generally the theory of quantum stochastic convolution cocycles is extended to the topological context of compact quantum groups and operator space coalgebras quantum stochastic convolution cocycles on a c hyperbialgebra which are markov regular completely positive and contractive are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients and the structure of their stochastic generators is obtained automatic complete boundedness of a class of derivations is established leading to a characterisation of the stochastic generators of homomorphic convolution cocycles on a c bialgebra two tentative definitions of quantum levy process on a compact quantum group are given and with respect to both of these it is shown that an equivalent process on fock space may be reconstructed from the generator of the quantum levy process in the examples presented connection to the algebraic theory is emphasised by a focus on full compact quantum groups

upper bounds of rates of complex orthogonal space time block codes we derive some upper bounds of the rates of generalized complex orthogonal space time block codes we first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 3 4 we show that the rates of generalized complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 4 5 where the norms of column vectors may not be necessarily the same we also present another upper bound under a certain condition for a generalized complex orthogonal design its variables are not restricted to any alphabet sets but are on the whole complex plane a generalized complex orthogonal design with variables over some alphabet sets on the complex plane is also considered we obtain a condition on the alphabet sets such that a generalized complex orthogonal design with variables over these alphabet sets is also a conventional generalized complex orthogonal design and therefore the above upper bounds on its rate also hold we show that commonly used quadrature amplitude modulation qam constellations of sizes above 4 satisfy this condition

an adaptive conditional zero forcing decoder with full diversity least complexity and essentially ml performance for stbcs a low complexity essentially ml decoding technique for the golden code and the three antenna perfect code was introduced by sirianunpiboon howard and calderbank though no theoretical analysis of the decoder was given the simulations showed that this decoding technique has almost maximum likelihood ml performance inspired by this technique in this paper we introduce two new low complexity decoders for space time block codes stbcs the adaptive conditional zero forcing aczf decoder and the aczf decoder with successive interference cancellation aczf sic which include as a special case the decoding technique of sirianunpiboon we show that both aczf and aczf sic decoders are capable of achieving full diversity and we give a set of sufficient conditions for an stbc to give full diversity with these decoders we then show that the golden code the three and four antenna perfect codes the three antenna threaded algebraic space time code and the four antenna rate 2 code of srinath and rajan are all full diversity aczf aczf sic decodable with complexity strictly less than that of their ml decoders simulations show that the proposed decoding method performs identical to ml decoding for all these five codes these stbcs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for nt 4 transmit antennas we further provide a lower bound on the complexity of full diversity aczf aczf sic decoding all the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the aczf aczf sic decoding complexity both aczf and aczf sic decoders are amenable to sphere decoding implementation

quantum q white noise and a q central limit theorem we establish a connection between the azema martingales and certain quantum stochastic processes with increments satisfyingq commutation relations this leads to a theory ofq white noise onq bialgebras and to a generalization of the fock space representation theorem for white noise on bialgebras in particular quantum azema noise q interpolations between fermion and boson quantum brownian motion and unitary evolutions withq independent multiplicative increments are studied it follows from our results that the azema martingales and theq interpolations are central limits of sums ofq independent identically distributed quantum random variables

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

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

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

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

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

four group decodable space time block codes two new rate one full diversity space time block codes stbcs are proposed they are characterized by the lowest decoding complexity among the known rate one stbc arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection the first and the second codes are delay optimal if the number of transmit antennas is a power of 2 and even respectively the exact pairwise error probability is derived to allow for the performance optimization of the two codes compared with existing low decoding complexity stbc the two new codes offer several advantages such as higher code rate lower encoding decoding delay and complexity lower peak to average power ratio and better performance

structures on braided spaces structures on quantum and braided spaces of the type defined via an r matrix are studied these include q minkowski and q euclidean spaces as additive braided groups the duality between the braided groups of vectors and covectors is proved and some first applications to braided geometry are made

a fermion levy theorem the notion of quantum process with continuous trajectories is defined in terms of mutual quadratic variations and it is proved that for classical stochastic processes this notion of continuity of trajectories coincides with the usual one our main result is that any continuous trajectory difference martingale m which is a grassmann measure with scalar non atomic brackets is isomorphic to a fermion white noise mean zero fermi gaussian family whose covariance coincides with the brackets of m this is a fermion version of the levy representation theorem for classical brownian motion

pseudo differential operators and markov semigroups on compact lie groups abstract we extend the ruzhansky turunen theory of pseudo differential operators on compact lie groups into a tool that can be used to investigate group valued markov processes in the spirit of the work in euclidean spaces of n jacob and collaborators feller semigroups their generators and resolvents are exhibited as pseudo differential operators and the symbols of the operators forming the semigroup are expressed in terms of the fourier transform of the transition kernel the symbols are explicitly computed for some examples including the feller processes associated to stochastic flows arising from solutions of stochastic differential equations on the group driven by levy processes we study a family of levy type linear operators on general lie groups that are pseudo differential operators when the group is compact and find conditions for them to give rise to symmetric dirichlet forms

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

quantum independent increment processes on superalgebras on introduit la notion de processus quantique independant a increment stationnaire sur des superalgebres et on demontre un theoreme de reconstruction qui etablit une correspondance un a un entre ces processus et leurs generateurs infinitesimaux

the braided heisenberg group the braided groups and braided matrices b r for the solution r of the yang baxter equation associated to the quantum heisenberg group are computed it is also shown that a particular extension of the quantum heisenberg group is dual to the heisenberg universal enveloping algebra uq h and this result is used to derive an action of uq h on the braided groups the various covariance properties are then demonstrated using the braided heisenberg group as an explicit example in addition the braided heisenberg group is found to be self dual finally a physical application to a system of n braided harmonic oscillators is discussed an isomorphism is found between the n fold braided and unbraided tensor products and the usual free time evolution is shown to be equivalent to an action of a primitive generator of uq h on the braided tensor product

a martingale characterization of canonical commutation and anticommutation relations using a martingale condition and some restrictions on moments up to fourth order the characterisation problem of boson fermion and classical brownian motions is studied from a unified point of view entirely within the framework of elementary operator theory global commutation and anticommutation rules turn out to be consequences of corresponding commutation and anticommutation rules between past and future observables

an algebraic family of complex lattices for fading channels with application to space time codes a new approach is presented for the design of full modulation diversity fmd complex lattices for the rayleigh fading channel the fmd lattice design problem essentially consists of maximizing a parameter called the normalized minimum product distance d sub p sup 2 of the finite signal set carved out of the lattice we approach the problem of maximizing d sub p sup 2 by minimizing the average energy of the signal constellation obtained from a new family of fmd lattices the unnormalized minimum product distance for every lattice in the proposed family is lower bounded by a nonzero constant minimizing the average energy of the signal set translates to minimizing the frobenius norm of the generator matrices within the proposed family the two strategies proposed for the frobenius norm reduction are based on the concepts of successive minima sm and basis reduction of an equivalent real lattice the lattice constructions in this paper provide significantly larger normalized minimum product distances compared to the existing lattices in certain dimensions the proposed construction is general and works for any dimension as long as a list of number fields of the same degree is available

space time block coded spatial modulation a novel multiple input multiple output mimo transmission scheme called space time block coded spatial modulation stbc sm is proposed it combines spatial modulation sm and space time block coding stbc to take advantage of the benefits of both while avoiding their drawbacks in the stbc sm scheme the transmitted information symbols are expanded not only to the space and time domains but also to the spatial antenna domain which corresponds to the on off status of the transmit antennas available at the space domain and therefore both core stbc and antenna indices carry information a general technique is presented for the design of the stbc sm scheme for any number of transmit antennas besides the high spectral efficiency advantage provided by the antenna domain the proposed scheme is also optimized by deriving its diversity and coding gains to exploit the diversity advantage of stbc a low complexity maximum likelihood ml decoder is given for the new scheme which profits from the orthogonality of the core stbc the performance advantages of the stbc sm over simple sm and over v blast are shown by simulation results for various spectral efficiencies and are supported by the derivation of a closed form expression for the union bound on the bit error probability

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

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

high rate multisymbol decodable stbcs from clifford algebras it is well known that space time block codes stbcs obtained from orthogonal designs ods are single symbol decodable ssd and from quasi orthogonal designs qods are double symbol decodable dsd however there are ssd codes that are not obtainable from ods and dsd codes that are not obtainable from qods in this paper a method of constructing g symbol decodable g sd stbcs using representations of clifford algebras are presented which when specialized to g 1 2 gives ssd and dsd codes respectively for the number of transmit antennas 2a the rate in complex symbols per channel use of the g sd codes presented in this paper is a 1 g 2a g the maximum rate of the dsd stbcs from qods reported in the literature is a 2a 1 which is smaller than the rate a 1 2a 2 of the dsd codes of this paper for 2a transmit antennas in particular the reported dsd codes for 8 and 16 transmit antennas offer rates 1 and 3 4 respectively whereas the known stbcs from qods offer only 3 4 and 1 2 respectively the construction of this paper is applicable for any number of transmit antennas the diversity sum and diversity product of the new dsd codes are studied it is shown that the diversity sum is larger than that of all known qods and hence the new codes perform better than the comparable qods at low signal to noise ratios snrs for identical spectral efficiency simulation results for dsd codes at various spectral efficiencies are provided

filtered random variables bialgebras and convolutions we introduce the filtered bialgebra which is a multivariate generalization of the unital bialgebra c x x p of polynomials in noncommuting variables x x x x and a projection p p p2 endowed with the coproduct x x 1 1 x x x p p x with p being group like we study the associated convolutions random walks and filtered random variables the gns representations of the limit states lead to filtered fundamental operators which are the ccr fundamental operators on the multiple symmetric fock space h over h l2 r g where g is a separable hilbert space multiplied by appropriate projections the importance of filtered random variables and fundamental operators stems from the fact that by addition and strong limits one obtains from them the main types of noncommutative random variables and fundamental operators respectively regardless of the type of noncommutative independence

quantum stochastic convolution cocycles ii schurmann s theory of quantum levy processes and more generally the theory of quantum stochastic convolution cocycles is extended to the topological context of compact quantum groups and operator space coalgebras quantum stochastic convolution cocycles on a c hyperbialgebra which are markov regular completely positive and contractive are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients and the structure of their stochastic generators is obtained automatic complete boundedness of a class of derivations is established leading to a characterisation of the stochastic generators of homomorphic convolution cocycles on a c bialgebra two tentative definitions of quantum levy process on a compact quantum group are given and with respect to both of these it is shown that an equivalent process on fock space may be reconstructed from the generator of the quantum levy process in the examples presented connection to the algebraic theory is emphasised by a focus on full compact quantum groups

maximum likelihood sequence estimation from the lattice viewpoint considers the problem of data detection in multilevel lattice type modulation systems in the presence of intersymbol interference and additive white gaussian noise the conventional maximum likelihood sequence estimator using the viterbi algorithm has a time complexity of o m sup spl nu 1 operations per symbol and a space complexity of o spl delta m sup spl nu storage elements where m is the size of input alphabet spl nu is the length of channel memory and spl delta is the truncation depth by revising the truncation scheme and viewing the channel as a linear transform the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point from this lattice viewpoint the lattice sequence estimator for pam systems is developed which has the following desired properties 1 its expected time complexity grows as spl delta sup 2 as snr spl rarr spl infin 2 its space complexity grow as spl delta and 3 its error performance is effectively optimal for sufficiently large m a tight upper bound on the symbol error probability of the new estimator is derived and is confirmed by the simulation results of an example channel it turns out that the estimator is effectively optimal for m spl ges 4 and the loss in signal to noise ratio is less than 0 5 db even for m 2 finally limitations of the proposed estimator are also discussed

asymptotic properties of convolution operators and limits of triangular arrays on locally compact groups we consider a locally compact group g and a limiting measure of a commutative infinitesimal triangular system c i t s a of probability measures on g we show under some restrictions on g or a that belongs to a continuous one parameter convolution semigroup in particular this result is valid for symmetric c i t s a on any locally compact group g it is also valid for a limiting measure which has full support on a zariski connected f algebraic group g where f is a local field and any one of the following conditions is satisfied 1 g is a compact extension of a closed solvable normal subgroup in particular g is amenable 2 has finite one moment or 3 has density and in case the characteristic of f is positive the radical of g is f defined we also discuss the spectral radius of the convolution operator of a probability measure on a locally compact group g we show that it is always positive for any probability measure on g and it is also multiplicative in case of symmetric commuting measures