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

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

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

multiterminal source channel communication over an orthogonal multiple access channel we consider the problem of multiterminal source channel communication where a number of distributed and possibly correlated sources are transmitted through an orthogonal multiple access channel to a common destination we provide a characterization of the optimal tradeoff between the transmission cost gamma and the distortion vector d as measured against individual sources our approach consists of two steps 1 a multiple letter characterization of the rate distortion region of the multiterminal source coding and 2 a source channel separation theorem ensuring that all achievable pairs of gamma d can be obtained by combining the rate distortion region and the orthogonal multiple access channel capacity region as a corollary we determine the optimal power and distortion tradeoff in a quadratic gaussian sensor network under orthogonal multiple access and show that separate source and channel coding strictly outperforms the uncoded amplify forward transmission and is in fact optimal in this case this result is in sharp contrast to the case of nonorthogonal multiple access for which separate source and channel coding is not only suboptimal but also strictly inferior to uncoded transmission

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

a unified construction of space time codes with optimal rate diversity tradeoff the problem of constructing space time st block codes over a fixed desired signal constellation is considered in this situation there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code the transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal to noise ratio snr in the setting of a quasi static channel model let n sub t denote the number of transmit antennas and t the block interval for any n sub t spl les t a unified construction of n sub t spl times t st codes is provided here for a class of signal constellations that includes the familiar pulse amplitude pam quadrature amplitude qam and 2 sup k ary phase shift keying psk modulations as special cases the construction is optimal as measured by the rate diversity tradeoff and can achieve any given integer point on the rate diversity tradeoff curve an estimate of the coding gain realized is given other results presented here include i an extension of the optimal unified construction to the multiple fading block case ii a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes iii the providing of a linear dispersion form for the underlying binary block codes iv a gray mapped version of the unified construction and v a generalization of construction of the ary case corresponding to constellations of size sup k items ii and iii are aimed at simplifying the decoding of this class of st codes

hybrid arq in multiple antenna slow fading channels performance limits and optimal linear dispersion code design this paper focuses on studying the fundamental performance limits and linear dispersion code design for the mimo arq slow fading channel the optimal average rate of well known harq protocols is analyzed the optimal design of space time coding for the mimo arq channel is discussed information theoretic measures are used to optimize the rate assignment and derive the optimum design criterion which is then used to evaluate the optimality of existing space time codes a different design criterion which is obtained from the error probability analysis of space time coded mimo harq is presented examples are studied to reveal the gain of arq feedback in space time coded mimo systems

coded modulation in the block fading channel coding theorems and code construction we consider coded modulation schemes for the block fading channel in the setting where a codeword spans a finite number n of fading degrees of freedom we show that coded modulations of rate r bit per complex dimension over a finite signal set spl chi spl sube spl copf of size 2 sup m achieve the optimal rate diversity tradeoff given by the singleton bound spl delta n m r 1 spl lfloor n 1 r m spl rfloor for r spl isin 0 m spl rfloor furthermore we show also that the popular bit interleaved coded modulation achieves the same optimal rate diversity tradeoff we present a novel coded modulation construction based on blockwise concatenation that systematically yields singleton bound achieving turbo like codes defined over an arbitrary signal set spl chi spl sub spl copf the proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block fading channel we analyze the ensemble average performance under maximum likelihood ml decoding of the proposed codes by means of upper bounds and tight approximations we show that differently from the additive white gaussian noise awgn and fully interleaved fading cases belief propagation iterative decoding performs very close to ml on the block fading channel for any signal to noise ratio snr and even for relatively short block lengths we also show that at constant decoding complexity per information bit the proposed codes perform close to the information outage probability for any block length while standard block codes e g obtained by trellis termination of convolutional codes have a gap from outage that increases with the block length this is a different and more subtle manifestation of the so called interleaving gain of turbo codes

the mimo arq channel diversity multiplexing delay tradeoff in this paper the fundamental performance tradeoff of the delay limited multiple input multiple output mimo automatic retransmission request arq channel is explored in particular we extend the diversity multiplexing tradeoff investigated by zheng and tse in standard delay limited mimo channels with coherent detection to the arq scenario we establish the three dimensional tradeoff between reliability i e diversity throughput i e multiplexing gain and delay i e maximum number of retransmissions this tradeoff quantifies the arq diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain interestingly arq diversity appears even in long term static channels where all the retransmissions take place in the same channel state furthermore by relaxing the input power constraint allowing variable power levels in different retransmissions we show that power control can be used to dramatically increase the diversity advantage our analysis reveals some important insights on the benefits of arq in slow fading mimo channels in particular we show that 1 allowing for a sufficiently large retransmission delay results in an almost flat diversity multiplexing tradeoff and hence renders operating at high multiplexing gain more advantageous 2 mimo arq channels quickly approach the ergodic limit when power control is employed finally we complement our information theoretic analysis with an incremental redundancy lattice space time ir last coding scheme which is shown through a random coding argument to achieve the optimal tradeoff s an integral component of the optimal ir last coding scheme is a list decoder based on the minimum mean square error mmse lattice decoding principle for joint error detection and correction throughout the paper our theoretical claims are validated by numerical results

coded modulation with mismatched csit over mimo block fading channels reliable communication over delay constrained multiple input multiple output mimo block fading channels with discrete inputs and mismatched imperfect channel state information at the transmitter csit is studied the csit mismatch is modeled as gaussian random variables whose variances decay as a power of the signal to noise ratio snr a special focus is placed on the large snr decay of the error and outage probabilities when power control with long term power constraints is used without explicitly characterizing the corresponding power allocation algorithms we derive the outage exponent as a function of the system parameters including the csit noise variance exponent and the exponent of the peak power constraint it is shown that csit even if noisy is always beneficial and leads to important gains in terms of exponents

on the average rate performance of hybrid arq in quasi static fading channels the problem of efficient communication over a scalar quasi static fading channel is considered the single layer transmission slt and multi layer transmission mlt schemes do not require any knowledge of the channel state information csi at the transmitter but their performance is also limited it is shown that using hybrid arq harq can significantly improve the average rate performance provided that the rate assignment between different arq rounds is carefully chosen the average rate performance of several harq schemes is optimized and compared in addition optimal power allocation among retransmissions is derived and shown to further increase the average rate this power allocation gain is remarkable at low signal to noise ratio snr but becomes negligible at high snr comparison of two different types of limited feedback sequential feedback arq and one shot feedback quantized csi is made from several perspectives although the optimization problem is formed with respect to the average rate simulation results give a comprehensive comparison under different metrics including average rate outage probability and the combination of both substantial performance improvement is observed with even one arq retransmission in all simulations more importantly this gain appears to be robust with respect to the fading distributions

integrated semigroups and integrated solutions to abstract cauchy problems abstract concepts which have been developed in the theory of weakly continuous semigroups on dual banach spaces are extended to integrated semigroups the relation to integrated solutions of homogeneous and inhomogeneous abstract cauchy problems is established the results are illustrated for the wave equation in l2 rm

critical points for multiple integrals of the calculus of variations in this paper we deal with the existence of critical points of functional defined on the sobolev space w01 p p 1 by j u int limits omega vartheta x u du dx text where is a bounded open subset of n even for very simple examples in n the differentiability of j u can fail to overcome this difficulty we prove a suitable version of the ambrosetti rabinowitz mountain pass theorem applicable to functionals which are not differentiable in all directions existence and multiplicity of nonnegative critical points are also studied through the use of this theorem

on low complexity space time coding for quasi static channels we propose a new space time coding scheme for the quasi static multiple antenna channel with perfect channel state information at the receiver and no channel state information at the transmitter in our scheme codewords produced by a trellis encoder are formatted into space time codeword arrays such that decoding can be implemented efficiently by minimum mean square error mmse decision feedback interference mitigation coupled with viterbi decoding through the use of per survivor processing we discuss the code design for the new scheme and show that finding codes with optimal diversity is much easier than for conventional trellis space time codes stcs we provide an upper bound on the word error rate wer of our scheme which is both accurate and easy to evaluate then we find upper and lower bounds on the information outage probability with discrete independent and identically distributed i i d inputs as opposed to gaussian inputs as in most previous works and we show that the mmse front end yields a large advantage over the whitened matched filter i e zero forcing front end finally we provide a comprehensive performance complexity comparison of our scheme with coded vertical bell labs layered space time v blast architecture and with the recently proposed threaded space time codes we also discuss the concatenation of our scheme with block space time precoders such as the linear dispersion codes

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

on the required number of antennas in a point to point large but finite mimo system outage limited scenario this paper investigates the performance of the point to point multiple input multiple output mimo systems in the presence of a large but finite numbers of antennas at the transmitters and or receivers considering the cases with and without hybrid automatic repeat request harq feedback we determine the minimum numbers of the transmit receive antennas which are required to satisfy different outage probability constraints our results are obtained for different fading conditions and the effect of the power amplifiers efficiency feedback error probability on the performance of the mimo harq systems is analyzed then we use some recent results on the achievable rates of finite block length codes to analyze the effect of the codewords lengths on the system performance moreover we derive closed form expressions for the asymptotic performance of the mimo harq systems when the number of antennas increases our analytical and numerical results show that different outage requirements can be satisfied with relatively few transmit receive antennas

new nonasymptotic channel coding theorems for structured codes new nonasymptotic random coding theorems with error probability epsilon and finite block length n based on gallager parity check ensemble and general parity check ensembles are derived in this paper the resulting nonasymptotic achievability bounds when combined with nonasymptotic equipartition properties developed in this paper can be easily computed analytically these nonasymptotic achievability bounds are shown to be asymptotically tight up to the second order of the coding rate as n goes to infinity with either constant or subexponentially decreasing epsilon in the case of gallager parity check ensemble and to imply that low density parity check ldpc codes be capacity achieving in the case of ldpc ensembles numerically they are also compared favorably for finite n and epsilon of practical interest with existing nonasymptotic achievability bounds in the literature

unequal message protection asymptotic and non asymptotic tradeoffs we study a form of unequal error protection that we term unequal message protection ump the message set of a ump code is a union of m disjoint message classes each class has its own error protection requirement with some classes needing better error protection than others we analyze the tradeoff between rates of message classes and the levels of error protection our analysis reveals new tradeoffs which were not captured by prior works on ump codes to obtain our results we generalize finite block length achievability and converse bounds due to polyanskiy poor verdu we evaluate our bounds for the binary symmetric and binary erasure channels and analyze the asymptotic characteristic of the bounds in the fixed error and moderate deviations regimes in addition we consider two questions related to the practical construction of ump codes first we study a header construction that prefixes the message class into a header followed by data protection using a standard homogeneous classical code we show that in general this construction is not optimal at finite block lengths we further demonstrate that our main ump achievability bound can be obtained using coset codes which suggests a path to implementation of tractable ump codes

approximations of laplace transforms and integrated semigroups abstract let f m m n be a sequence of functions from 0 to a banach space e we give a new and essential condition on f m which is weaker than the usual local lipschitz continuity condition ensuring that the convergence of f m is equivalent to the convergence of their laplace transforms this enables us to establish new approximation theorems for r times integrated semigroups on e for all r 0 as a consequence an open problem for the convergence of integrated semigroups on the whole space e is solved in essence moreover we present an application to nonhomogeneous cauchy problems

optimum estimation via gradients of partition functions and information measures a statistical mechanical perspective in continuation to a recent work on the statistical mechanical analysis of minimum mean square error mmse estimation in gaussian noise via its relation to the mutual information the i mmse relation here we propose a simple and more direct relationship between optimum estimation and certain information measures e g the information density and the fisher information which can be viewed as partition functions and hence are amenable to analysis using statistical mechanical techniques the proposed approach has several advantages most notably its applicability to general sources and channels as opposed to the i mmse relation and its variants which hold only for certain classes of channels e g additive white gaussian noise channels we then demonstrate the derivation of the conditional mean estimator and the mmse in a few examples two of these examples turn out to be generalizable to a fairly wide class of sources and channels for this class the proposed approach is shown to yield an approximate conditional mean estimator and an mmse formula that has the flavor of a single letter expression we also show how our approach can easily be generalized to situations of mismatched estimation

on the convergence and approximation of integrated semigroups abstract we extend the well known theorem on convergence and approximation of c 0 semigroups due to h f trotter and t kato to the context of integrated semigroups the result is obtained as a consequence of an integrated version of the trotter kato theorem based on the laplace transform an application to the complete second order equation is given

convoluted c cosine functions and semigroups relations with ultradistribution and hyperfunction sines abstract convoluted c cosine functions and semigroups in a banach space setting extending the classes of fractionally integrated c cosine functions and semigroups are systematically analyzed structural properties of such operator families are obtained relations between convoluted c cosine functions and analytic convoluted c semigroups introduced and investigated in this paper are given through the convoluted version of the abstract weierstrass formula which is also proved in the paper ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups several examples of operators generating convoluted cosine functions analytic convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors as an application it is proved that the polyharmonic operator 2 n n n acting on l 2 0 with appropriate boundary conditions generates an exponentially bounded k n convoluted cosine function and consequently an exponentially bounded analytic k n 1 convoluted semigroup of angle 2 for suitable exponentially bounded kernels k n and k n 1

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

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

the hille yosida and trotter kato theorems for integrated semigroups abstract we completely characterize the generators of non degenerate exponentially bounded n times integrated semigroups we deduce some perturbation results we also give a proof of the trotter kato theorem inspired from the classical one

the capacity of finite state markov channels with feedback we consider a class of finite state markov channels with feedback we first introduce a simplified equivalent channel model and then construct the optimal stationary and nonstationary input processes that maximize the long term directed mutual information furthermore we give a sufficient condition under which the channel s shannon capacity can be achieved by a stationary input process the corresponding converse coding theorem and direct coding theorem are proved

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

a linear program for the finite block length converse of polyanskiy poor verdu via nonsignaling codes motivated by recent work on entanglement assisted codes for sending messages over classical channels the larger easily characterized class of nonsignaling codes is defined analyzing the optimal performance of these codes yields an alternative proof of the finite block length converse of polyanskiy poor and verdu and shows that they achieve this converse this provides an explicit formulation of the converse as a linear program which has some useful features for discrete memoryless channels it is shown that nonsignaling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero

epsilon capacity of binary symmetric averaged channels we consider the channel model obtained by averaging binary symmetric channel bsc components with respect to a weighting distribution a nonempty open interval a b is called a capacity gap for this channel model if no channel component has capacity in a b and this property fails for every open interval strictly containing a b for a fixed epsi 0 suppose one wishes to compute the epsi capacity of the channel which is the maximum asymptotic rate at which the channel can be encoded via a sequence of channel codes each achieving block error probability lesepsi in 1963 parthasarathy provided a formula for epsi capacity which is valid for all but at most countably many values of epsi when the formula fails there exists a unique capacity gap a b such that the epsi capacity lies in a b but one does not know precisely where via a coding theorem and converse we establish a formula for computing epsi capacity as a function of the endpoints a b of the associated capacity gap a b the formula holds whenever the capacity gap is sufficiently narrow in width

a formula for the capacity of the general gel fand pinsker channel we consider the gel fand pinsker problem in which the channel and state are general i e possibly non stationary non memoryless and non ergodic using the information spectrum method and a non trivial modification of the piggyback coding lemma by wyner we prove that the capacity can be expressed as an optimization over the difference of a spectral inf and a spectral sup mutual information rate we consider various specializations including the case where the channel and the state are memoryless but not necessarily stationary

a lower bound on the probability of error in multihypothesis testing consider two random variables x and y where x is finitely or countably infinitely valued and where y is arbitrary let spl epsiv denote the minimum probability of error incurred in estimating x from y it is shown that spl epsiv spl ges sub 0 spl les spl alpha spl les 1 sup sup 1 spl alpha p spl pi x y spl les spl alpha where spl pi x y denotes the posterior probability of x given y this bound finds information theoretic applications in the proof of converse channel coding theorems it generalizes and strengthens previous lower bounds due to shannon and to verdu and han 1994

further results on convolutional code search for block fading channels this correspondence presents results of code search for convolutional codes over block fading channels bfcs search criteria are based on a union bound approach which exploits the concept of generalized transfer function gtf of the error trellis diagram a new asymptotic bound is derived and the performance of the codes found using our search criterion is compared analytically and by numerical simulation with already existing codes