extensions of the i mmse relationship to gaussian channels with feedback and memory unveiling a fundamental link between information theory and estimation theory the i mmse relationship by guo et al together with its numerous extensions has great theoretical significance and various practical applications on the other hand its influences to date have been restricted to channels without feedback or memory due to the absence of its extensions to such channels in this paper we propose the extensions of the i mmse relationship to discrete time and continuous time gaussian channels with feedback and or memory our approach is based on a very simple observation which can be applied to other scenarios such as a simple and direct proof of the classical de bruijn s identity

the l component of the unipotent albanese map we prove a finiteness theorem for the local l p component of the qp unipotent albanese map for curves as an application we refine the non abelian selmer varieties arising in the study of global points and deduce thereby a new proof of siegel s theorem for affine curves over q of genus one with mordell weil rank at most one

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

precoding for outage probability minimization on block fading channels the outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading this limit is mainly determined by two parameters the diversity order and the coding gain with linear precoding full diversity on a block fading channel can be achieved without error correcting code however the effect of precoding on the coding gain is not well known mainly due to the complicated expression of the outage probability using a geometric approach this paper establishes simple upper bounds on the outage probability the minimization of which yields to precoding matrices that achieve very good performance for discrete alphabets it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i i d gaussian input distribution thus essentially maximizing the coding gain

nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

optimal power control for ldpc codes in block fading channels we study the error probability of ldpc codes in delay limited block fading channels with channel state information csi at the transmitter and the receiver we derive the optimal power allocation algorithms for ldpc codes with specific degree distributions using multi edge type density evolution error boundaries the resulting performance approaches the outage probability for a number of power constraints furthermore we adapt the algorithm for finite length codes and show that the proposed algorithm enables gains larger than 10 db over uniform power allocation the method is valid for general possibly correlated fading distributions this represents the first analysis of specific ldpc codes over block fading channels with full csi

generalized quadratic matrix programming a unified framework for linear precoding with arbitrary input distributions this paper investigates a new class of nonconvex optimization which provides a unified framework for linear precoding in single multiuser multiple input multiple output channels with arbitrary input distributions the new optimization is called generalized quadratic matrix programming gqmp due to the nondeterministic polynomial time hardness of gqmp problems instead of seeking globally optimal solutions we propose an efficient algorithm that is guaranteed to converge to a karush kuhn tucker point the idea behind this algorithm is to construct explicit concave lower bounds for nonconvex objective and constraint functions and then solve a sequence of concave maximization problems until convergence in terms of application we consider a downlink underlay secure cognitive radio network where each node has multiple antennas we design linear precoders to maximize the average secrecy sum rate with finite alphabet inputs and statistical channel state information at the transmitter the precoding problems under secure multicast broadcast scenarios are gqmp problems and thus they can be solved efficiently by our proposed algorithm several numerical examples are provided to show the efficacy of our algorithm

globally optimal linear precoders for finite alphabet signals over complex vector gaussian channels we study the design optimization of linear precoders for maximizing the mutual information between finite alphabet input and the corresponding output over complex valued vector channels this mutual information is a nonlinear and non concave function of the precoder parameters posing a major obstacle to precoder design optimization our work presents three main contributions first we prove that the mutual information is a concave function of a matrix which itself is a quadratic function of the precoder matrix second we propose a parameterized iterative algorithm for finding optimal linear precoders to achieve the global maximum of the mutual information the proposed iterative algorithm is numerically robust computationally efficient and globally convergent third we demonstrate that maximizing the mutual information between a discrete constellation input and the corresponding output of a vector channel not only provides the highest practically achievable rate but also serves as an excellent criterion for minimizing the coded bit error rate our numerical examples show that the proposed algorithm achieves mutual information very close to the channel capacity for channel coding rate under 0 75 and also exhibits a large gain over existing linear precoding and or power allocation algorithms moreover our examples show that certain existing methods are susceptible to being trapped at locally optimal precoders

linear precoding for finite alphabet inputs over mimo fading channels with statistical csi this paper investigates the linear precoder design that maximizes the average mutual information of multiple input multiple output fading channels with statistical channel state information known at the transmitter it formulates the design from the standpoint of finite alphabet inputs which leads to a problem that is very important in practice but extremely difficult in theory first the average mutual information lacks closed form expression and involves prohibitive computational burden second the optimization over the precoder is nonconcave and thus easily gets stuck in local maxima to address these issues this study first derives lower and upper bounds for the average mutual information in which the computational complexity is reduced by several orders of magnitude compared to calculating the average mutual information directly it proves that maximizing the bounds is asymptotically optimal and shows that with a constant shift the lower bound actually offers a very accurate approximation to the average mutual information for various fading channels this paper further proposes utilizing the lower bound as a low complexity and accurate alternative for developing a two step algorithm to find a near global optimal precoder numerical examples demonstrate the convergence and efficacy of the proposed algorithm compared to its conventional counterparts the proposed linear precoding method provides significant performance gain over existing precoding algorithms the gain becomes more substantial when the spatial correlation of mimo channels increases

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

it formulae for gamma target mutual information and relative entropy in this paper we introduce new stein identities for gamma target distribution as well as a new non linear channel specifically designed for gamma inputs from these two ingredients we derive an explicit and simple formula for the derivative of the input output mutual information of this non linear channel with respect to the channel quality parameter this relation is reminiscent of the well known link between the derivative of the input output mutual information of additive gaussian noise channel with respect to the signal to noise ratio and the minimum mean square error the proof relies on a rescaled version of de bruijn identity for gamma target distribution together with a stochastic representation for the gamma specific fisher information finally we are able to derive precise bounds and asymptotics for the input output mutual information of the non linear channel with gamma inputs

on albanese torsors and the elementary obstruction we show that the elementary obstruction to the existence of 0 cycles of degree 1 on an arbitrary variety x over an arbitrary field can be expressed in terms of the albanese 1 motives associated with dense open subsets of x arithmetic applications are given

optimum power allocation and bit loading for bicm systems this paper introduces a joint bit loading and power allocation algorithm for systems combining bit interleaved coded modulation bicm with multicarrier transmission the proposed algorithm maximizes the mutual information so it can be regarded as a generalization of mercury waterfilling policy that incorporates bit loading the followed approach relies on irregular modulation and power to cast the problem in the framework of convex optimization this allows to derive the optimum solution without resorting to greedy algorithms embedding the bit loading in the definition of an equivalent constellation such that the complexity increase with respect to mercury waterfilling is negligible while irregular modulation plays a key role in algorithm definition it is proved that only a few subcarriers employ it and it is shown that a practical low complexity algorithm can be obtained with minimal losses that does not use irregular modulation

multiple antenna fading channels with arbitrary inputs characterization and optimization of the information rate we investigate the high snr capacity of multiple antenna fading coherent channels driven by inputs that are constrained to obey a certain equiprobable discrete distribution rather than the optimal capacity achieving gaussian one in particular we capitalize on the machinery of asymptotic analysis most notably the asymptotic expansion of integrals in order to construct high snr expansions to the average minimum mean squared error mmse and via the relation between mmse and mutual information high snr expansions to the average mutual information thereby providing immediately a high snr expansion to the so called constrained capacity we use the expansions to characterize the constrained capacity of various multiple antenna fading coherent channels including rayleigh fading models ricean fading models and antenna correlated models the analysis unveils in detail the impact of the number of transmit and receive antennas transmit and receive antenna correlation line of sight components and the geometry of the signaling scheme on the reliable information transmission rate we also use the expansions to optimize the constrained capacity of multiple antenna fading coherent channels as an example we focus on the derivation of design criteria for space time signaling schemes

mismatched estimation and relative entropy a random variable with distribution p is observed in gaussian noise and is estimated by a mismatched minimum mean square estimator that assumes that the distribution is q instead of p this paper shows that the integral over all signal to noise ratios snrs of the excess mean square estimation error incurred by the mismatched estimator is twice the relative entropy d p q in nats this representation of relative entropy can be generalized to nonreal valued random variables and can be particularized to give new general representations of mutual information in terms of conditional means inspired by the new representation we also propose a definition of free relative entropy which fills a gap in and is consistent with the literature on free probability

the local pro p anabelian geometry of curves let x be a connected scheme then one can associate after grothendieck to x its algebraic fundamental group 1 x this group 1 x is a profinite group which is uniquely determined up to inner automorphisms by the property that the category of finite discrete sets equipped with a continuous 1 x action is equivalent to the category of finite etale coverings of x moreover the assignment x 1 x is a functor from the category of connected schemes and morphisms of schemes to the category of profinite topological groups and continuous outer homomorphisms i e continuous homomorphisms of topological groups where we identify any two homomorphisms that can be obtained from one another by composition with an inner automorphism

level crossing probabilities for multipath acoustic processes with bimodal spectra a general method of evaluating upcrossing probabilities for a class of random processes consisting of two narrow band signals is presented one of the two significant frequencies of the corresponding bimodal spectra is assumed to be dominant the method approximates the maxima of these processes by the corresponding values of the envelope processes it is also assumed that the discrete processes of the maxima are markov the results have several applications two prominent examples are detection problems of multipath partially saturated processes in underwater acoustics and the problem of the structural reliability of marine diesel engine shafting systems

construction of minimum euclidean distance mimo precoders and their lattice classifications this correspondence deals with the construction of minimum euclidean distance precoders for multiple input multiple output mimo systems with up to four transmit antennas by making use of a state of the art technique for optimization over the unitary group we can numerically optimize the mimo precoders the correspondence then proceeds by identifying the obtained precoders as well known lattices square z2 schlafli d4 d6 gosset e8 with three transmit antennas the results are slightly different compared with other numbers of transmit antennas since the obtained precoder is not an instance of the densest 6 dimensional lattice the overall conclusions of the correspondence are that the found precoders for mimo transmission are highly structured and that even with small constellations lattice theory can be used for the design of mimo precoders

estimation in gaussian noise properties of the minimum mean square error consider the minimum mean square error mmse of estimating an arbitrary random variable from its observation contaminated by gaussian noise the mmse can be regarded as a function of the signal to noise ratio snr as well as a functional of the input distribution of the random variable to be estimated it is shown that the mmse is concave in the input distribution at any given snr for a given input distribution the mmse is found to be infinitely differentiable at all positive snr and in fact a real analytic function in snr under mild conditions the key to these regularity results is that the posterior distribution conditioned on the observation through gaussian channels always decays at least as quickly as some gaussian density furthermore simple expressions for the first three derivatives of the mmse with respect to the snr are obtained it is also shown that as functions of the snr the curves for the mmse of a gaussian input and that of a non gaussian input cross at most once over all snrs these properties lead to simple proofs of the facts that gaussian inputs achieve both the secrecy capacity of scalar gaussian wiretap channels and the capacity of scalar gaussian broadcast channels as well as a simple proof of the entropy power inequality in the special case where one of the variables is gaussian

on the section conjecture in anabelian geometry let x be a smooth projective curve of genus 1 over a field k which is finitely generated over the rationals the section conjecture in grothendieck s anabelian geometry says that the sections of the canonical projection from the arithmetic fundamental group of x onto the absolute galois group of k are up to conjugation in one to one correspondence with k rational points of x the birational variant conjectures a similar correspondence where the fundamental group is replaced by the absolute galois group of the function field k x the present paper proves the birational section conjecture for all x when k is replaced e g by the field of p adic numbers it disproves both conjectures for the field of real or p adic algebraic numbers and it gives a purely group theoretic characterization of the sections induced by k rational points of x in the birational setting over almost arbitrary fields as a biproduct we obtain galois theoretic criteria for radical solvability of polynomial equations in more than one variable and for a field to be pac to be large or to be hilbertian

hybrid beamforming in mm wave mimo systems having a finite input alphabet recently there has been significant research effort toward achieving high data rates in the millimeter wave bands by employing large antenna systems these systems are considered to have only a fraction of the rf chains compared with the total number of antennas and employ analog phase shifters to steer the transmit and receive beams in addition to the conventional beamforming bf combining invoked in the baseband domain this scheme which is popularly known as hybrid bf has been extensively studied in the literature to the best of our knowledge all the existing schemes focus on obtaining the bf combining matrices that maximize the system capacity computed using a gaussian input alphabet however this choice of matrices may be suboptimal for practical systems since they employ a finite input alphabet such as quadrature amplitude modulation phase shift keying constellations hence in this paper we consider a hybrid bf combining system operating with a finite input alphabet and optimize the analog as well as digital bf combining matrices by maximizing the mutual information mi this is achieved by an iterative gradient ascent algorithm that exploits the relationship between the minimum mean squared error and the mi furthermore an iterative algorithm is proposed for designing a codebook for the analog and digital bf combining matrices based on a vector quantization approach our simulation results demonstrate that the proposed gradient ascent algorithm achieves an ergodic rate improvement of up to 0 4 bits per channel use bpcu compared with the gaussian input scenario furthermore the gain in the ergodic rate achieved by employing the vector quantization based codebook is about 0 5 bpcu compared with the gaussian input scenario

linear precoding gain for large mimo configurations with qam and reduced complexity in this paper the problem of designing a linear precoder for multiple input multiple output mimo systems in conjunction with quadrature amplitude modulation qam is addressed first a novel and efficient methodology to evaluate the input output mutual information for a general mimo system as well as its corresponding gradients is presented based on the gauss hermite quadrature rule then the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the mimo input output mutual information for qam systems with relatively moderate mimo channel sizes the proposed methodology is next applied in conjunction with the complexity reducing per group processing technique to both perfect channel state information csi at the transmitter as well as statistical csi statistical csi scenarios with large transmitting and receiving antenna sizes and for constellation size up to m 64 we show by the numerical results that the precoders developed offer significantly better performance than the configuration with no precoder as well as the maximum diversity precoder for qam with constellation sizes m 16 32 and 64 and for mimo channel size up to 100 times 100

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

new models on the ocean acoustic detection process the basic problem of the ocean acoustic detection process is formulated analytically under the assumption of fully developed saturated phase random multipath acoustic fluctuations detection is defined as occurring whenever p the root mcan square pressure at the receiver exceeds a specified threshold level p two models one exact and one approximate are developed for obtaining the probability density functions of the time between two successive detections and of the time p is above p0 holding time the two models are compared with one another and with the extensively used 2 r model one of the reasons that the latter model has a limited success in practice is the inability to estimate the appropriate value for 2 a parameter which is determined empirically in this paper we have derived an appropriate value for 2 in terms of v the single path root mcan square phase rate r half the long time average mean square pressure at the receiver and po the threshold level using this equivalent value for t we observe that our exact and approximate detection models exhibit similar long term behavior but markedly different short term characteristics as compared with th t a model this is due to the memory of the process a property that cannot be accounted for in the t a model a comparison of these models with data obtained from various field experiments demonstrates in most cases an improved capability over the 2 a model

complexity reduction for the optimization of linear precoders over random mimo channels precoder optimization with full channel state information for finite alphabet signals over multiple input multiple output random channels is investigated in this paper the precoder is represented by a product of power allocation matrix and constellation forming matrix there was an optimal algorithm introduced in the literature to globally maximize the channel mutual information by iteratively optimizing these two matrices however the computational complexity of the optimal algorithm is painfully high especially when it is used with the high order modulation and the high data stream number in this paper we propose a novel sub optimal low complexity precoding algorithm and compare it with the optimal one the new algorithm proceeds in two steps first the constellation forming matrix is fixed in order to maximize the minimum euclidean distance between the received symbols which ensures high channel mutual information then given the constellation forming matrix an iterative algorithm searches for the power allocation matrix that maximizes the channel mutual information since optimizing only one matrix instead of two the new algorithm not only achieves a lower computational complexity but also avoids the use of initial values which must be carefully selected for each channel and signal to noise ratio for fast convergence another advantage of the new algorithm is that the resulting precoder has a fixed form of received constellation thanks to the fixed constellation forming matrix this allows us to optimize the symbol mapping on the received constellation simulation results show that the proposed low complexity precoder achieves error rate performance that is close to performance of the optimal one when the conventional mapping is used in addition the new precoder used with optimized mapping at received constellation shows significant error rate performance improvement

linear precoder design for mimo interference channels with finite alphabet signaling this paper investigates the linear precoder design for k user interference channels of multiple input multiple output mimo transceivers under finite alphabet inputs we first obtain general explicit expressions of the achievable rate for users in the mimo interference channel systems we study optimal transmission strategies in both low and high signal to noise ratio snr regions given finite alphabet inputs we show that a simple power allocation design achieves optimal performance at high snr whereas the well known interference alignment technique for gaussian inputs only utilizes a partial interference free signal space for transmission and leads to a constant rate loss when applied naively to finite alphabet inputs moreover we establish necessary conditions for the linear precoder design to achieve weighted sum rate maximization we also present an efficient iterative algorithm for determining precoding matrices of all the users our numerical results demonstrate that the proposed iterative algorithm achieves considerably higher sum rate under practical qam inputs than other known methods

the cuspidalisation of sections of arithmetic fundamental groups abstract in this paper which is a sequel to 7 we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i th and 2 p th step prosolvable arithmetic fundamental groups as a consequence we exhibit two necessary and sufficient conditions for sections of arithmetic fundamental groups of hyperbolic curves over p adic local fields to arise from rational points we also exhibit a class of sections of arithmetic fundamental groups of p adic curves which are orthogonal to pic and which satisfy unconditionally one of the above conditions

arithmetic of p adic curves and sections of geometrically abelian fundamental groups let x be a proper smooth and geometrically connected curve of genus g x ge 1 over a p adic local field we prove that there exists an effectively computable open affine subscheme u subset x with the property that text period x 1 and text index x equals 1 or 2 resp text period x text index x 1 assuming text period x text index x if resp if and only if the exact sequence of the geometrically abelian fundamental group of usplits we compute the torsor of splittings of the exact sequence of the geometrically abelian absolute galois group associated to x and give a new characterisation of sections of arithmetic fundamental groups of curves over p adic local fields which are orthogonal to text pic 0 resp text pic wedge as a consequence we observe that the non geometric geometrically pro p section constructed by hoshi 3 is orthogonal to text pic 0

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

on abelian birational sections for a smooth and geometrically irreducible variety x over a field k the quotient of the absolute galois group gk x by the commutator subgroup of g k x projects onto gk we investigate the sections of this projection we show that such sections correspond to infinite divisions of the elementary obstruction of colliot thelene and sansuc if k is a number field and the tate shafarevich group of the picard variety of x is finite then such sections exist if and only if the elementary obstruction vanishes for curves this condition also amounts to the existence of divisors of degree 1 finally we show that the vanishing of the elementary obstruction is not preserved by extensions of scalars

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

gradient of mutual information in linear vector gaussian channels this paper considers a general linear vector gaussian channel with arbitrary signaling and pursues two closely related goals i closed form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system and ii fundamental connections between information theory and estimation theory generalizing the fundamental relationship recently unveiled by guo shamai and verdu spl acute we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output gradients and derivatives with respect to other parameters are then found via the differentiation chain rule

optimum compression of a noisy measurement for transmission over a noisy channel this paper is motivated by sensing and wireless communication where data compression or dimension reduction may be used to reduce the required communication bandwidth high dimensional measurements are converted into low dimensional representations through linear compression our aim is to compress a noisy sensor measurement allowing for the fact that the compressed measurement will then be transmitted over a noisy channel we give the closed form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix we show that the solutions share a common architecture consisting of a canonical coordinate transformation scaling by coefficients which account for canonical correlations and channel noise variance followed by a coordinate transformation into the sub dominant invariant subspace of the channel noise furthermore we explore the design problem with respect to more general criteria and provide a unified factorization for the corresponding optimal compression matrix a necessary condition is obtained for the optimal compression

hessian and concavity of mutual information differential entropy and entropy power in linear vector gaussian channels within the framework of linear vector gaussian channels with arbitrary signaling the jacobian of the minimum mean square error and fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper capitalizing on prior research where the minimum mean square error and fisher information matrices were linked to information theoretic quantities through differentiation the hessian of the mutual information and the entropy are derived these expressions are then used to assess the concavity properties of mutual information and entropy under different channel conditions and also to derive a multivariate version of an entropy power inequality due to costa

on mimo detection under non gaussian target scattering in this paper we consider a multiple input multiple output mimo detection problem with m widely spaced transmit antennas and l widely spaced receive antennas and we study the problem of designing the signal waveforms transmitted by each source node under non gaussian target scattering and temporally correlated gaussian clutter two figures of merit are investigated for space time code stc optimization under a semidefinite rank constraint 1 the lower chernoff bound lcb to the detection probability for fixed probability of false alarm and 2 the mutual information mi between the observations available at the receive nodes and the channel response generated by a point like target assumed present tout court both receive and transmit power constraints are discussed if the scattering distribution possesses some suitably defined properties of unitary invariance see both mi optimal and lcb optimal stcs have a simple canonical structure the same set of clutter dependant temporal codewords are employed at the transmit nodes the only difference among the many solutions being the amount of power radiated by each antenna such a spatial power allocation critically depends upon the adopted figure of merit the specified power constraint and the underlying scattering model sufficient conditions to determine the optimal power allocation for all design criteria are provided asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal to clutter ratios proving that assuming gaussian scattering at the design stage is a robust choice a case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non gaussianity on the system performances

delay limited capacity in the low power regime outage performance of the m block fading with additive white gaussian noise bf awgn is investigated in the low power regime we consider delay constrained constant rate communications with perfect channel state information csi at both the transmitter and the receiver csi tr under a short term power constraint stpc and a long term power constraint ltpc subject to stpc we show that selection diversity that allocates all the power to the strongest block is asymptotically optimal then we provide a simple characterization of the outage probability in the regime of interest we quantify the reward due to csi tr over the constant rate constant power scheme and show that this reward increases with the delay constraint for instance for rayleigh fading we find that a power gain up to 4 3 db is achievable subject to ltpc we show that the above guidelines still holds and that the outage performance improves due to the flexibility of the ltpc over the stpc more interestingly we prove that ltpc allows zero outage communication even at low snr and characterize the delay limited capacity at low snr in a simple form more precisely we establish that the delay limited capacity scales linearly with the power constraint for a given m our framework highlights the benefit of fading at low snr as the delay limited capacity may outperform the awgn capacity for instance for rayleigh fading and with m 3 the delay limited capacity is 16 higher than the capacity of an awgn channel

on secrecy rate analysis of mimo wiretap channels driven by finite alphabet input this work investigates the effect of finite alphabet input constraint on the secrecy rate of a multi antenna wiretap channel most existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on gaussian source signals and secrecy code for practical considerations we study the effect of finite discrete constellation on the achievable secrecy rate of multiple antenna wire tap channels our proposed precoding scheme converts the underlying multi antenna system into a bank of parallel channels based on this precoding strategy we develop a decentralized power allocation algorithm based on dual decomposition to maximize the achievable secrecy rate in addition we analyze the achievable secrecy rate for finite alphabet inputs in low and high snr regions our results demonstrate substantial difference in secrecy rate between systems given finite alphabet inputs and systems with gaussian inputs

precoding by pairing subchannels to increase mimo capacity with discrete input alphabets we consider gaussian multiple input multiple output mimo channels with discrete input alphabets we propose a non diagonal precoder based on the x codes in to increase the mutual information the mimo channel is transformed into a set of parallel subchannels using singular value decomposition svd and x codes are then used to pair the subchannels x codes are fully characterized by the pairings and a 2 2 real rotation matrix for each pair parameterized with a single angle this precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs the problem of finding the optimal precoder with the above structure which maximizes the total mutual information is solved by i optimizing the rotation angle and the power allocation within each pair and ii finding the optimal pairing and power allocation among the pairs it is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal pre coder by cruz et al and is significantly better than mercury waterfllling strategy by lozano et al our approach greatly simplifies both the precoder optimization and the detection complexity making it suitable for practical applications

on the existence of non geometric sections of arithmetic fundamental groups we show the existence of group theoretic sections of the etale by geometrically abelian quotient of the arithmetic fundamental group of hyperbolic curves over p adic local fields relative to a proper and flat model which are non geometric i e which do not arise from rational points

large system analysis of multiuser detection with an unknown number of users a high snr approach we analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver in this environment users activity must be estimated along with any other parameters such as data power and location our main goal is to determine the performance loss caused by the need for estimating the identities of active users which are not known a priori to prevent a loss of optimality we assume that identities and data are estimated jointly rather than in two separate steps we examine the performance of multiuser detectors when the number of potential users is large statistical physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency special attention is paid to the fixed point equation whose solution yields the multiuser efficiency of the optimal maximum a posteriori detector in the large signal to noise ratio regime our analysis yields closed form approximate bounds to the minimum mean squared error in this regime these illustrate the set of solutions of the fixed point equation and their relationship with the maximum system load next we study the maximum load that the detector can support for a given quality of service specified by error probability

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

galois sections for abelianized fundamental groups given a smooth projective curve x of genus at least 2 over a number field k grothendieck s section conjecture predicts that the canonical projection from the etale fundamental group of x onto the absolute galois group of k has a section if and only if the curve has a rational point we show that there exist curves where the above map has a section over each completion of k but not over k in the appendix victor flynn gives explicit examples in genus 2 our result is a consequence of a more general investigation of the existence of sections for the projection of the etale fundamental group with abelianized geometric part onto the galois group we also point out the relation to the elementary obstruction of colliot thelene and sansuc

on the precoder design of a wireless energy harvesting node in linear vector gaussian channels with arbitrary input distribution a wireless energy harvesting node wehn operating in linear vector gaussian channels with arbitrarily distributed input symbols is considered in this paper the precoding strategy that maximizes the mutual information along n independent channel accesses is studied under non causal knowledge of the channel state and harvested energy commonly known as offline approach it is shown that at each channel use the left singular vectors of the precoder are equal to the eigenvectors of the gram channel matrix additionally an expression that relates the optimal singular values of the precoder with the energy harvesting profile through the minimum mean square error mmse matrix is obtained then the specific situation in which the right singular vectors of the precoder are set to the identity matrix is considered in this scenario the optimal offline power allocation named mercury water flowing is derived and an intuitive graphical representation is presented two optimal offline algorithms to compute the mercury water flowing solution are proposed and an exhaustive study of their computational complexity is performed moreover an online algorithm is designed which only uses causal knowledge of the harvested energy and channel state finally the achieved mutual information is evaluated through simulation

second order statistics and discrete time detection modeling for partially saturated processes the basic problem in underwater detection is formulated under the general assumptions of partially saturated propagation of narrow band and acoustic signals expressions for the joint probability density function pdf of the short time average root mean square pressure at the receiver are obtained this joint pdf is a general result reducing to the pdf s for the fully saturated and the unsaturated cases for limiting values of the appropriate variables subsequently defining detection as occurring whenever exceeds a specified threshold level 0 and using the above results the upcrossing and downcrossing statistics of the envelope process are studied closed form expressions for the probability mass functions pmf s of the interarrival time time between two successive detections and holding time time between an upcrossing and the first subsequent downcrossing are obtained results using our partially saturated detection model reduce in limiting cases to results already obtained in the literature for fully saturated and unsaturated propagation

lattice structures of precoders maximizing the minimum distance in linear channels this paper investigates linear precoding over nonsingular linear channels with additive white gaussian noise with lattice type inputs the aim is to maximize the minimum distance of the received lattice points where the precoder is subject to an energy constraint it is shown that the optimal precoder only produces a finite number of different lattices namely perfect lattices at the receiver the well known densest lattice packings are instances of perfect lattices but are not always the solution this is a counter intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance since there are only finite many different perfect lattices they can theoretically be enumerated offline a new upper bound on the optimal minimum distance is derived which significantly improves upon a previously reported bound and is useful when actually constructing the precoders

on the period index problem in light of the section conjecture period and index of a curve x k over a p adic local field k such that the fundamental group pi 1 x k admits a splitting are shown to be powers of p as a consequence examples of curves over number fields are constructed where having sections is obstructed locally at a p adic place hence the section conjecture holds for these curves as there are neither sections nor rational points

monotonic decrease of the non gaussianness of the sum of independent random variables a simple proof artstein ball barthe and naor have recently shown that the non gaussianness divergence with respect to a gaussian random variable with identical first and second moments of the sum of independent and identically distributed i i d random variables is monotonically nonincreasing we give a simplified proof using the relationship between non gaussianness and minimum mean square error mmse in gaussian channels as artstein we also deal with the more general setting of nonidentically distributed random variables

mmse dimension if n is standard gaussian the minimum mean square error mmse of estimating a random variable x based on snr x n vanishes at least as fast as 1 snr as snr we define the mmse dimension of x as the limit as snr of the product of snr and the mmse mmse dimension is also shown to be the asymptotic ratio of nonlinear mmse to linear mmse for discrete absolutely continuous or mixed distribution we show that mmse dimension equals renyi s information dimension however for a class of self similar singular x e g cantor dis tribution we show that the product of snr and mmse oscillates around information dimension periodically in snr db we also show that these results extend considerably beyond gaussian noise under various technical conditions

convex separable problems with linear constraints in signal processing and communications in this work we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints the solution is given in closed form as a function of some lagrange multipliers that can be computed through an iterative procedure in a finite number of steps graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water filling policy it turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates we also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm

mimo gaussian channels with arbitrary inputs optimal precoding and power allocation in this paper we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple input multiple output mimo gaussian channels with arbitrary input distributions by capitalizing on the relationship between mutual information and minimum mean square error mmse the optimal linear precoder satisfies a fixed point equation as a function of the channel and the input constellation for non gaussian inputs a nondiagonal precoding matrix in general increases the information transmission rate even for parallel noninteracting channels whenever precoding is precluded the optimal power allocation policy also satisfies a fixed point equation we put forth a generalization of the mercury waterfilling algorithm previously proposed for parallel noninterfering channels in which the mercury level accounts not only for the non gaussian input distributions but also for the interference among inputs

optimized power allocation for packet retransmissions of non gaussian inputs through sequential awgn channels this work investigates the optimization of power allocation for hybrid arq h arq retransmissions of non gaussian inputs over a bank of independent parallel gaussian channels we establish a general solution for maximizing generic transceiver objective utility functions that are monotonically non decreasing and concave function with respect to the accumulated signal to noise ratio snr specifically we investigate optimized solutions under two performance metrics namely the mutual information mi and the union bound of symbol error rate ubser under maximal ratio combining mrc reception we establish that efficient utilization of parallel channels in h arq retransmissions requires sequential updating of signal channel pairing as well as optimizing power allocation applying geometric analysis of power loading for h arq retransmission we show that for i i d inputs that are not necessarily gaussian the optimum pairing policy should match signals of the lowest cumulative signal to noise ratio with channels of the best quality in each transmission which is consistent with a similar result of for gaussian input signals we further propose a generalized mercury waterfilling algorithm for the optimal power assignment problem in h arq simulation results illustrate substantial improvements over designs based on gaussian input assumptions

high snr asymptotics of mutual information for discrete constellations with applications to bicm asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white gaussian noise channel are presented in the limit as the signal to noise ratio snr tends to infinity asymptotic expressions of the symbol error probability sep and the minimum mean square error mmse achieved by estimating the channel input given the channel output are also developed it is shown that for any input distribution the conditional entropy of the channel input given the output mmse and sep have an asymptotic behavior proportional to the gaussian q function the argument of the q function depends only on the minimum euclidean distance med of the constellation and the snr and the proportionality constants are functions of the med and the probabilities of the pairs of constellation points at med the developed expressions are then generalized to study the high snr behavior of the generalized mutual information gmi for bit interleaved coded modulation bicm by means of these asymptotic expressions the long standing conjecture that gray codes are the binary labelings that maximize the bicm gmi at high snr is proven it is further shown that for any equally spaced constellation whose size is a power of two there always exists an anti gray code giving the lowest bicm gmi at high snr

optimum power allocation for parallel gaussian channels with arbitrary input distributions the mutual information of independent parallel gaussian noise channels is maximized under an average power constraint by independent gaussian inputs whose power is allocated according to the waterfilling policy in practice discrete signaling constellations with limited peak to average ratios m psk m qam etc are used in lieu of the ideal gaussian signals this paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions such policy admits a graphical interpretation referred to as mercury waterfilling which generalizes the waterfilling solution and allows retaining some of its intuition the relationship between mutual information of gaussian channels and nonlinear minimum mean square error mmse proves key to solving the power allocation problem

the relationship between causal and noncausal mismatched estimation in continuous time awgn channels a continuous time finite power process with distribution p is observed through an awgn channel at a given signal to noise ratio snr and is estimated by an estimator that would have minimized the mean square error if the process had distribution q we show that the causal filtering mean square error mse achieved at snr level snr is equal to the average value of the noncausal smoothing mse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr emerging as the bridge for equating these two quantities are mutual information and relative entropy our result generalizes that of guo shamai and verdu 2005 from the nonmismatched case where p q to general p and q among our intermediate results is an extension of duncan s theorem that relates mutual information and causal mmse to the case of mismatched estimation some further extensions and implications are discussed key to our findings is the recent result of verdu on mismatched estimation and relative entropy

on the minimum mean p th error in gaussian noise channels and its applications the problem of estimating an arbitrary random vector from its observation corrupted by additive white gaussian noise where the cost function is taken to be the minimum mean p th error mmpe is considered the classical minimum mean square error mmse is a special case of the mmpe several bounds properties and applications of the mmpe are derived and discussed the optimal mmpe estimator is found for gaussian and binary input distributions properties of the mmpe as a function of the input distribution signal to noise ratio snr and order p are derived the single crossing point property scpp which provides an upper bound on the mmse and which together with the mutual information mmse relationship is a powerful tool in deriving converse proofs in multi user information theory is extended to the mmpe moreover a complementary bound to the scpp is derived as a first application of the mmpe a bound on the conditional differential entropy in terms of the mmpe is provided which then yields a generalization of the ozarow wyner lower bound on the mutual information achieved by a discrete input on a gaussian noise channel as a second application the mmpe is shown to improve on previous characterizations of the phase transition phenomenon that manifests in the limit as the length of the capacity achieving code goes to infinity as a discontinuity of the mmse as a function of snr as a final application the mmpe is used to show new bounds on the second derivative of mutual information or the first derivative of the mmse

comparison of the achievable rates in ofdm and single carrier modulation with i i d inputs we compare the maximum achievable rates in single carrier sc and orthogonal frequency division multiplexing ofdm modulation schemes under the practical assumptions of independent identically distributed finite alphabet inputs and linear intersymbol interference with additive gaussian noise we show that the shamai laroia approximation serves as a bridge between the two rates while it is well known that this approximation is often a lower bound on the sc achievable rate it is revealed to also essentially upper bound the ofdm achievable rate we apply information estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used pulse amplitude modulation pam and quadratic amplitude modulation constellations to this end novel bounds on minimum mean square error estimation of pam inputs to a scalar gaussian channel are derived which may be of general interest our results show that under reasonable assumptions optimal sc schemes may offer spectral efficiency significantly superior to that of ofdm motivating further research of such systems

discrete time detection modeling for unsaturated ocean acoustic propagation the basic problem in ocean acoustic detection is formulated under the assumption of unsaturated sound propagation the latter essentially amounts to a constant signal plus gaussian noise detection is defined as occurring whenever the root mean square pressure at the receiver exceeds a specified threshold level 0 a two state discrete time markov model is derived and closed form expressions for the probability mass functions of the number of time steps separating two successive detections interarrival time or one detection and the first subsequent downcrossing holding time are presented expressions for the joint probability density function of at two different points in time are obtained and used to determine the relevant one step transition probabilities of the markov model sample results using the model are finally presented

cooperative multi cell mimo downlink precoding with finite alphabet inputs this work investigates the design of linear precoders in cooperative multi cell mimo downlink coverage for finite alphabet source signals traditional design of multi cell mimo downlink precoder relies on gaussian input assumption which may lead to performance loss when true data inputs consist of discrete non gaussian symbols this work presents optimized precoders for finite alphabet input by maximizing the sum rate under per base station power constraints specifically we propose two distributed algorithms a finite alphabet signal gaussian interference gradient projection algorithm and a block diagonalization alternating optimization algorithm while supporting interference cancellation our numerical results demonstrate considerable performance gain in terms of approximate transmission data rate as well as decoded bit error rate over precoding schemes designed by using the non realistic gaussian input assumption

lower bounds and approximations for the information rate of the isi channel we consider the discrete time intersymbol interference isi channel model with additive gaussian noise and fixed independent identically distributed inputs in this setting we investigate the expression put forth by shamai and laroia as a conjectured lower bound for the input output mutual information after application of a minimum mean square error decision feedback equalizer receiver a low signal to noise ratio snr expansion is used to prove that the conjectured bound does not hold under general conditions and to characterize inputs for which it is particularly ill suited one such input is used to construct a counterexample indicating that the shamai laroia expression does not always bound even the achievable rate of the channel thus excluding a natural relaxation of the original conjectured bound however this relaxed bound is then shown to hold for any finite entropy input and isi channel when the snr is sufficiently high we derive two conditions under which the relaxed bound holds involving compound channel capacity and quasiconvexity arguments finally new simple bounds for the achievable rate are proven and compared with other known bounds information estimation relations and estimation theoretic bounds play a key role in establishing our results