comparison of two capacities in ℂ n in the past few years several capacitary set functions have been introduced in connection with the study of analytic and plurisubharmonic functions of several variables 1 1 5 9 13 there are many different such functions and the relationship between them is not at all clear we shall consider here the relative capacity of bedford and taylor and the capacity defined in terms of certain tchebycheff constants as studied by zaharjata 13 and alexander 1 see sect 2 for the definitions we show that these capacities are essentially the same our main result theorem 2 1 gives the quantitative relationship between them it happens that the relationship between the two capacities is closely connected with a result of josefson 8 on the equivalence of locally and globally pluripolar sets the quantitative estimates of theorem 2 1 allow us to give in sect 4 a new proof of josefson s lemma about normalized polynomials which are very small on the sets where a given plurisubharmonic function is nearly o e josefson s own proof is a direct construction our original motivation was to give a proof based on capacity notions it turns out that the tchebycheff polynomials themselves already do the job e1 mir 7 has obtained an extension of josefson s theorem given a function v psh on an open set he obtains a global psh function u of small growth at infinity such that u is dominated by a function h v of v his choice of h is essentially h x l o g xl thus he gets u l o g iv and so the value of the global function u is o e whenever v oe our methods give a short proof of this in fact they apply to functions h satisfying

exponential error bounds for random codes in the arbitrarily varying channel random codes for the arbitrarily varying channel are investigated the code ensemble is restricted to increase only exponentially with codeword length a quantity called key rate is used as a measure of the rate of increase the reliability function for such codes is related to the reliability function for codes with unlimited key rate explicit results are obtained in some examples of practical interest

a compute and forward scheme for gaussian bi directional relaying with inter symbol interference we provide inner and outer bounds on the capacity region for the gaussian bi directional relaying over inter symbol interference channels the outer bound is obtained by the conventional cut set argument for the inner bound we propose a compute and forward coding scheme based on lattice partition chains and study its achievable rate the coding scheme is a time domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords the proposed compute and forward coding scheme substantially outperforms decode and forward schemes while it is well known that for the point to point communication case both independent coding along sub channels and time domain coding can approach the capacity limit as a byproduct of the proposed scheme we show that for the bi directional relay case independent coding along sub channels is not optimal in general and joint coding across sub channels can improve the capacity for some channel realizations

duality between channel capacity and rate distortion with two sided state information we show that the duality between channel capacity and data compression is retained when state information is available to the sender to the receiver to both or to neither we present a unified theory for eight special cases of channel capacity and rate distortion with state information which also extends existing results to arbitrary pairs of independent and identically distributed i i d correlated state information s sub 1 s sub 2 available at the sender and at the receiver respectively in particular the resulting general formula for channel capacity c max sub p u x s sub 1 i u s sub 2 y i u s sub 1 assumes the same form as the generalized wyner ziv 1976 rate distortion function r d min sub p u x s sub 1 p x spl i cap u s sub 2 i u s sub 1 x 1 u s sub 2

achieving the gaussian rate distortion function by prediction the ldquowater fillingrdquo solution for the quadratic rate distortion function of a stationary gaussian source is given in terms of its power spectrum this formula naturally lends itself to a frequency domain ldquotest channelrdquo realization we provide an alternative time domain realization for the rate distortion function based on linear prediction the predictive test channel has some interesting implications including the optimality at all distortion levels of pre post filtered vector quantized differential pulse code modulation dpcm and a duality relationship with decision feedback equalization dfe for intersymbol interference isi channels

achievable error exponents for channels with side information erasure and list decoding we consider a decoder with an erasure option and a variable size list decoder for channels with non casual side information at the transmitter first a universally achievable region of error exponents is offered for decoding with an erasure option using a parameterized decoder in the spirit of csiszar and korner s decoder then the proposed decoding rule is generalized by extending the range of its parameters to allow variable size list decoding this extension gives a unified treatment for erasure list decoding an achievable region of exponential bounds on the probability of list error and the average number of incorrect messages on the list are given relations to forney s and csiszar and korner s decoders for discrete memoryless channel are discussed these results are obtained by exploring a random binning code with conditionally constant composition codewords proposed by moulin and wang but with a different decoding rule and a modified analysis

selecting wavelengths for least squares range estimation we consider the problem of estimating the distance or range between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations traditional estimators developed for optical interferometry include the beat wavelength and excess fractions methods more recently estimators based on the chinese remainder theorem crt and least squares have appeared recent research suggests the least squares estimator to be the most accurate in many cases the accuracy of all of these range estimators depends upon the wavelengths chosen this leads to the problem of selecting wavelengths that maximize accuracy procedures for selecting wavelengths for the beat wavelength and excess fractions methods have previously been described but procedures for the crt and least squares estimators are yet to be developed in this paper we develop an algorithm to automatically select wavelengths for use with the least square range estimator the algorithm minimizes an optimization criterion connected with the mean square error interesting properties of a particular class of lattices simplify the criterion allowing minimization by depth first search monte carlo simulations indicate that wavelengths that minimize the criterion can result in considerably more accurate range estimates than wavelengths selected by ad hoc means

joint wyner ziv dirty paper coding by modulo lattice modulation the combination of source coding with decoder side information the wyner ziv problem and channel coding with encoder side information the gel fand pinsker problem can be optimally solved using the separation principle in this work we show an alternative scheme for the quadratic gaussian case which merges source and channel coding this scheme achieves the optimal performance by applying a modulo lattice modulation to the analog source thus it saves the complexity of quantization and channel decoding and remains with the task of ldquoshapingrdquo only furthermore for high signal to noise ratio snr the scheme approaches the optimal performance using an snr independent encoder thus it proves for this special case the feasibility of universal joint source channel coding

estimation of von bertalanffy growth curve parameters from recapture data a simple method of constructing estimating functions for parameters in the von bertalanffy growth model e y t l 1 exp kt is presented for tag recapture data when the age of the animal is unknown the estimating functions are unbiased under very general distributional assumptions provided k does not vary between animals simulations of growth in lobsters and whelks indicate that the method performs well provided the initial capture times and recapture intervals vary over reasonable ranges comparison is made with methods based on least squares which have been shown to be generally inconsistent

arbitrarily varying channels with constrained inputs and states random coding theorems are proved for discrete memoryless arbitrarily varying channels avcs with constraints on the transmitted codewords and channel state sequences two types of constraints are considered peak i e required for each n length sequence almost surely and average over the message set or over an ensemble for peak constraints on the codewords and on the channel state sequences the avc is shown to have a strong random coding capacity if the codewords and or the channel state sequences are constrained in the average sense the avcs do not possess strong capacities only epsilon capacities are shown to exist

robust lattice alignment for k user mimo interference channels with imperfect channel knowledge in this paper we consider a robust lattice alignment design for k user quasi static multiple input multiple output mimo interference channels with imperfect channel knowledge with random gaussian inputs the conventional interference alignment ia method has the feasibility problem when the channel is quasi static on the other hand structured lattices can create structured interference as opposed to the random interference caused by random gaussian symbols the structured interference space can be exploited to transmit the desired signals over the gaps however the existing alignment methods on the lattice codes for quasi static channels either require infinite signal to noise ratio snr or symmetric interference channel coefficients furthermore perfect channel state information csi is required for these alignment methods which is difficult to achieve in practice in this paper we propose a robust lattice alignment method for quasi static mimo interference channels with imperfect csi at all snr regimes and a two stage decoding algorithm to decode the desired signal from the structured interference space we derive the achievable data rate based on the proposed robust lattice alignment method where the design of the precoders decorrelators scaling coefficients and interference quantization coefficients is jointly formulated as a mixed integer and continuous optimization problem the effect of imperfect csi is also accommodated in the optimization formulation and hence the derived solution is robust to imperfect csi we also design a low complex iterative optimization algorithm for our robust lattice alignment method by using the existing iterative ia algorithm that was designed for the conventional ia method numerical results verify the advantages of the proposed robust lattice alignment method compared with the time division multiple access tdma two stage maximum likelihood ml decoding generalized han kobayashi hk distributive ia and conventional ia methods in the literature

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

duality between source coding and channel coding and its extension to the side information case we explore the information theoretic duality between source coding with side information at the decoder and channel coding with side information at the encoder we begin with a mathematical characterization of the functional duality between classical source and channel coding formulating the precise conditions under which the optimal encoder for one problem is functionally identical to the optimal decoder for the other problem we then extend this functional duality to the case of coding with side information by invoking this duality we are able to generalize the result of wyner and ziv 1976 relating to no rate loss for source coding with side information from gaussian to more arbitrary distributions we consider several examples corresponding to both discrete and continuous valued cases to illustrate our formulation for the gaussian cases of coding with side information we invoke geometric arguments to provide further insights into their duality our geometric treatment inspires the construction and dual use of practical coset codes for a large class of emerging applications for coding with side information such as distributed sensor networks watermarking and information hiding communication systems

on the dispersions of the gel fand pinsker channel and dirty paper coding this paper studies the second order coding rates for memoryless channels with a state sequence known non causally at the encoder in the case of finite alphabets an achievability result is obtained using constant composition random coding and by using a small fraction of the block to transmit the empirical distribution of the state sequence for error probabilities less than 0 5 it is shown that the second order rate improves on an existing one based on independent and identically distributed random coding in the gaussian case dirty paper coding with an almost sure power constraint an achievability result is obtained using random coding over the surface of a sphere and using a small fraction of the block to transmit a quantized description of the state power it is shown that the second order asymptotics are identical to the single user gaussian channel of the same input power without a state

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

determination of the unknown age at first capture of western rock lobsters panulims cygnus by random effects model summary we propose a method for fitting growth curves to multiple recapture data of lobsters when the age at first capture is unknown the von bertalanffy growth curve is used to model the growth to account for individual variability the unknown age in logarithmic scale of a lobster at first capture the individual asymptotic size and the individual growth coefficient of its carapace length are modeled as random effects with a trivariate normal distribution unlike previously suggested models the present model permits correlation between the growth coefficient and the age at first capture and can be fitted readily using existing software the error structures between consecutive recaptures of a lobster are assumed to be a first order autoregressive process with unequally spaced time points a comparison between this model and the fabens growth equation is given the proposed method is a flexible method and can be applied to fit different growth equations when the age at first capture is unknown

error exponents of modulo additive noise channels with side information at the transmitter consider the optimum strategy for using channel state side information in transmission over a modulo additive noise channel with state dependent noise where the receiver does not have access to the side information si previous work showed that capacity wise the optimum transmitter shifts each code letter by a prediction of the noise sample based on the si we show that this structure achieves also the random coding error exponent and therefore is optimum at some range of rates below capacity specifically the optimum transmitter predictor minimizes the renyi entropy of the prediction error the renyi order depends on the rate and goes to one corresponding to shannon entropy for rates close to capacity in contrast it is shown that this prediction strategy may not be optimal at low transmission rates

joint physical layer coding and network coding for bidirectional relaying we consider a communication system where two transmitters wish to exchange information through a central relay the transmitter and relay nodes exchange data over synchronized average power constrained additive white gaussian noise channels with a real input with signal to noise ratio snr of snr an upper bound on the capacity is 1 2 log 1 snr bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel we show that using lattice codes and lattice decoding we can obtain a rate of 1 2 log 1 2 snr bits per transmitter which is essentially optimal at high snr the main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs slepian wolf coding we also show that if the two transmitters use identical lattices with minimum angle decoding we can achieve the same rate of 1 2 log 1 2 snr the proposed scheme can be thought of as a joint physical layer network layer code which outperforms other recently proposed analog network coding schemes

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

weighted polynomials and weighted pluripotential theory let e be a compact subset of c n and w 0 an admissible weight function on e to e we associate a canonical circular set z c we obtain precise relations between the weighted pluricomplex green function and weighted equilibrium measure of e w and the pluricomplex green function and equilibrium measure of z these results combined with an appropriate form of the bernstein markov inequality are used to obtain asymptotic formulas for the leading coefficients of orthonormal polynomials with respect to certain exponentially decreasing weights in r n

on error exponents for arbitrarily varying channels the minimum probability of error achievable by random codes on the arbitrarily varying channel avc is investigated new exponential error bounds are found and applied to the avc with and without input and state constraints also considered is a simple subclass of random codes called randomly modulated codes in which encoding and decoding operations are separate from code randomization a universal coding theorem is proved which shows the existence of randomly modulated codes that achieve the same error bounds as fully random codes for all avcs

corrected proof of de buda s theorem lattice channel codes an error in de buda s see ieee j select areas commun vol 7 no 6 p 893 1989 proof on the asymptotic optimality of lattice channel codes is pointed out and corrected using a modification of de buda s approach comments are given on the correct interpretation and the limitations of this result

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

finite dimensional infinite constellations in the setting of a gaussian channel without power constraints proposed by poltyrev in 1994 the codewords are points in an n dimensional euclidean space an infinite constellation and the tradeoff between their density and the error probability is considered the normalized log density nld plays the role of the communication rate and capacity as well as error exponent bounds for this setting are known this paper considers the infinite constellation setting in the finite block length dimension regime a simplified expression for poltyrev s achievability bound is found and it is shown to be closely related to the sphere converse bound and to a recently proposed achievability bound based on point processes the bounds are then analyzed asymptotically for growing n for fixed nld the bounds turn out to be extremely tight compared to previous error exponent analysis for fixed error probability e it is shown that the gap of the highest achievable nld to the optimal nld poltyrev s capacity is approximately 1 2n q 1 e where q is the standard complementary gaussian cumulative distribution function thus extending the channel dispersion analysis to infinite constellations connections to the error exponent of the power constrained gaussian channel and to the volume to noise ratio as a figure of merit are discussed finally the new tight bounds are compared to state of the art coding schemes

feedback based collaborative secrecy encoding over binary symmetric channels in this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties over an eavesdropped communication link relative to wyner s traditional encoding scheme our feedback based encoding often yields larger rate equivocation regions and achievable secrecy rates more importantly by exploiting the channel randomness inherent in the feedback channels our scheme achieves a strictly positive secrecy rate even when the eavesdropper s channel is less noisy than the legitimate receiver s channel all channels are modeled as binary and symmetric we demonstrate the versatility of our feedback based encoding method by using it in three different configurations the stand alone configuration the mixed configuration when it combines with wyner s scheme and the reversed configuration depending on the channel conditions significant improvements over wyner s secrecy capacity can be observed in all configurations

generalized compute compress and forward compute and forward cf harnesses interference in wireless communications by exploiting structured coding the key idea of cf is to compute integer combinations of code words from multiple source nodes rather than to decode individual code words by treating others as noise compute compress and forward ccf can further enhance the network performance by introducing compression operations at receivers in this paper we develop a more general compression framework termed generalized ccf gccf where the compression function involves the selection of message segments over finite fields we show that gccf achieves a broader compression rate region than ccf we also compare our compression rate region with the fundamental slepian wolf sw region we show that gccf is optimal in the sense of achieving the minimum total compression rate we also establish the criteria under which gccf achieves the sw region in addition we consider a two hop relay network employing the gccf scheme we formulate a sum rate maximization problem and develop an approximate algorithm to solve the problem numerical results are presented to demonstrate the performance superiority of gccf over ccf and other schemes

on the reliability function of the discrete memoryless relay channel bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types two achievable error exponents are derived based on partial decode forward and compress forward which are well known superposition block markov coding schemes the derivations require combinations of the techniques involved in the proofs of csiszar korner marton s packing lemma for the error exponent of channel coding and marton s type covering lemma for the error exponent of source coding with a fidelity criterion the decode forward error exponent is evaluated on sato s relay channel from this example it is noted that to obtain the fastest possible decay in the error probability for a fixed effective coding rate one ought to optimize the number of blocks in the block markov coding scheme assuming the blocklength within each block is large an upper bound on the reliability function is also derived using ideas from haroutunian s lower bound on the error probability for point to point channel coding with feedback

achievable rates of multi antenna downlink channels with peak power constraints this paper considers a gaussian multiple input single output miso broadcast channel with a per antenna peak power constraint or simply peak power constraint it is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier assuming the perfect knowledge of the channel state information csi at the transmitter we propose an achievable scheme using dirty tape coding dtc the ideal dirty paper coding dpc which is a capacity achieving scheme for the gaussian multiple input multiple output mimo broadcast channel cannot be used for our model because its optimal input distribution is gaussian and thus the peak power constraint is violated on the other hand the channel input of dtc is uniformly distributed in a fixed range which helps to control the peak power of the transmit signal easily we also present an algorithm that finds capacity achieving beamforming vectors and power allocation factors under a per antenna average power constraint and use the optimized parameters in the proposed scheme simulation results show that the proposed scheme provides gains of 2 7db over a non dtc scheme based on minimum mean square error mmse beamforming at high signal to noise ratio snr when there are three receivers and the transmitter has three antennas

the degrees of freedom of compute and forward we analyze the asymptotic behavior of compute and forward relay networks in the regime of high signal to noise ratios we consider a section of such a network consisting of k transmitters and k relays the aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters an upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays transforming the network into a k k multiple input multiple output mimo channel the number of degrees of freedom of compute and forward is hence at most k in this paper we analyze the degrees of freedom achieved by the lattice coding implementation of compute and forward proposed recently by nazer and gastpar we show that this lattice implementation achieves at most 2 1 1 k 2 degrees of freedom thus exhibiting a very different asymptotic behavior than the mimo upper bound this raises the question if this gap of the lattice implementation to the mimo upper bound is inherent to compute and forward in general we answer this question in the negative by proposing a novel compute and forward implementation achieving k degrees of freedom

colored gaussian multiple descriptions spectral and time domain forms it is well known that shannon s rate distortion function rdf in the colored quadratic gaussian qg case can be parametrized via a single lagrangian variable the water level in the reverse water filling solution in this paper we show that the symmetric colored qg multiple description md rdf in the case of two descriptions can be parametrized in the spectral domain via two lagrangian variables which control the tradeoff between the side distortion the central distortion and the coding rate this spectral domain analysis is complemented by a time domain scheme design approach we show that the symmetric colored qg md rdf can be achieved by combining ideas of delta sigma modulation and differential pulse code modulation in particular two source prediction loops one for each description are embedded within a common noise shaping loop whose parameters are explicitly found from the spectral domain characterization

on the generalized degrees of freedom of the gaussian interference relay channel the symmetric two user gaussian interference relay channel irc is studied from a generalized degrees of freedom gdof perspective while it is known that the relay does not in crease the dof of the irc such a characterization has not been reported for the gdof yet the focus of this paper is on all cases where the interference link is stronger than the link from the source to the relay this regime basically covers half the space of all possible parameters of the irc by using genie aided approaches new sum capacity upper bounds are derived these bounds are then compared with rates achieved with a novel transmission scheme which is based on a functional decode and forward fdf strategy it is shown that the gdof of the irc is achieved by fdf in the given regime and that a relay can indeed increase the gdof of irc finally the fdf scheme is compared with other schemes like decode and forward as well as compress and forward at low moderate and high signal to noise ratios

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

estimation of growth parameters from multiple recapture data this article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown the existing approaches either impute the initial ages or model them as random effects assumptions about the initial age are not verifiable because all the initial ages are unknown we present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity simulation studies indicate that the proposed method works well two real data sets are analyzed for illustration one from whelks dicathais aegaota and the other from southern rock lobster jasus edwardsii in south australia

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

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

non random coding error bounds for lattices an upper bound on the error probability of specific lattices based on their distance spectrum is constructed the derivation is accomplished using a simple alternative to the minkowski hlawka mean value theorem of the geometry of numbers in many ways the new bound greatly resembles the shulman feder bound for linear codes based on the new bound error exponent and channel dispersion expressions are derived for specific lattice sequences of increasing dimension over the awgn channel measuring a sequence s gap to capacity using the new asymptotics is demonstrated additional finite dimension results encountered along the way are presented

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

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

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

realizable spatio temporal tomlinson harashima precoders theory and fast computation we derive the optimal realizable tomlinson harashima precoder for frequency selective multiple input multiple output mimo channels with respect to a simplified mean square error mse criterion realizability means that in contrast to other works we do not restrict the internal filters of the precoder to have finite impulse responses firs but nevertheless ensure that the precoder can be operated in real time subject to a finite latency time which can be chosen by the system designer in particular this allows us to consider channels with infinite impulse responses iirs as they occur e g in digital subscriber lines the feedforward filter is located at the transmitter in our system model and an additional scalar gain is employed at the receiver the relocation of the feedforward filter allows us to consider decentralized receivers however it also makes it necessary to impose a transmit power constraint the power constraint often has the effect that the input signals at the receiver have to be rescaled we argue that the inclusion of the additional scalar gain allows us to incorporate the effect of the rescaling operation into the optimization special emphasis is put on the fast computation of the realizable tomlinson harashima precoder via displacement structure theory we propose a fast algorithm which includes a successive construction of a close to optimal ordering of the data streams the complexity of this algorithm is only cubic in the number of channel inputs and quadratic in the latency time the algorithm can also be applied in situations where certain fir constraints have to be fulfilled because we find that the optimal realizable tomlinson harashima precoder involves only fir filters as soon as the channel is fir our results are reproducible

on error exponents of modulo lattice additive noise channels modulo lattice additive noise mlan channels appear in the analysis of structured binning codes for costa s dirty paper channel and of nested lattice codes for the additive white gaussian noise awgn channel in this paper we derive a new lower bound on the error exponents of the mlan channel with a proper choice of the shaping lattice and the scaling parameter the new lower bound coincides with the random coding lower bound on the error exponents of the awgn channel at the same signal to noise ratio snr in the sphere packing and straight line regions this result implies that at least for rates close to channel capacity 1 writing on dirty paper is as reliable as writing on clean paper and 2 lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes with maximum likelihood decoding for the awgn channel

on the capacity of the carbon copy onto dirty paper channel the carbon copy onto dirty paper ccdp channel is the compound writing on dirty paper channel in which the channel output is obtained as the sum of the channel input white gaussian noise and a gaussian state sequence randomly selected among a set possible realizations the transmitter has non causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output we study the capacity of the ccdp channel for two scenarios 1 the state sequences are independent and identically distributed and 2 the state sequences are scaled versions of the same sequence in the first scenario we show that a combination of superposition coding time sharing and gel fand pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations in the second scenario we derive capacity to within 4 bits per channel use for the case of two possible state sequences this result is extended to the ccdp channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as strong fading regime we conclude by providing some remarks on the capacity of the ccdp channel in which the state sequences have any jointly gaussian distribution

towards the asymptotic sum capacity of the mimo cellular two way relay channel in this paper we consider the transceiver and relay design for the multiple input multiple output mimo cellular two way relay channel ctwrc where a multi antenna base station bs exchanges information with multiple multiantenna mobile stations via a multi antenna relay station rs we propose a novel two way relaying scheme to approach the sum capacity of the mimo ctwrc a key contribution of this work is a new nonlinear lattice based precoding technique to precompensate the interstream interference so as to achieve efficient interference free lattice decoding at the relay we derive sufficient conditions for the proposed scheme to asymptotically achieve the sum capacity of the mimo ctwrc in the high signal to noise ratio snr regime to fully exploit the potential of the proposed scheme we also investigate the optimal power allocation at the bs and the rs to maximize the weighted sum rate of the mimo ctwrc in the general snr regime it is shown that the problem can be formulated as a monotonic program and a polyblock outer approximation algorithm is developed to find the globally optimal solution with guaranteed convergence we demonstrate by numerical results that the proposed scheme significantly outperforms the existing schemes and closely approaches the sum capacity of the mimo ctwrc in the high snr regime

multiple description quantization via gram schmidt orthogonalization the multiple description md problem has received considerable attention as a model of information transmission over unreliable channels a general framework for designing efficient md quantization schemes is proposed in this paper we provide a systematic treatment of the el gamal cover egc achievable md rate distortion region and show it can be decomposed into a simplified egc segc region and a superimposed refinement operation furthermore any point in the segc region can be achieved via a successive quantization scheme along with quantization splitting for the quadratic gaussian case the proposed scheme has an intrinsic connection with the gram schmidt orthogonalization which implies that the whole gaussian md rate distortion region is achievable with a sequential dithered lattice based quantization scheme as the dimension of the optimal lattice quantizers becomes large moreover this scheme is shown to be universal for all independent and identically distributed i i d smooth sources with performance no worse than that for an i i d gaussian source with the same variance and asymptotically optimal at high resolution a class of md scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically the performance is analyzed in the high resolution regime which exhibits a noticeable improvement over the existing md scalar quantization schemes

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

lattices for distributed source coding jointly gaussian sources and reconstruction of a linear function consider a pair of correlated gaussian sources x 1 x 2 two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder the decoder is interested in reconstructing a linear combination of x 1 and x 2 to within a mean square distortion of d we obtain an inner bound to the optimal rate distortion region for this problem a portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components x 1 and x 2 first this results in a better rate region for certain parameter values our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory we then consider the case of linear reconstruction of k sources and provide an inner bound to the optimal rate distortion region some parts of the inner bound are achieved using the following coding structure lattice vector quantization followed by ldquocorrelatedrdquo lattice structured binning

perfectly secure steganography capacity error exponents and code constructions an analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper following embedding of the message into the covertext the resulting stegotext is required to have exactly the same probability distribution as the covertext then no statistical test can reliably detect the presence of the hidden message we refer to such steganographic schemes as perfectly secure a few such schemes have been proposed in recent literature but they have vanishing rate we prove that communication performance can potentially be vastly improved specifically our basic setup assumes independent and identically distributed i i d covertext and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code the permutation is a secret key shared between encoder and decoder we derive positive capacity and random coding exponents for perfectly secure steganographic systems the error exponents provide estimates of the code length required to achieve a target low error probability in some applications steganographic communication may be disrupted by an active warden modeled here by a compound discrete memoryless channel dmc the transmitter and warden are subject to distortion constraints we address the potential loss in communication performance due to the perfect security requirement this loss is the same as the loss obtained under a weaker order 1 steganographic requirement that would just require matching of first order marginals of the covertext and stegotext distributions furthermore no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric steganographic capacity is then achieved by randomized linear codes our framework may also be useful for developing computationally secure steganographic systems that have near optimal communication performance

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

distance spectrum and performance of channel coded physical layer network coding for binary input gaussian two way relay channels we investigate a channel coded physical layer network coding cpnc scheme for binary input gaussian two way relay channels in this scheme the codewords of the two users are transmitted simultaneously the relay computes and forwards a network coded nc codeword without complete decoding of the two users individual messages we propose a new punctured codebook method to explicitly find the distance spectrum of the cpnc scheme based on that we derive an asymptotically tight performance bound for the error probability our analysis shows that compared to the single user scenario the cpnc scheme exhibits the same minimum euclidean distance but an increased multiplicity of error events with minimum distance at a high snr this leads to an snr penalty of at most ln2 in linear scale for long channel codes of various rates our analytical results match well with the simulated performance

random coding lower bounds for the error exponent of joint quantization and watermarking systems we establish random coding lower bounds to the error exponent of discrete and gaussian joint quantization and private watermarking systems in the discrete system both the covertext and the attack channel are memoryless and have finite alphabets in the gaussian system the covertext is memoryless gaussian and the attack channel has additive memoryless gaussian noise in both cases our bounds on the error exponent are positive in the interior of the achievable quantization and watermarking rate region

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

a close to capacity dirty paper coding scheme the writing on dirty paper channel model offers an information theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter it indicates that lossless precoding is theoretically possible at any signal to noise ratio snr and thus dirty paper coding may serve as a basic building block in both single user and multiuser communication systems we design an end to end coding realization of a system materializing a significant portion of the promised gains we employ multidimensional quantization based on trellis shaping at the transmitter coset decoding is implemented at the receiver using virtual bits combined with iterative decoding of capacity approaching codes we achieve an improvement of 2db over the best scalar quantization scheme code design is done using the exit chart technique

ring compute and forward over block fading channels the compute and forward c f protocol in quasi static channels normally employs lattice codes based on the rational integers mathbb z the gaussian integers mathbb z i or the eisenstein integers mathbb z omega while its extension to more general channels often assumes channel state information at transmitters csit in this paper we propose a novel scheme for c f in block fading channels without csit which is referred to as ring c f because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers owing to the multiplicative closure of the algebraic lattices employed a relay is able to decode an algebraic integer linear combination of lattice codewords we analyze its achievable computation rates and show it outperforms conventional c f based on the mathbb z lattices by investigating the effect of the diophantine approximation by algebraic conjugates we prove that the degrees of freedom dofs of the optimized computation rate are n l where n is the number of blocks and l is the number of users

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

monge ampere measures associated to extremal plurisubharmonic functions in ⁿ we consider the extremal plurisubharmonic functions le and ue associated to a nonpluripolar compact subset e of the unit ball b c c and show that the corresponding monge ampere measures dd l and dd ue are mutually absolutely continuous we then discuss the polynomial growth condition l a generalization of leja s polynomial condition in the plane and study the relationship between the asymptotic behavior of the orthogonal polynomials associated to a measure on e and the l condition

low density lattice codes low density lattice codes ldlc are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white gaussian noise awgn channel in ldlc a codeword x is generated directly at the n dimensional euclidean space as a linear transformation of a corresponding integer message vector b i e x gb 1 where h g 1 is restricted to be sparse the fact that h is sparse is utilized to develop a linear time iterative decoding scheme which attains as demonstrated by simulations good error performance within 0 5 db from capacity at block length of n 100 000 symbols the paper also discusses convergence results and implementation considerations

trellis shaping the author discusses trellis shaping a method of selecting a minimum weight sequence from an equivalence class of possible transmitted sequences by a search through the trellis diagram of a shaping convolutional code c sub s shaping gains on the order of 1 db may be obtained with simple four state shaping codes and with moderate constellation expansion the shaping gains obtained with more complicated codes approach the ultimate shaping gain of 1 53 db with a feedback free syndrome former for c sub s transmitted data can be recovered without catastrophic error propagation constellation expansion and peak to average energy ratio may be effectively limited by peak constraints with lattice theoretic constellations the shaping operation may be characterized as a decoding of an initial sequence in a channel trellis code by a minimum distance decoder for a shaping trellis code based on the shaping convolutional code and the set of possible transmitted sequences is then the set of code sequences in the channel trellis code that lie in the voronoi region of the trellis shaping code

residual quantization based code design for compressing noisy sources with arbitrary decoder side information this paper considers noisy wyner ziv coding wzc in which a remote noisy source is compressed with side information at the decoder only the decoder side information is not limited to being gaussian thus this noisy wzc problem cannot be transformed into the conventional one tailored for noiseless sources a new coding structure named the residual quantization rq based noisy wzc is proposed to solve the problem this scheme explicitly constructs the theoretical auxiliary random variable to facilitate optimal reconstruction of the noisy source in this two stage encoder the noisy source is quantized twice and the quantization error residue of the first stage is the input of the second stage by sending only the quantization index of the second stage to the decoder the corresponding code rate can theoretically approach the noisy wzc bound moreover the rq based noisy wzc is implemented using graph based codes the main challenge is that it is necessary to design a codebook that is simultaneously good for source and channel coding for the first stage quantization since this quantization code also acts as a channel code at the decoder this problem is solved by constructing a low density parity check ldpc code with edge degrees optimized for channel coding and enhancing its performance for source coding by using a modified reinforced belief propagation quantization algorithm simulation results show that the noisy wyner ziv bounds can be practically approached by our implementation in addition the proposed implementation offers more flexibility in the code rates compared with the existing practical designs making it more suitable for emerging applications such as fronthaul compression

on the error exponent and capacity games of private watermarking systems watermarking systems are analyzed as a game between an information hider a decoder and an attacker the information hider is allowed to cause some tolerable level of distortion to the original data within which the message is hidden and the resulting distorted data can suffer some additional amount of distortion caused by an attacker who aims at erasing the message two games are investigated the error exponent game and the coding capacity game motivated by a worst case approach we assume that the attacker is informed of the hiding strategy taken by the information hider and the decoder which are uninformed of the attacking scheme this approach leads to the maximin error exponent and maximin coding capacity as objective functions it is assumed that the host data is drawn from a finite alphabet memoryless stationary source and its realization side information is available at the encoder and the decoder a single letter expression for the maximin error exponent is found under large deviations distortion constraints moreover we find an asymptotically optimal random coding distribution a universal decoder and a worst case attack channel it is proved that there is a saddle point in the asymptotic exponent and that the minimax and the maximin error exponents are equal finally a single letter expression for the coding capacity i e the maximin reliable information rate is found

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

spatially coupled ensembles universally achieve capacity under belief propagation we investigate spatially coupled code ensembles for transmission over the binary erasure channel it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble this explains why convolutional ldpc ensembles originally introduced by felstrom and zigangirov perform so well over this channel we show that the equivalent result holds true for transmission over general binary input memoryless output symmetric channels more precisely given a desired error probability and a gap to capacity we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding in fact most codes in this ensemble have this property the quantifier universal refers to the single ensemble code that is good for all channels but we assume that the channel is known at the receiver the key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble we conclude by discussing some interesting open problems

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

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

invariance of polynomial inequalities under polynomial maps abstract we prove the invariance under simple polynomial maps of a few useful multivariate polynomial inequalities the proofs are elementary and based on an algebraic decomposition of any polynomial as a sum of polynomials which we call q coordinates composed with the polynomial map q balanced with monomials of bounded degree

capacity and random coding exponents for channel coding with side information capacity formulas and random coding exponents are derived for a generalized family of gel fand pinsker coding problems these exponents yield asymptotic upper bounds on the achievable log probability of error in our model information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence and the channel is selected by a hypothetical adversary partial information about the state sequence is available to the encoder adversary and decoder the design of the transmitter is subject to a cost constraint two families of channels are considered 1 compound discrete memoryless channels cdmc and 2 channels with arbitrary memory subject to an additive cost constraint or more generally to a hard constraint on the conditional type of the channel output given the input both problems are closely connected the random coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder which may be thought of as an empirical generalized maximum a posteriori decoder for channels with arbitrary memory the random coding exponents are larger than their cdmc counterparts applications of this study include watermarking data hiding communication in presence of partially known interferers and problems such as broadcast channels all of which involve the fundamental idea of binning

unequally spaced longitudinal data with ar 1 serial correlation this paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points observations within subjects are assumed to be either uncorrelated or to have a continuous time first order autoregressive structure possibly with observation error the random coefficients are assumed to have an arbitrary between subject covariance matrix covariates can be included in the fixed effects part of the model exact maximum likelihood estimates of the unknown parameters are computed using the kalman filter to evaluate the likelihood which is then maximized with a nonlinear optimization program an example is presented where a large number of subjects are each observed at a small number of observation times hypothesis tests for selecting the best model are carried out using wald s test on contrasts or likelihood ratio tests based on fitting full and restricted models

application of nonlinear models with random coefficients to growth data summary the application of nonlinear random coefficient models to the analysis of growth curve data is described the approach is further developed for the estimation of mean growth curves and their variability from mark recapture data when the age of an animal at first capture is unknown but the time between successive captures is known these methods are of wide applicability as shown by the analysis of data on the growth of emus dromaius novaehollandiae noisy scrub birds atrichornis clamosus and whelks dicathais aegaota simulations of a mark recapture experiment on the rock spiny lobster panulirus argus in mexico using a known growth curve showed the effectiveness of the approach in estimating both the population s growth curve and the variability in individual growth

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n