lattice coding and decoding achieve the optimal diversity multiplexing tradeoff of mimo channels this paper considers communication over coherent multiple input multiple output mimo flat fading channels where the channel is only known at the receiver for this setting we introduce the class of lattice space time last codes we show that these codes achieve the optimal diversity multiplexing tradeoff defined by zheng and tse under generalized minimum euclidean distance lattice decoding our scheme is based on a generalization of erez and zamir mod lambda scheme to the mimo case in our construction the scalar scaling of erez zamir and costa gaussian dirty paper schemes is replaced by the minimum mean square error generalized decision feedback equalizer mmse gdfe this result settles the open problem posed by zheng and tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity multiplexing tradeoff moreover our results shed more light on the structure of optimal coding decoding techniques in delay limited mimo channels and hence open the door for novel approaches for space time code constructions in particular 1 we show that mmse gdfe plays a fundamental role in approaching the limits of delay limited mimo channels in the high signal to noise ratio snr regime unlike the additive white gaussian noise awgn channel case and 2 our random coding arguments represent a major departure from traditional space time code designs based on the rank and or mutual information design criteria

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

on the upper critical dimension of lattice trees and lattice animals we give a rigorous proof of mean field critical behavior for the susceptibility 1 2 and the correlation length v 1 4 for models of lattice trees and lattice animals in two cases i for the usual model with trees or animals constructed from nearest neighbor bonds in sufficiently high dimensions and ii for a class of spread out or long range models in which trees and animals are constructed from bonds of various lengths above eight dimensions this provides further evidence that for these models the upper critical dimension is equal to eight the proof involves obtaining an infrared bound and showing that a certain square diagram is finite at the critical point and uses an expansion related to the lace expansion for the self avoiding walk

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

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

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

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

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

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

an upper bound on the number of self avoiding polygons via joining for d 2d 2 and n nn n even let pn pn d pn pn d denote the number of length nn self avoiding polygons in zdzd up to translation the polygon cardinality grows exponentially and the growth rate limn 2np1 nn 0 limn 2npn1 n 0 is called the connective constant and denoted by madras j stat phys 78 1995 681 699 has shown that pn n cn 1 2pn n cn 1 2 in dimension d 2d 2 here we establish that pn n n 3 2 o 1 pn n n 3 2 o 1 for a set of even nn of full density when d 2d 2 we also consider a certain variant of self avoiding walk and argue that when d 3d 3 an upper bound of n 2 d 1 o 1 n 2 d 1 o 1 holds on a full density set for the counterpart in this variant model of this normalized polygon cardinality

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

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

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

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

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

self avoiding walk in 5 or more dimensions using an expansion based on the renormalization group philosophy we prove that for a t step weakly self avoiding random walk in five or more dimensions the variance of the endpoint is of order t and the scaling limit is gaussian as t

cramer rao bound for nonlinear filtering with pd 1 and its application to target tracking the paper investigates the cramer rao bound for discrete time nonlinear filtering in the case where the probability of detection of a sensor is less than unity the theoretical formula involves the evaluation of exponentially growing number of possible miss detection sequences an approximation of the theoretical bound for practical applications such as target tracking where the number of sensor scans is large is proposed an application of the developed techniques to the well known filtering problem of tracking a re entry ballistic object is also presented

self attracting self avoiding walk this article is concerned with self avoiding walks saw on mathbb z d that are subject to a self attraction the attraction which rewards instances of adjacent parallel edges introduces difficulties that are not present in ordinary saw ueltschi has shown how to overcome these difficulties for sufficiently regular infinite range step distributions and weak self attractions ueltschi in probab theory relat fields 124 2 189 203 2002 this article considers the case of bounded step distributions for weak self attractions we show that the connective constant exists and in d ge 5 carry out a lace expansion analysis to prove the mean field behaviour of the critical two point function hereby addressing a problem posed by den hollander random polymers vol 1974 springer verlag berlin 2009

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

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

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

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

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

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

complex lattice reduction algorithm for low complexity full diversity mimo detection recently lattice reduction aided detectors have been proposed for multiinput multioutput mimo systems to achieve performance with full diversity like the maximum likelihood receiver however these lattice reduction aided detectors are based on the traditional lenstra lenstra lovasz lll reduction algorithm that was originally introduced for reducing real lattice bases in spite of the fact that the channel matrices are inherently complex valued in this paper we introduce the complex lll algorithm for direct application to reducing the basis of a complex lattice which is naturally defined by a complex valued channel matrix we derive an upper bound on proximity factors which not only show the full diversity of complex lll reduction aided detectors but also characterize the performance gap relative to the lattice decoder our analysis reveals that the complex lll algorithm can reduce the complexity by nearly 50 compared to the traditional lll algorithm and this is confirmed by simulation interestingly our simulation results suggest that the complex lll algorithm has practically the same bit error rate performance as the traditional lll algorithm in spite of its lower complexity

practical encoders and decoders for euclidean codes from barnes wall lattices we address the application of barnes wall bw lattice codes for communication over additive white gaussian noise awgn channels we introduce construction a prime of complex bw lattices that makes new connection between linear codes over polynomial rings and lattices we show that construction a prime of bw lattices is equivalent to the multilevel construction from reed muller codes proposed by forney to decode the bw lattice code we adapt the low complexity sequential bw lattice decoder sbwd proposed by micciancio and nicolosi first we study the error performance of sbwd for decoding the infinite lattice and demonstrate that it is powerful in making correct decisions well beyond the packing radius subsequently we use the sbwd to decode lattice codes through a novel noise trimming technique where the received vector is appropriately scaled before applying the sbwd we show that the noise trimming technique is most effective for decoding bw lattice codes in smaller dimensions while the gain diminishes for decoding codes in larger dimensions

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

lace expansion for the ising model the lace expansion has been a powerful tool for investigating mean field behavior for various stochastic geometrical models such as self avoiding walk and percolation above their respective upper critical dimension in this paper we prove the lace expansion for the ising model that is valid for any spin spin coupling for the ferromagnetic case we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace expansion coefficients for self avoiding walk as a result we obtain gaussian asymptotics of the critical two point function for the nearest neighbor model with d gg 4 and for the spread out model with d 4 and l gg 1 without assuming reflection positivity

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

on the error performance of the a_ n lattices we consider the root lattice a n and derive explicit recursive formulas for the moments of its voronoi cell these formulas enable accurate prediction of the error probability of lattice codes constructed from a n

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

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

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

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

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

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

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

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

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

some classes of global cramer rao bounds on considere des bornes de type cramer rao pour l erreur d estimation d un parametre dans un contexte bayesien cette classe de bornes introduite par van trees s avere utile dans divers problemes de communication et de commande stochastiques

a self avoiding walk with attractive interactions a self avoiding walk with small attractive interactions is described here the existence of the connective constant is established and the diffusive behavior is proved using the method of the lace expansion

codebook based lattice reduction aided precoding for limited feedback coded mimo systems lattice reduction aided precoding lrp provides near capacity rates with the use of low complexity linear receivers for coded multiple input multiple output mimo systems however a large amount of feedback in the feedback for an integer or binary precoding matrix has been a bottleneck in its implementation in this paper we propose a codebook based lrp scheme for limited feedback coded mimo systems the proposed lrp scheme follows the fundamentals of the previous lrp scheme that employed multilevel binary coset coding so that the precoding matrix is binary in the proposed lrp scheme the conventional precoding matrix obtained from the lenstra lenstra lovasz algorithm is modified to specific forms that are predefined in a codebook set the new precoding matrix is selected such that the lower bound on the capacity is maximized for a given codebook set while the codebook set is designed offline such that the upper bound of the average capacity loss induced by the limitation on the codebook size is minimized the simulation results show that the proposed lrp scheme nearly achieves the achievable rate of the conventional lrp scheme with a greatly reduced amount of feedback

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

a generalised inductive approach to the lace expansion the lace expansion is a powerful tool for analysing the critical behaviour of self avoiding walks and percolation it gives rise to a recursion relation which we abstract and study using an adaptation of the inductive method introduced by den hollander and the authors we give conditions under which the solution to the recursion relation behaves as a gaussian both in fourier space and in terms of a local central limit theorem these conditions are shown elsewhere to hold for sufficiently spread out models of networks of self avoiding walks in dimensions d 4 and for sufficiently spread out models of critical oriented percolation in dimensions d 1 5 providing a unified approach and an essential ingredient for a detailed analysis of the branching behaviour of these models

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

four dimensional weakly self avoiding walk with contact self attraction we consider the critical behaviour of the continuous time weakly self avoiding walk with contact self attraction on mathbb z 4 for sufficiently small attraction we prove that the susceptibility and correlation length of order p for any p 0 have logarithmic corrections to mean field scaling and that the critical two point function is asymptotic to a multiple of x 2 this shows that small contact self attraction results in the same critical behaviour as no contact self attraction a collapse transition is predicted for larger self attraction the proof uses a supersymmetric representation of the two point function and is based on a rigorous renormalisation group method that has been used to prove the same results for the weakly self avoiding walk without self attraction

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

limited feedback unitary precoding for orthogonal space time block codes orthogonal space time block codes ostbcs are a class of easily decoded space time codes that achieve full diversity order in rayleigh fading channels ostbcs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information when channel state information is available at the transmitter though precoding the space time codeword can be used to support different numbers of transmit antennas and to improve array gain unfortunately transmitters in many wireless systems have no knowledge about current channel conditions this motivates limited feedback precoding methods such as channel quantization or antenna subset selection this paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver the receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error free zero delay feedback channel a criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system low average distortion codebooks are derived based on the optimal codeword selection criterion the resulting design is found to relate to the famous applied mathematics problem of subspace packing in the grassmann manifold codebooks designed by this method are proven to provide full diversity order in rayleigh fading channels monte carlo simulations show that limited feedback precoding performs better than antenna subset selection

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

the recursive form of error bounds for rfs state and observation with p_d this paper presents recursive performance bounds for dynamic estimation and tracking problems in both single and multiple target cases within the framework of finite set statistics because the targets can appear and disappear when the detection probability of a sensor is less than unity pd 1 we must determine the existence or nonexistence of the state as well as its value following the possible detection miss sequences within the framework of a random vector possible observation sets sequences are first defined based on these sequences the performance bounds can be represented by a multivariate function of some time based auxiliary elements recursive relations for all the auxiliary elements are derived rigorously for the multitarget case this recursive estimated bound can be applied without data association applications are analyzed through simulations to verify our theoretical results and show that our bounds are tighter than all other bounds for the case where detection probability pd 1

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

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

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

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

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

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

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

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

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

a crame spl acute r rao type estimation lower bound for systems with measurement faults a crame spl acute r rao type lower bound is presented for systems with measurements prone to discretely distributed faults which are a class of hybrid systems lower bounds for both the state and the markovian interruption variables fault indicators of the system are derived using the recently presented sequential version of the crame spl acute r rao lower bound crlb for general nonlinear systems because of the hybrid nature of the systems addressed the crlb cannot be directly applied due to violation of its associated regularity conditions to facilitate the calculation of the lower bound the hybrid system is first approximated by a system in which the discrete distribution of the fault indicators is replaced by an approximating continuous one the lower bound is then obtained via a limiting process applied to the approximating system the results presented herein facilitate a relatively simple calculation of a nontrivial lower bound for the state vector of systems with fault prone measurements the crlb type lower bound for the interruption process variables turns out to be trivially zero however a nontrivial non crlb type bound for these variables has been recently presented elsewhere by the authors the utility and applicability of the proposed lower bound are demonstrated via a numerical example involving a simple global positioning system gps aided navigation system where the gps measurements are fault prone due to their sensitivity to multipath errors

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

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

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

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

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

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

weiss weinstein lower bounds for markovian systems part 2 applications to fault tolerant filtering characterized by sudden structural changes fault prone systems are modeled using the framework of systems with switching parameters or hybrid systems since a closed form mean square optimal filtering algorithm for this class of systems does not exist it is of particular interest to derive a lower bound on the state estimation error covariance the well known crameacuter rao bound is not applicable to fault prone systems because of the discrete distribution of the fault indicators which violates the regularity conditions associated with this bound on the other hand the weiss weinstein lower bound is essentially free from regularity conditions moreover a sequential version of the weiss weinstein bound suitable for markovian dynamic systems is presented by the authors in a companion paper in the present paper this sequential version is applied to several classes of fault prone dynamic systems the resulting bounds can be used to examine fault detectability and identifiability in these systems moreover it is shown that several recently reported lower bounds for fault prone systems are special cases of or closely related to the sequential version of the weiss weinstein lower bound

analysis and approximation of performance bound for two observer bearings only tracking this paper presents the analytic recursive formulas of cramer rao lower bound crlb for the switching models system in which the target moves either with a constant velocity or with a constant speed and a constant turn rate for the case of two observer bearings only maneuvering target tracking a reliable maneuver detection method is investigated and then utilized to approximate the theoretic crlb finally to demonstrate the agreement between the approximated crlb using the proposed maneuver detection method and the theoretic one a large number of monte carlo runs under different maneuvering scenarios are conducted correctness of the analytic recursive formulas of crlb and effectiveness of the proposed maneuver detection method are verified from these simulations

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

lll reduction achieves the receive diversity in mimo decoding diversity order is an important measure for the performance of communication systems over multiple input multiple output mimo fading channels in this correspondence we prove that in mimo multiple access systems or mimo point to point systems with v blast transmission lattice reduction aided decoding achieves the maximum receive diversity which is equal to the number of receive antennas also we prove that the naive lattice decoding which discards the out of region decoded points achieves the maximum diversity

a comparison of two crame spl acute r rao bounds for nonlinear filtering with p sub d 1 the paper presents a comparative study of two recently reported crame spl acute r rao lower bounds crlbs for nonlinear filtering both applicable when the probability of detection is less than unity the first bound is the information reduction factor crlb the second is the enumeration method crlb the enumeration method is accurate but computationally expensive we prove in the paper that the information reduction factor bound is overoptimistic being always less than the enumeration crlb the theory is illustrated by two target tracking applications ballistic object tracking and bearings only tracking the simulations studies confirm the theory and reveal that the information reduction factor crlb rapidly approaches the enumeration crlb as the scan number increases

critical two point functions and the lace expansion for spread out high dimensional percolation and related models we consider spread out models of self avoiding walk bond percolation lattice trees and bond lattice animals on mathbb z d having long finite range connections above their upper critical dimensions d 4 self avoiding walk d 6 percolation and d 8 trees and animals the two point functions for these models are respectively the generating function for self avoiding walks from the origin to x in mathbb z d the probability of a connection from 0 to x and the generating function for lattice trees or lattice animals containing 0 and x we use the lace expansion to prove that for sufficiently spread out models above the upper critical dimension the two point function of each model decays at the critical point as a multiple of x 2 d as x to infty we use a new unified method to prove convergence of the lace expansion the method is based on x space methods rather than the fourier transform our results also yield unified and simplified proofs of the bubble condition for self avoiding walk the triangle condition for percolation and the square condition for lattice trees and lattice animals for sufficiently spread out models above the upper critical dimension