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

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

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

cut set bound is loose for gaussian relay networks the cut set bound developed by cover and el gamal in 1979 has since remained the best known upper bound on the capacity of the gaussian relay channel we develop a new upper bound on the capacity of the gaussian primitive relay channel which is tighter than the cut set bound our proof uses gaussian measure concentration to establish geometric relations satisfied with high probability between the n letter random variables associated with a reliable code for communicating over this channel we then translate these geometric relations into new information inequalities that cannot be obtained with classical methods combined with a tensorization argument proposed by courtade and ozgur in 2015 our result also implies that the current capacity approximations for gaussian relay networks which have linear gap to the cut set bound in the number of nodes are order optimal and lead to a lower bound on the pre constant

lattice network codes based on eisenstein integers in this paper we investigate lattice network codes lncs constructed from eisenstein integer based lattices quantization and encoding algorithms over eisenstein integers are first introduced then a union bound estimation ube of the decoding error probability is derived when the shaping region of the lnc is a product of regular hexagons next the gaussian reduction algorithm is generalized to be applicable to complex lattices over eisenstein integers such that an optimal coefficient vector can be found in the two transmitter single relay system based on the ube design criteria for optimal lncs with minimum decoding error probability are formulated and applied to construct both gaussian integer and eisenstein integer based good lncs from rate 1 2 feed forward convolutional codes by complex construction a the constructed codes provide up to 7 65 db nominal coding gains over rayleigh fading channels furthermore we introduce the construction of lncs from linear codes by complex construction b the nominal coding gains and error performance of the lncs thus constructed are explicitly analyzed examples show that the lncs constructed by complex construction b provide a better tradeoff between code rate and nominal coding gain

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

beamforming design for multiuser two way relaying a unified approach via max min sinr in this paper we develop a unified framework for beamforming designs in non regenerative multiuser two way relaying twr the core of our framework is the solution to the max min signal to interference plus noise ratio sinr problem for multiuser twr we solve this problem using a dinkelbach type algorithm with near optimal performance and superlinear convergence we show that using the max min sinr solution as a corner stone the beamforming designs under various important criteria such as weighted sum rate maximization weighted sum mean square error mse minimization and average bit error rate ber or symbol error rate ser minimization etc can be reformulated into a monotonic program a polyblock outer approximation algorithm is then used to find the desired solutions with guaranteed convergence and optimal performance provided that the core max min sinr solver is optimal furthermore the proposed unified approach can provide important insights for tackling the optimal beamforming designs in other emerging network models and settings for instances we extend the proposed framework to address the beamforming design in collaborative twr and multi pair mimo twr extensive numerical results are presented to demonstrate the merits of the proposed beamforming solutions

distributed source coding using abelian group codes a new achievable rate distortion region a distributed source coding problem with a joint distortion criterion that depends on the sources and the reconstruction is considered in this work while the prevalent trend in information theory has been to prove achievability results using shannon s random coding arguments using structured random codes offer rate gains over unstructured random codes for many problems motivated by this a new achievable rate distortion region an inner bound to the performance limit is presented for this problem for discrete memoryless sources based on good structured random nested codes built over abelian groups for certain sources and distortion functions the new rate region is shown to be strictly bigger than the berger tung rate region which has been the best known achievable rate region for this problem till now this is done using numerical plots achievable rates for single user source coding using abelian group codes are also obtained as a corollary of the main coding theorem it is shown that nested linear codes achieve the shannon rate distortion function in the arbitrary discrete memoryless case

nested lattice codes for gaussian relay networks with interference in this paper we consider a class of single source multicast relay networks we assume that all outgoing channels of a node in the network to its neighbors are orthogonal while the incoming signals from its neighbors can interfere with each other we first focus on gaussian relay networks with interference and find an achievable rate using a lattice coding scheme we show that the achievable rate of our scheme is within a constant bit gap from the information theoretic cut set bound where the constant depends only on the network topology but not on the transmit power noise variance and channel gains this is similar to a recent result by avestimehr diggavi and tse who showed an approximate capacity characterization for general gaussian relay networks however our achievability uses a structured code instead of a random one using the idea used in the gaussian case we also consider a linear finite field symmetric network with interference and characterize its capacity using a linear coding scheme

on the capacity region of asymmetric gaussian two way line channel lattice codes are known to outperform random codes for certain networks especially in the gaussian two way relay channels gtwrcs where lattice codes are able to exploit their linearity as an extension of the gtwrc in this paper we consider the asymmetric gaussian two way line network where two nodes exchange their messages through multiple relays we first investigate the capacity region of the full duplex two way two relay line network the results can be extended to an arbitrary number of relays and to half duplex scenarios this channel consists of four nodes 1 leftrightarrow 2 leftrightarrow 3 leftrightarrow 4 where nodes 1 and 4 with the help of two full duplex relays i e nodes 2 and 3 exchange their messages with each other using lattice codes we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region in the proposed scheme each relay decodes the sum of lattice points and then re encodes it into another lattice codeword which satisfies the transmit power constraint at the relay it is shown that the proposed scheme achieves the capacity region of asymmetric two way line network within 0 5 bit independent of the number of relays

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

global well posedness for an inhomogeneous lsw model in unbounded domains the lsw theory of domain coarsening describes the evolution of the size distribution of a system of particles evolving by diffusional mass exchange to reduce their total surface area we prove existence and uniqueness of solutions to an inhomogeneous extension of the lsw model in unbounded domains this model arises naturally as a homogenization limit of the underlying free boundary problem in the case of a system of particles for which the screening length the effective range of particle interactions is smaller than the system size the crucial ingredients in the analysis are first to establish the screening property by showing that the corresponding green s function decreases exponentially over the relevant distances second we have to control the mass fluxes between different regions to prevent aggregation of mass in few particles which would result in blow up of the solution

theory and numerical analysis for exact distributions of functionals of a dirichlet process the distribution of a mean or more generally of a vector of means of a dirichlet process is considered some characterizing aspects of this paper are i a review of a few basic results providing new formulations free from many of the extra assumptions considered to date in the literature and giving essentially new simpler and more direct proofs ii new numerical evaluations with any prescribed error of approximation of the distribution at issue iii a new form for the law of a vector of means moreover as applications of these results we give iv the sharpest condition sufficient for the distribution of a mean to be symmetric v forms for the probability distribution of the variance of the dirichlet random measure vi some hints for determining the finite dimensional distributions of a random function connected with bayesian methods for queuing models

communication over mimo x channels interference alignment decomposition and performance analysis in a multiple antenna system with two transmitters and two receivers a scenario of data communication known as the x channel is studied in which each receiver receives data from both transmitters in this scenario it is assumed that each transmitter is unaware of the other transmitter s data noncooperative scenario this system can be considered as a combination of two broadcast channels from the transmitters points of view and two multiple access channels from the receivers points of view taking advantage of both perspectives two signaling schemes for such a scenario are developed in these schemes some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple antenna broadcast subchannels or two noninterfering multiple antenna multiple access subchannels the main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain mg it is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable mg in particular it is shown that in some specific cases the achieved mg is the same as the mg of the system if full cooperation is provided either between the transmitters or between the receivers in the second part of the paper it is shown that by using mixed design schemes rather than decomposition schemes and taking the statistical properties of the interference terms into account the power offset of the system can be improved the power offset represents the horizontal shift in the curve of the sum rate versus the total power in decibels

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

ostwald ripening for dilute systems under quasistationary dynamics we consider a dilute mixture in 3d of a finite number of particles initially close to spherical but of varying size evolving according to quasistationary dynamics under the scaling hypotheses that 1 size distance 2 deviation from sphericity size are both initially small we show robustness of the almost spherical shape by associating centers and radii to each particle and then derive rigorously a set of o d e s for the radii which we relate to the lifschitz slyozov wagner theory of coarsening and also establish an estimate for the speed of the centers

multiple input multiple output two way relaying a space division approach we propose a novel space division based network coding scheme for multiple input multiple output mimo two way relay channels twrcs in which two multiantenna users exchange information via a multiantenna relay in the proposed scheme the overall signal space at the relay is divided into two subspaces in one subspace the spatial streams of the two users have nearly orthogonal directions and are completely decoded at the relay in the other subspace the signal directions of the two users are nearly parallel and linear functions of the spatial streams are computed at the relay following the principle of physical layer network coding based on the recovered messages and message functions the relay generates and forwards network coded messages to the two users we show that at high signal to noise ratio the proposed scheme achieves the asymptotic sum rate capacity of the mimo twrc within 1 2 log 5 4 0 161 bits per user antenna for any antenna configuration and any channel realization we perform large system analysis to derive the average sum rate of the proposed scheme over rayleigh fading mimo twrcs we show that the average asymptotic sum rate gap to the capacity is at most 0 053 bits per relay antenna it is demonstrated that the proposed scheme significantly outperforms the existing 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

user antenna selection for physical layer network coding based on euclidean distance in this paper we present the error performance analysis of a multiple input multiple output mimo physical layer network coding pnc system with two different user antenna selection as schemes in asymmetric channel conditions for the first antenna selection scheme as1 where the user antenna is selected in order to maximize the overall channel gain between the user and the relay we give an explicit analytical proof that for binary modulations the system achieves full diversity order of min n a n b times n r in the multiple access ma phase where n a n b and n r denote the number of antennas at user a user b and relay r respectively we present a detailed investigation of the diversity order for the mimo pnc system with as1 in the ma phase for any modulation order a tight closed form upper bound on the average ser is also derived for the special case when n r 1 which is valid for any modulation order we show that in this case the system fails to achieve transmit diversity in the ma phase as the system diversity order drops to 1 irrespective of the number of transmit antennas at the user nodes additionally we propose a euclidean distance ed based user antenna selection scheme as2 that outperforms the first scheme in terms of error performance moreover by deriving upper and lower bounds on the diversity order for the mimo pnc system with as2 we show that this system enjoys both transmit and receive diversity achieving full diversity order of min n a n b times n r in the ma phase for any modulation order monte carlo simulations are provided which confirm the correctness of the derived analytical results

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

optimal distributed codes for feedback aided cooperative relay networks a novel transmission scheme for cooperative relay networks is presented in this paper the proposed scheme is based on the non orthogonal selection decode and forward protocol with an additional assumption of having a low rate feedback channel from the destination to relays benefited from the feedback information an optimal distributed code that has an extremely short delay equal to four is constructed and the same code is applicable to networks with the arbitrary number of relays to yield optimal cooperative diversity the proposed code is sphere decodable with a decoding complexity again independent of the number of relays in high snr regime in particular when operating at multiplexing gain 1 2 the lattice decoder at the destination has a zero complexity exponent meaning a constant decoding complexity and independent of transmission rate analyses for the decoding complexity of other existing diversity optimal distributed codes are also provided it is shown that these codes have a linear growth in delay and an exponential growth in decoding complexity as the number of relays increases

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

ergodic interference alignment this paper develops a new communication strategy ergodic interference alignment for the k user interference channel with time varying fading at any particular time each receiver will see a superposition of the transmitted signals plus noise the standard approach to such a scenario results in each transmitter receiver pair achieving a rate proportional to 1 k its interference free ergodic capacity however given two well chosen time indices the channel coefficients from interfering users can be made to exactly cancel by adding up these two observations each receiver can obtain its desired signal without any interference if the channel gains have independent uniform phases this technique allows each user to achieve at least 1 2 its interference free ergodic capacity at any signal to noise ratio prior interference alignment techniques were only able to attain this performance as the signal to noise ratio tended to infinity extensions are given for the case where each receiver wants a message from more than one transmitter as well as the x channel case with two receivers where each transmitter has an independent message for each receiver finally it is shown how to generalize this strategy beyond gaussian channel models for a class of finite field interference channels this approach yields the ergodic capacity region

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

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

the approximate capacity of the many to one and one to many gaussian interference channels recently etkin tse and wang found the capacity region of the two user gaussian interference channel to within 1 bit s hz a natural goal is to apply this approach to the gaussian interference channel with an arbitrary number of users we make progress towards this goal by finding the capacity region of the many to one and one to many gaussian interference channels to within a constant number of bits the result makes use of a deterministic model to provide insight into the gaussian channel the deterministic model makes explicit the dimension of signal level a central theme emerges the use of lattice codes for alignment of interfering signals on the signal level

on an elaboration of m kac s theorem concerning eigenvalues of the laplacian in a region with randomly distributed small obstacles we removem balls of centersw 1 w m with the same radius m from a bounded domain inr 3 with smooth boundary let k m w m denote thek th eigenvalue of the laplacian in m balls under the dirichlet condition we consider k m w m as a random variable on a probability space w 1 w m and we examine a precise behaviour of k m w m asm we give an elaboration of m kac s theorem

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

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

error bounds for numerical inversion of a probability characteristic function given the characteristic function of a continuous real random variable it is possible to construct a finite fourier series that approximates the density over any specified finite interval this series converges in mean square if the density decays faster than x 1 and the characteristic function decays faster than t 1 2 it converges in minimax if the density decays faster than x 1 and the characteristic function decays faster than t 1 it is also possible to construct a finite fourier series for the distribution function that has arbitrarily small maximum error over any finite interval provided that the characteristic function decays as t beta for some beta 0 and that either the distribution or the density decays to 0 or 1 as appropriate as x alpha for some alpha 1 these conditions are weak enough to include most continuous distributions of practical interest explicit error bounds can be obtained directly from the characteristic function without prior knowledge of either the distribution or density making these series useful for numerical inversion

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

on the loss of single letter characterization the dirty multiple access channel for general memoryless systems the existing information theoretic solutions have a ldquosingle letterrdquo form this reflects the fact that optimum performance can be approached by a random code or a random binning scheme generated using independent and identically distributed copies of some scalar distribution is that the form of the solution of any information theoretic problem in fact some counter examples are known the most famous one is the ldquotwo help onerdquo problem korner and marton showed that if we want to decode the modulo two sum of two correlated binary sources from their independent encodings then linear coding is better than random coding in this paper we provide another counter example the ldquodoubly dirtyrdquo multiple access channel mac like the korner marton problem this is a multiterminal scenario where side information is distributed among several terminals each transmitter knows part of the channel interference while the receiver only observes the channel output we give an explicit solution for the capacity region of the binary doubly dirty mac demonstrate how this region can be approached using a linear coding scheme and prove that the ldquobest known single letter regionrdquo is strictly contained in it we also state a conjecture regarding the capacity loss of single letter characterization in the gaussian case

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

polynomially solvable instances of the shortest and closest vector problems with applications to compute and forward a particular instance of the shortest vector problem svp appears in the context of compute and forward despite the np hardness of the svp we will show that this certain instance can be solved in complexity order o n psi log n psi where psi sqrt p text h 2 1 depends on the transmission power and the norm of the channel vector we will then extend our results to integer forcing and finally introduce a more general class of lattices for which the svp and the closest vector problem can be approximated within a constant factor

the degrees of freedom of the k user gaussian interference channel is discontinuous at rational channel coefficients the degrees of freedom of a k user gaussian interference channel gic has been defined to be the multiple of 1 2 log 2 p at which the maximum sum of achievable rates grows with increasing power p in this paper we establish that the degrees of freedom of three or more user real scalar gics viewed as a function of the channel coefficients is discontinuous at points where all of the coefficients are nonzero rational numbers more specifically for all k 2 we find a class of k user gics that is dense in the gic parameter space for which k 2 degrees of freedom are exactly achievable and we show that the degrees of freedom for any gic with nonzero rational coefficients is strictly smaller than k 2 these results are proved using new connections with number theory and additive combinatorics

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

amplify and forward in wireless relay networks rate diversity and network size a wireless network with fading and a single source destination pair is considered the information reaches the destination via multiple hops through a sequence of layers of single antenna relays at high signal to noise ratio snr the simple amplify and forward strategy is shown to be optimal in terms of degrees of freedom because it achieves the degrees of freedom equal to a point to point multiple input multiple output mimo system hence the lack of coordination in relay nodes does not reduce the achievable degrees of freedom the performance of this amplify and forward strategy degrades with increasing network size this phenomenon is analyzed by finding the tradeoffs between network size rate and diversity a lower bound on the diversity multiplexing tradeoff for concatenation of multiple random gaussian matrices is obtained also it is shown that achievable network size in the outage formulation short codes is a lot smaller than the ergodic formulation long codes

ostwald ripening in two dimensions the rigorous derivation of the equations from the mullins sekerka dynamics we consider a dilute mixture of a finite number of particles and we are interested in the coarsening of the spatial distribution in two space dimensions under mullins sekerka dynamics under the appropriate scaling hypotheses we associate radii and centers to each particle and derive equations for the whole evolution

the method of reflections homogenization and screening for poisson and stokes equations in perforated domains we study the convergence of the method of reflections for the dirichlet problem of the poisson and the stokes equations in perforated domains which exist in the exterior of balls we prove that the method converges if the balls are contained in a bounded region and the density of the electrostatic capacity of the balls is sufficiently small if the capacity density is too large or the balls extend to the whole space the method diverges but we provide a suitable modification of the method that converges to the solution of the dirichlet problem also in this case we give new proofs of classical homogenization results for the dirichlet problem of the poisson and the stokes equations in perforated domains using the modified method of reflections

capacity bounds for the k user gaussian interference channel the capacity region of the k user gaussian interference channel gic is a long standing open problem and even capacity outer bounds are little known in general a significant progress on degrees of freedom dof analysis a first order capacity approximation for the k user gic has provided new important insights into the problem of interest in the high signal to noise ratio snr limit however such capacity approximation has been observed to have some limitations in predicting the capacity at finite snr in this paper we develop a new upper bounding technique that utilizes a new type of genie signal and applies time sharing to genie signals at k receivers based on this technique we derive new upper bounds on the sum capacity of the three user gic with constant complex channel coefficients and then generalize to the k user case to better understand sum rate behavior at finite snr we also provide closed form expressions of our upper bounds on the capacity of the k user symmetric gic easily computable for any k from the perspectives of our results some sum rate behavior at finite snr is in line with the insights given by the known dof results while some others are not in particular the well known k 2 dof achievable for almost all constant real channel coefficients turns out to be not embodied as a substantial performance gain over a certain range of the cross channel coefficient in the k user symmetric real case especially for large k we further investigate the impact of phase offset between the direct channel coefficient and the cross channel coefficients on the sum rate upper bound for the three user complex gic as a consequence we aim to provide new findings that could not be predicted by the prior works on dof of gics

precoding designs based on minimum distance for two way relaying mimo systems with physical network coding in this paper we propose new precoding methods for two way multiple input multiple output physical network coding pnc systems which employ the modulo operation in our work the transmit and receive filters are determined to maximize the minimum distance of the received constellations assuming global channel state information the precoding operations are separately optimized for the multiple access ma and the broadcast stages and the optimal precoding is obtained by applying a semidefinite relaxation method especially we prove that for the system with linear detection the modulo operation for the pnc achieves optimality with the derived precoding for the ma stage in terms of the minimum distance also we present a closed form solution for the optimal filter designs for two special cases for computing solutions we transform our max min problem into a simple maximization problem by imposing additional constraints also we propose a suboptimal non iterative precoding scheme whose performance is within 1 db at a bit error rate ber of 10 4 compared to the optimum iterative method with much reduced complexity finally the simulation results show that the proposed systems achieve 2 3 db gains at a ber of 10 4 compared to the optimal amplify and forward systems

linear vector physical layer network coding for mimo two way relay channels design and performance analysis in this paper we propose a new linear vector physical layer network coding nc scheme for spatial multiplexing multiple input multiple output mimo two way relay channel twrc where the channel state information csi is not available at the transmitters in this scheme each user transmits m independent quadrature amplitude modulation signal streams respectively from its m antennas to the relay based on the receiver side csi the relay determines a nc generator matrix for linear vector network coding and reconstructs the associated m linear combinations of all messages we present an explicit solution for the generator matrix that minimizes the error probability at a high snr as well as an efficient algorithm to find the optimized solution we propose a novel typical error event analysis that exploits a new characterization of the deep fade events for the twrc we derive a new closed form expression for the average error probability of the proposed scheme over a rayleigh fading mimo twrc our analysis shows that the proposed scheme achieves the optimal error rate performance at a high snr numerical results show that the proposed scheme significantly outperforms existing schemes and match well with our analytical results

the effect of the geometry of the particle distribution in ostwald ripening based on 1 we derive equations for the radii and the centers that we relate to the lifshitz slyozov wagner theory

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

on the effect of stochastic fluctuations in the dynamics of the lifshitz slyozov wagner model in this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed corrections to the lifshitz slyozov wagner lsw model that take into account the stochastic character of the problem are computed it is proved under suitable smallness assumptions for the volume fraction filled by the particles that the effect of these corrections does not modify much the dynamics of the self similar solutions of the lsw system of equations

lattice strategies for the dirty multiple access channel in costa s dirty paper channel gaussian random binning is able to eliminate the effect of interference which is known at the transmitter and thus achieve capacity we examine a generalization of the dirty paper problem to a multiple access channel mac setup where structured lattice based binning seems to be necessary to achieve capacity in the dirty mac two additive interference signals are present one known to each transmitter but none to the receiver the achievable rates using costa s gaussian binning vanish if both interference signals are strong in contrast it is shown that lattice strategies lattice precoding can achieve positive rates independent of the interference power furthermore in some cases which depend on the noise variance and power constraints high dimensional lattice strategies are in fact optimal in particular they are optimal in the limit of high snr where the capacity region of the dirty mac with strong interference approaches that of a clean mac whose power is governed by the minimum of the users powers rather than their sum the rate gap at high snr between lattice strategies and optimum rather than gaussian random binning is conjectured to be 1 2 log2 e 6 0 254 bit thus the doubly dirty mac is another instance of a network setting like the korner marton problem where linear structured coding is potentially better than random binning

on first order corrections to the lsw theory ii finite systems we consider first order corrections to the classical theory by lifshitz slyozov and wagner lsw for systems with a finite number of particles numerical simulations in v e fradkov etal phys rev e 53 3925 3932 1996 show a cross over in the scaling of the correction term from 1 3 to 1 2 is the volume fraction of particles when the system size becomes larger than the screening length we rigorously derive this cross over for the rate of change of the energy starting from the monopole approximation the proof exploits the fact that the rate of change of energy has a variational characterization

asymptotic capacity of the separated mimo two way relay channel a multiple input multiple output two way relay channel consisting of two communication nodes and a full duplex relay node in which no direct link exists between the two communication nodes is considered we propose an achievable scheme that employs horizontally encoded lattice codes combined with generalized singular value decomposition based precoding for the first phase the second phase of the proposed scheme follows the fundamentals of the previous scheme which uses vertically encoded structural bining with the only difference that the added codeword of the two codewords from the communication nodes instead of those two individual codewords is decoded and retransmitted in the proposed scheme we show that the proposed scheme achieves the cut set bound asymptotically as the signal to noise ratios of the channels tend to infinity

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

blind compute and forward compute and forward c f is a promising new approach to interference management enjoying several advantages over other information theoretic schemes c f usually requires channel state information csi at the receivers so that an optimal scaling factor can be computed for the purposes of decoding in this paper a blind c f scheme i e one not requiring csi is developed rather than attempting to compute the optimal scaling factor this new scheme seeks one or more good scalars i e scalars that allow correct decoding despite possibly being suboptimal the region of all such good scalars is characterized to find a good scalar a computationally efficient scheme is proposed which involves error detection a hierarchically organized list as well as a use of the smoothing lemma from lattice theory simulation results show that our blind c f scheme achieves for a class of nested lattice codes the same throughput as its csi enabled counterpart at the expense of approximately a two fold increase in computational complexity in the high throughput region moreover our blind c f scheme can be applied to multisource multirelay networks with a good performance complexity tradeoff

self similar behaviour for noncompactly supported solutions of the lsw model in this paper a method of approximating the classical lsw model near self similar solutions for initial data with infinite support is developed the resulting problem is an integrodifferential equation having two time scales that can be studied using multiple scale methods the analysis provides a detailed description of the precise manner in which the characteristics leak through the critical radius associated to the self similar solutions the analysis in this paper makes precise the meaning of the iterated logarithmic asymptotics in the dynamics of the lsw model that were already obtained in the original lifshitz slyozov paper examples of noncompactly supported solutions of the lsw model that do not behave in a self similar manner are also given

the approximate sum capacity of the symmetric gaussian k user interference channel interference alignment has emerged as a powerful tool in the analysis of multiuser networks despite considerable recent progress the capacity region of the gaussian k user interference channel is still unknown in general in part due to the challenges associated with alignment on the signal scale using lattice codes this paper develops a new framework for lattice interference alignment based on the compute and forward approach within this framework each receiver decodes by first recovering two or more linear combinations of the transmitted codewords with integer valued coefficients and then solving these linear combinations for its desired codeword for the special case of symmetric channel gains this framework is used to derive the approximate sum capacity of the gaussian interference channel up to an explicitly defined outage set of the channel gains the key contributions are the capacity lower bounds for the weak through strong interference regimes where each receiver should jointly decode its own codeword along with part of the interfering codewords as part of the analysis it is shown that decoding k linear combinations of the codewords can approach the sum capacity of the k user gaussian multiple access channel up to a gap of no more than k 2 log k bits

two way mimo relay precoder design with channel state information in this paper a two way relay precoder is designed for multiple input multiple output mimo distributed cooperative relay systems a constrained optimization problem with respect to w r t the relay precoder is formulated for the most general relay and antenna scenario namely multiple relays each with multiple antennas it is shown that due to the difficulty of two way distributed relaying mechanism as well as the block diagonal nature of the relay precoding matrix this optimization problem cannot be solved by existing one way relaying methods it is then proved that with full channel state information available at relays the underlying problem can be converted to a convex optimization w r t the non zero entries of the relay precoding matrix only such that the lagrangian multiplier method is applicable to the relay precoder design leading to a closed form relay precoding solution a simulation study is conducted to justify the superior performance of the proposed two way relaying scheme

on vector linear solvability of multicast networks vector linear network coding lnc is a generalization of the conventional scalar lnc such that the data unit transmitted on every edge is an l dimensional vector of data symbols over a base field gf q vector lnc enriches the choices of coding operations at intermediate nodes and there is a popular conjecture on the benefit of vector lnc over scalar lnc in terms of alphabet size of data units there exist single source multicast networks that are vector linearly solvable of dimension l over gf q but not scalar linearly solvable over any field of size q leq q l this paper introduces a systematic way to construct such multicast networks and subsequently establish explicit instances to affirm the positive answer of this conjecture for infinitely many alphabet sizes p l with respect to an arbitrary prime p on the other hand this paper also presents explicit instances with the special property that they do not have a vector linear solution of dimension l over gf 2 but have scalar linear solutions over gf q for some q where q can be odd or even this discovery also unveils that over a given base field a multicast network that has a vector linear solution of dimension l does not necessarily have a vector linear solution of dimension l l

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

screening in interacting particle systems we consider the green s function of the laplace operator in domains with spherical holes particles under natural assumptions on the distribution of particles we show that the green s function decays exponentially over distances larger than the screening length this result is fundamental for example when deriving effective equations for coarsening systems in unbounded domains