design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

information theoretic lengths of jacobi polynomials the information theoretic lengths of the jacobi polynomials p n x which are information theoretic measures renyi shannon and fisher of their associated rakhmanov probability density are investigated they quantify the spreading of the polynomials along the orthogonality interval 1 1 in a complementary but different way as the root mean square or standard deviation because contrary to this measure they do not refer to any specific point of the interval the explicit expressions of the fisher length are given the renyi lengths are found by the use of the combinatorial multivariable bell polynomials in terms of the polynomial degree n and the parameters the shannon length which cannot be exactly calculated because of its logarithmic functional form is bounded from below by using sharp upper bounds to general densities on 1 1 given in terms of various expectation values moreover its asymptotics is also pointed out finally several computational issues relative to these three quantities are carefully analyzed

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

degrees of freedom of two hop wireless networks everyone gets the entire cake we show that fully connected two hop wireless networks with k sources k relays and k destinations have k degrees of freedom both in the case of time varying channel coefficients and constant channel coefficients in which case the result holds for almost all values of constant channel coefficients our main contribution is a new achievability scheme which we call aligned network diagonalization this scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations thus being received free of interference by their intended destination in addition we extend our scheme to multihop networks with fully connected hops and multihop networks with mimo nodes for which the degrees of freedom are also fully characterized

optimal spectrum management in multiuser interference channels in this paper we study the problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels we assume that interference is treated as noise by the decoders and separate encoding is applied first a simple pair wise channel condition for frequency division multiple access schemes to achieve all pareto optimal points of the rate region is derived it enables fully distributed global optimal decision making on whether any two users should use orthogonal channels next we present an analytical solution to finding the maximum sum rate in two user symmetric frequency flat channels generalizing this solution to frequency selective channels a convex optimization is established that yields the global optimum finally we show that our method generalizes to k user k 2 weighted sum rate maximization in asymmetric frequency selective channels and we transform this classic nonconvex optimization to an equivalent convex optimization in the primal domain

soliton solutions of the kadomtsev petviashvili ii equation we study a general class of line soliton solutions of the kadomtsev petviashvili ii kpii equation by investigating the wronskian form of its tau function we show that in addition to the previously known line soliton solutions of kpii this class also contains a large variety of multisoliton solutions many of which exhibit nontrivial spatial interaction patterns we also show that in general such solutions consist of unequal numbers of incoming and outgoing line solitons from the asymptotic analysis of the tau function we explicitly characterize the incoming and outgoing line solitons of this class of solutions we illustrate these results by discussing several examples

capacity regions and sum rate capacities of vector gaussian interference channels the capacity regions of vector or multiple input multiple output gaussian interference channels are established for very strong interference and aligned strong interference furthermore the sum rate capacities are established for z interference noisy interference and mixed aligned weak intermediate and aligned strong interference these results generalize known results for scalar gaussian interference channels

ldpc codes for fading gaussian broadcast channels in this work we study coding over a class of two user broadcast channels bcs with additive white gaussian noise and multiplicative fading known at the receivers only joint decoding of low density parity check ldpc codes is analyzed the message update rule at the mapping node linking the users codes is derived and is found to exhibit an interesting soft interference cancellation property high performance codes are found using the differential evolution optimization technique and extrinsic information transfer analysis adapted to our multiuser setting the optimized codes have rates very close to the boundary of the achievable region for binary constrained input for both faded and unfaded channels simulation results for moderate block lengths show that our codes operate within less than 1 db of their respective threshold

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

bilayer low density parity check codes for decode and forward in relay channels this paper describes an efficient implementation of binning for decode and forward df in relay channels using low density parity check ldpc codes bilayer ldpc codes are devised to approach the theoretically promised rate of the df relaying strategy by incorporating relay generated parity bits in specially designed bilayer graphical code structures while conventional ldpc codes are sensitively tuned to operate efficiently at a certain channel parameter the proposed bilayer ldpc codes are capable of working at two different channel parameters and two different rates that at the relay and at the destination to analyze the performance of bilayer ldpc codes bilayer density evolution is devised as an extension of the standard density evolution algorithm based on bilayer density evolution a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming further in order to approach to the theoretical df rate for a wide range of channel parameters this paper proposes two different forms of bilayer codes the bilayer expurgated and bilayer lengthened codes it is demonstrated that the rate of a properly designed bilayer ldpc code can closely approach the theoretical df limit finally it is shown that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays

a receiver centric approach to interference management fairness and outage optimization effective interference management in the multiuser interference channel necessitates that the users form their transmission and interference management decisions in coordination and adapt them to the state of the channel establishing such coordination often facilitated through information exchange is prohibitive in fast varying channels especially when the network size grows this paper focuses on the multiuser gaussian interference channel and offers a receiver centric approach to interference management in this approach the transmitters deploy rate splitting and superposition coding to generate their messages according to independent gaussian codebooks the receivers can freely decode any arbitrary set of interfering messages along with their designated messages in any desired joint or ordered fashion and treat the rest of the interferers as gaussian noise the proposed receiver centric interference management approach is applied to two class of problems outage optimization and fairness constrained rate allocation and constructive proofs are provided to establish the following properties for the proposed approach 1 the optimal set of codebooks to be decoded by each receiver is a local decision made by each receiver based on its local channel state information csi 2 the globally optimal transmission rates are related to locally optimal rates computed by the receivers based on their local information which implies that the transmitters do not require explicit knowledge of the csi and can determine their rates via limited feedback from the receivers and 3 obtaining the optimal interference management strategy at each receiver has controlled complexity

randomized resource allocation in decentralized wireless networks in this paper we consider a decentralized wireless communication network with a fixed number u of frequency subbands to be shared among n transmitter receiver pairs it is assumed that the number of active users is a realization of a random variable with a given probability mass function moreover users are unaware of each other s codebooks and hence no multiuser detection is possible we propose a randomized frequency hopping fh scheme in which each transmitter randomly hops over a subset of u subbands from transmission slot to transmission slot assuming all users transmit gaussian signals the distribution of the noise plus interference is mixed gaussian which makes calculation of the mutual information between the transmitted and received signals of each user intractable we derive lower and upper bounds on the mutual information of each user and demonstrate that for large signal to noise ratio snr values the two bounds coincide this observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity we compare the performance of the fh system to that of the frequency division fd system in terms of the following performance measures average sum multiplexing gain 1 and average minimum multiplexing gain per user 2 we show that depending on the probability mass function of the number of active users the fh system can offer a significant improvement in terms of 1 and 2 implying a more efficient usage of the spectrum in the sequel we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains developing a new upper bound on the differential entropy of a mixed gaussian random vector and using entropy power inequality we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given snr level we demonstrate that the so called outage capacity can be considerably higher in the fh scheme than in the fd scenario for reasonable distributions on the number of active users this guarantees a higher spectral efficiency in fh compared to fd

on the capacity of the k user cyclic gaussian interference channel this paper studies the capacity region of a k user cyclic gaussian interference channel where the kth user interferes with only the k 1 th user mod k in the network inspired by the work of etkin tse and wang who derived a capacity region outer bound for the two user gaussian interference channel and proved that a simple han kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters this paper shows that a similar strategy also achieves the capacity region of the k user cyclic interference channel to within a constant gap in the weak interference regime specifically for the k user cyclic gaussian interference channel a compact representation of the han kobayashi achievable rate region using fourier motzkin elimination is first derived a capacity region outer bound is then established it is shown that the etkin tse wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime for the special three user case this gap can be sharpened to 1 bits by time sharing of several different strategies the capacity result of the k user cyclic gaussian interference channel in the strong interference regime is also given further based on the capacity results this paper studies the generalized degrees of freedom gdof of the symmetric cyclic interference channel it is shown that the gdof of the symmetric capacity is the same as that of the classic two user interference channel no matter how many users are in the network

a convex approach to near optimal beamforming designs for two user miso fading interference channels based on a convex approach with side information we propose transmit beamforming designs for two user multiple input single output fading interference channels main contribution of this paper is to provide a novel methodology for solving a non convex optimization problem efficiently based on the effective side information consequently the proposed scheme exhibits near optimal average sum rate performance under single user detection with gaussian inputs which is validated through numerical results as a by product we show that the proposed scheme requires almost no parameter optimization on the average over multiple coding blocks

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

soliton fusion and fission in a generalized variable coefficient fifth order korteweg de vries equation in fluids under investigation in this paper is a generalized variable coefficient fifth order korteweg de vries equation which describes the interaction between a water wave and a floating ice cover or the gravity capillary waves via the hirota method bell polynomial approach and symbolic computation bilinear forms n soliton solutions backlund transformation and lax pair are derived infinitely many conservation laws are obtained based on the bell polynomial typed backlund transformation soliton fusion and fission and influence of the variable coefficients from the equation are analyzed both variable coefficients c t and n t are in direct proportion to the soliton velocities but have no effect on the amplitudes while another constant coefficient can affect the types of the interactions in the sense of the elastic or inelastic elastic inelastic interactions among the three solitons are presented as well

resonance and web structure in discrete soliton systems the two dimensional toda lattice and its fully discrete and ultra discrete analogues we present a class of solutions of the two dimensional toda lattice equation its fully discrete analogue and its ultra discrete limit these solutions demonstrate the existence of soliton resonance and web like structure in discrete integrable systems such as differential difference equations difference equations and cellular automata ultra discrete equations

a digital interface for gaussian relay and interference networks lifting codes from the discrete superposition model for every gaussian network there exists a corresponding deterministic network called the discrete superposition network we show that this discrete superposition network provides a near optimal digital interface for operating a class consisting of many gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the gaussian network while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network this constant depends only on the number of nodes in the network and not on the channel gains or snr moreover the capacities of the two networks are within a constant of each other again independent of channel gains and snr we show that the class of gaussian networks for which this interface property holds includes relay networks with a single source destination pair interference networks multicast networks and the counterparts of these networks with multiple transmit and receive antennas the code for the gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it this lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for gaussian relay networks we present similar results for the k k gaussian interference network mimo gaussian interference networks mimo gaussian relay networks and multicast networks with the constant gap depending additionally on the number of antennas in case of mimo networks

efficient computation of pareto optimal beamforming vectors for the miso interference channel with successive interference cancellation we study the two user multiple input single output miso gaussian interference channel where the transmitters have perfect channel state information and employ single stream beamforming the receivers are capable of performing successive interference cancellation so when the interfering signal is strong enough it can be decoded treating the desired signal as noise and subtracted from the received signal before the desired signal is decoded we propose efficient methods to compute the pareto optimal rate points and corresponding beamforming vector pairs by maximizing the rate of one link given the rate of the other link we do so by splitting the original problem into four subproblems corresponding to the combinations of the receivers decoding strategies either decode the interference or treat it as additive noise we utilize recently proposed parameterizations of the optimal beamforming vectors to equivalently reformulate each subproblem as a quasi concave problem which we solve very efficiently either analytically or via scalar numerical optimization the computational complexity of the proposed methods is several orders of magnitude less than the complexity of the state of the art methods we use the proposed methods to illustrate the effect of the strength and spatial correlation of the channels on the shape of the rate region

implementing the han kobayashi scheme using low density parity check codes over gaussian interference channels we focus on gaussian interference channels gics and study the han kobayashi coding strategy for the two user case with the objective of designing implementable explicit channel codes specifically low density parity check codes are adopted for use over the channel their benefits are studied and suitable codes are designed iterative joint decoding is used at the receivers where independent and identically distributed channel adapters are used to prove that log likelihood ratios exchanged among the nodes of the tanner graph enjoy symmetry when bpsk or qpsk with gray coding is employed this property is exploited in the proposed code optimization algorithm adopting a random perturbation technique code optimization and convergence threshold computations are carried out for different gics employing finite constellations by tracking the average mutual information furthermore stability conditions for the admissible degree distributions under strong and weak interference levels are determined via examples it is observed that the optimized codes using bpsk or qpsk with gray coding operate close to the capacity boundary for strong interference for the case of weak interference it is shown that nontrivial rate pairs are achievable via the newly designed codes which are not possible by single user codes with time sharing performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions where for one instance the results are compared with those of some structured designs

capacity bounds for the gaussian interference channel the capacity region of the two user gaussian interference channel ic is studied three classes of channels are considered weak one sided and mixed gaussian ics for the weak gaussian ic a new outer bound on the capacity region is obtained that outperforms previously known outer bounds the sum capacity for a certain range of channel parameters is derived for this range it is proved that using gaussian codebooks and treating interference as noise are optimal it is shown that when gaussian codebooks are used the full han kobayashi achievable rate region can be obtained by using the naive han kobayashi achievable scheme over three frequency bands equivalently three subspaces for the one sided gaussian ic an alternative proof for the sato s outer bound is presented we derive the full han kobayashi achievable rate region when gaussian codebooks are utilized for the mixed gaussian ic a new outer bound is obtained that outperforms previously known outer bounds for this case the sum capacity for the entire range of channel parameters is derived it is proved that the full han kobayashi achievable rate region using gaussian codebooks is equivalent to that of the one sided gaussian ic for a particular range of channel parameters

on various solutions of the coupled kp equation the coupled kp ckp equation possesses n soliton solutions with many more degrees of freedom than the solitons for the usual kp equation have in comparison ckp solutions can therefore be expected to model far more complex interactions than their kp counterparts in this paper we present some typical solutions for the ckp system and for some of its reductions a complex coupled kdv equation and a coupled boussinesq equation and we analyse their interaction and asymptotic properties

complete eigenfunctions of linearized integrable equations expanded around a soliton solution complete eigenfunctions for an integrable equation linearized around a soliton solution are the key to the development of a direct soliton perturbation theory in this article we explicitly construct such eigenfunctions for a large class of integrable equations including the kdv nls and mkdv hierarchies we establish the striking result that the linearization operators of all equations in the same integrable hierarchy share the same complete set of eigenfunctions furthermore these eigenfunctions are precisely the squared eigenfunctions of the associated eigenvalue problem the key step in our derivation is to show that the linearization operator of an integrable equation can be factored into a function of the integro differential operator which generates the integrable equation and the linearization operator of the lowest order integrable equation in the same hierarchy we also obtain similar results for the adjoint linearization operator of an integrable equation even though our analysis is conducted only for the kdv nls and mkdv hierarchies similar results are expected for other integrable hierarchies as well we further explicitly present the complete eigenfunctions for the kdv nls and mkdv hierarchy equations and give their inner products thus they can be readily used to develop a direct soliton perturbation theory for any of those hierarchy equations

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

degrees of freedom of interference channels with comp transmission and reception we study the degrees of freedom dof of the k user interference channel with coordinated multipoint comp transmission and reception each message is jointly transmitted by m t successive transmitters and is jointly received by m r successive receivers we refer to this channel as the comp channel with a transmit cooperation order of m t and receive cooperation order of m r since the channel has a total of k transmit antennas and k receive antennas the maximum possible dof is equal to k we show that the comp channel has k dof if and only if m t m r geq k 1 the key idea is that the zero forcing of the interference corresponding to the i rm th message at the decoder of the j rm th message where j ne i can be viewed as a shared responsibility between the m t transmitters carrying the i rm th message and the m r receivers decoding the j rm th message for the general case we derive an outer bound that states that the dof is bounded above by left lceil k m t m r 2 2 right rceil for the special case with only comp transmission i e m r 1 we propose a scheme that can achieve k m t 1 2 dof for all k and conjecture that the result holds true for all k in the proposed coding scheme the m t transmitters carrying each message are used to cancel the interference introduced by this message at the first m t 1 receivers thereby allowing each of these receivers to enjoy 1 dof and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space the achievability proofs are based on the notion of algebraic independence from algebraic geometry

the approximate capacity region of the symmetric k user gaussian interference channel with strong interference the symmetric k user interference channel ic is studied with the goal of characterizing its capacity region in the strong interference regime within a constant gap the achievable rate region of a scheme combining rate splitting at the transmitters and interference alignment and successive decoding computation at the receivers is derived next it is shown that this scheme achieves the so called greedy max corner points of the capacity region within a constant gap by combining this result with previous results by ordentlich et al on the sum capacity of the symmetric ic a constant gap characterization of the capacity region for the strong interference regime is obtained this leads to the first approximate characterization of the capacity region of the symmetric k user ic furthermore a new scheme that achieves the sum capacity of the channel in the strong interference regime within a constant gap is also proposed and the corresponding gap is calculated the advantage of the new scheme is that it leads to a characterization within a constant gap without leaving an outage set contrary to the scheme by ordentlich et al

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

simple strong glass forming models mean field solution with activation we introduce simple models inspired by previous models for froths and covalent glasses with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems these models are also a generalization of backgammon or urn models to a non constant number of particles where entropic barriers are replaced by energy barriers allowing for the existence of activated processes we formulate a mean field version of the models which keeps most of the features of the finite dimensional ones and solve analytically the out of equilibrium dynamics in the low temperature regime where activation plays an essential role

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

outer bounds on the capacity of gaussian interference channels two outer bounds on the capacity region of the two user gaussian interference channel ifc are derived the idea of the first bound is to let a genie give each receiver just enough information to decode both messages this bound unifies and improves the best known outer bounds of sato and carleial furthermore the bound extends to discrete memoryless ifcs and is shown to be equivalent to another bound of carleial the second bound follows directly from existing results of costa and sato and possesses certain optimality properties for weak interference

the generalized degrees of freedom region of the mimo interference channel and its achievability the generalized degrees of freedom gdof region of the mimo gaussian interference channel ic is obtained for the general case of an arbitrary number of antennas at each node and where the signal to noise ratios snrs and interference to noise ratios vary with arbitrary exponents to a nominal snr the gdof optimal coding scheme involves message splitting and partial interference decoding and consists of linear gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal space and signal level interference alignment the admissible degree of freedom dof splits between the private and common messages are also specified a study of the gdof region reveals various insights through the joint dependence of optimal interference management techniques at high snr on the snr exponents and the numbers of antennas at the four terminals for instance it reveals that unlike in the scalar ic treating interference as noise is not always gdof optimal even in the very weak interference regime moreover while the dof optimal strategy that relies just on transmit receive zero forcing beamforming and time sharing is not gdof optimal and thus has an unbounded gap to capacity the precise characterization of the very strong interference regime where single user dof performance can be achieved simultaneously for both users depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single input single output case for asymmetric numbers of antennas at the four nodes the shape of the symmetric gdof curve can be a distorted w curve to the extent that for certain multiple input multiple output ics it is a v curve

gaussian z interference channel with a relay link achievability region and asymptotic sum capacity this paper studies a gaussian z interference channel with a rate limited digital relay link from one receiver to another achievable rate regions are derived based on a combination of a han kobayashi common private power splitting technique and either a compress and forward relay strategy or a decode and forward strategy for interference subtraction at the other end for the gaussian z interference channel with a digital link from the interference free receiver to the interfered receiver the capacity region is established in the strong interference regime an achievable rate region is established in the weak interference regime in the weak interference regime the decode and forward strategy is shown to be asymptotically sum capacity achieving in the high signal to noise ratio and high interference to noise ratio limit in this case each relay bit asymptotically improves the sum capacity by one bit for the gaussian z interference channel with a digital link from the interfered receiver to the interference free receiver the capacity region is established in the strong interference regime achievable rate regions are established in the moderately strong and weak interference regimes in addition the asymptotic sum capacity is established in the limit of a large relay link rate in this case the sum capacity improvement due to the digital link is bounded by half a bit when the interference link is weaker than a certain threshold but the sum capacity improvement becomes unbounded when the interference link is strong

on the optimality of treating interference as noise it is shown that in the k user interference channel if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all values in decibel scale then the simple scheme of using point to point gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise tin at every receiver in short tin scheme achieves all points in the capacity region to within a constant gap the generalized degrees of freedom gdof region under this condition is a polyhedron which is shown to be fully achieved by the same scheme without the need for time sharing the results are proved by first deriving a polyhedral relaxation of the gdof region achieved by tin and then providing a dual characterization of this polyhedral region via the use of potential functions and finally proving the optimality of this region in the desired regime

on the soliton solutions of the two dimensional toda lattice the two dimensional toda lattice 2dtl is a well known 2 1 dimensional integrable system that admits a large class of line soliton solutions we classify these soliton solutions by exploiting the structure of the casoratian expression for its tau function in general these solutions consist of unequal numbers of incoming and outgoing line solitons we classify the incoming and outgoing line solitons based on asymptotic analysis of the tau function of the 2dtl as the discrete variable tends to infinity we also identify various subclasses of solutions and characterize some of them in terms of the amplitudes and directions of the interacting solitons as a special case we obtain the reduction in the soliton solutions of the one dimensional toda lattice throughout we point out the similarities with and the differences from the corresponding results for the kadomtsev petviashvili equation

a discrete variational identity on semi direct sums of lie algebras the discrete variational identity under general bilinear forms on semi direct sums of lie algebras is established the constant involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation an application of the resulting variational identity to a class of semi direct sums of lie algebras in the volterra lattice case furnishes hamiltonian structures for the associated integrable couplings of the volterra lattice hierarchy

numerical algorithms for the direct spectral transform with applications to nonlinear schrodinger type systems we implement two different algorithms for computing numerically the direct zakharov shabat eigenvalue problem on the infinite line the first algorithm replaces the potential in the eigenvalue problem by a piecewise constant approximation which allows one to solve analytically the corresponding ordinary differential equation the resulting algorithm is of second order in the step size the second algorithm uses the fourth order runge kutta method we test and compare the performance of these two algorithms on three exactly solvable potentials we find that even though the runge kutta method is of higher order this extra accuracy can be lost because of the additional dependence of its numerical error on the eigenvalue this limits the usefulness of the runge kutta algorithm to a region inside the unit circle around the origin in the complex plane of the eigenvalues for the computation of the continuous spectrum density this limitation is particularly severe as revealed by the spectral decomposition of thel2 norm of a solution to the nonlinear schrodinger equation we show that no such limitations exist for the piecewise constant algorithm in particular this scheme converges uniformly for both continuous and discrete spectrum components

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

high accuracy implicit variable mesh methods for numerical study of special types of fourth order non linear parabolic equations in this paper we propose a new implicit high order two level finite difference method of o k 2 k h l h l 3 for the solution of special type of 1d fourth order non linear parabolic partial differential equation of the form u x x x x 2 u x x t u t t f x t u u x u x x u t u x x x u x t a 0 and hl 0 are the mesh sizes in time and space coordinates respectively the third order variable mesh methods proposed are based on only three spatial grid points xl xl 1 meaning that no fictitious points are required for incorporating the boundary conditions we discuss how our formulation is able to handle linear singular problem the proposed two level finite difference method is shown to be unconditionally stable for a model linear problem we applied the proposed methods to find the numerical solution of more complex fourth order non linear equations like second order benjamin ono equation and the good boussinesq equation it is evident from the numerical experiments that the numerical results agree well with the exact solutions hence demonstrating the efficiency of the methods derived

transmit optimization with improper gaussian signaling for interference channels this paper studies the achievable rates of gaussian interference channels with additive white gaussian noise awgn when improper or circularly asymmetric complex gaussian signaling is applied for the gaussian multiple input multiple output interference channel mimo ic with the interference treated as gaussian noise we show that the user s achievable rate can be expressed as a summation of the rate achievable by the conventional proper or circularly symmetric complex gaussian signaling in terms of the users transmit covariance matrices and an additional term which is a function of both the users transmit covariance and pseudo covariance matrices the additional degrees of freedom in the pseudo covariance matrix which is conventionally set to be zero for the case of proper gaussian signaling provide an opportunity to further improve the achievable rates of gaussian mimo ics by employing improper gaussian signaling to this end this paper proposes widely linear precoding which efficiently maps proper information bearing signals to improper transmitted signals at each transmitter for any given pair of transmit covariance and pseudo covariance matrices in particular for the case of two user gaussian single input single output interference channel siso ic we propose a joint covariance and pseudo covariance optimization algorithm with improper gaussian signaling to achieve the pareto optimal rates by utilizing the separable structure of the achievable rate expression an alternative algorithm with separate covariance and pseudo covariance optimization is also proposed which guarantees the rate improvement over conventional proper gaussian signaling

successive interference mitigation in multiuser mimo channels motivated by the work of dahrouj and yu in applying the han kobayashi transmission strategy for mitigating the intercell interference in a multi cell multi user multiple input single output interference network miso in this paper considers splitting messages into private and common parts in a multi cell multi user mimo in specifically the covariances of the private messages and common messages are designed to optimize either the sum rate or the minimal rate the common messages and private messages are decoded in sequence using successive decoding this paper shows how these difficult optimization problems can be adequately solved by means of d c d ifference of c oncave functions optimization over a simple convex set numerical and simulation results also reveal the great advantage of our proposed solutions for various types of ins in particular the proposed solutions are shown to outperform the algorithm developed by dahrouj and yu for the simpler case of the miso in

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

interference alignment and the generalized degrees of freedom of the x channel we explore the capacity and generalized degrees of freedom gdof of the two user gaussian x channel i e a generalization of the two user interference channel where there is an independent message from each transmitter to each receiver there are three main results in this paper first we characterize the sum capacity of the deterministic x channel under a symmetric setting second we characterize the gdof of the gaussian x channel under a similar symmetric model third we extend the sum capacity characterization previously obtained for the gaussian interference channel in the noisy interference regime to the gaussian x channel specifically we show that the gaussian x channel has the same sum capacity as the underlying gaussian interference channel in this regime

safe and effective importance sampling abstract we present two improvements on the technique of importance sampling first we show that importance sampling from a mixture of densities using those densities as control variates results in a useful upper bound on the asymptotic variance that bound is a small multiple of the asymptotic variance of importance sampling from the best single component density this allows one to benefit from the great variance reductions obtainable by importance sampling while protecting against the equally great variance increases that might take the practitioner by surprise the second improvement is to show how importance sampling from two or more densities can be used to approach a zero sampling variance even for integrands that take both positive and negative values

an extremal inequality motivated by multiterminal information theoretic problems we prove a new extremal inequality motivated by the vector gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems as a corollary this inequality yields a generalization of the classical entropy power inequality epi as another corollary this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables

on limiting characterizations of memoryless multiuser capacity regions the restriction to gaussian inputs in the limiting expression for the capacity regions of memoryless gaussian interference and multiple access channels is shown to fall short of achieving capacity even if the inputs are allowed to be dependent and nonstationary in addition the equality between the limiting and the single letter characterizations of memoryless multiple access channel capacity is established directly without recourse to independent coding theorems

outage analysis of block fading gaussian interference channels this paper considers the asymptotic behavior of the outage probability of a two source block fading single antenna gaussian interference channel in the high snr regime by means of the diversity multiplexing tradeoff a general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated this asymmetric scenario allows to analyze networks with mixed interference i e when different sources are at different distance from their intended destination that are not possible under the commonly used symmetric assumption inner and outer bounds for the diversity are derived the outer bound is based on the recent to within one bit capacity result of etkin for the unfaded gaussian channel and is a re derivation of a known bound for which an error is pointed out the inner bound is based on the han and kobayashi achievable region both without rate splitting and with a rate spitting inspired by the to within one bit capacity result an analytical comparison of the diversity upper and lower bounds for a general channel seems difficult by numerical evaluations the two bounds are shown to coincide for a fairly large set of channel parameters

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

noisy interference sum rate capacity for vector gaussian interference channels new sufficient conditions for a vector gaussian interference channel to achieve the sum rate capacity by treating interference as noise are derived which generalize and extend the existing results more concise conditions for multiple input single output and single input multiple output scenarios are obtained

soliton like behavior in automata abstract we propose a new kind of automaton that uses newly computed site values as soon as they are available we call them filter automata fa they are analogous to infinite impulse response iir digital filters whereas the usual cellular automata ca correspond to finite impulse response fir digital filters it is shown that as a class the fa s are equivalent to ca s in the sense that the same array of space generation values can be produced they must be generated in a different order however a particular class of irreversible totalistic fa s are described that support a profusion of persistent structures that move at different speeds and these particle like patterns collide in nondestructive ways they often pass through one another with nothing more than a phase jump much like the solitons that arise in the solution of certain nonlinear differential equations histograms of speed displacement and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide we then present statistics for neighborhood radii 2 to 9 which show that collisions which preserve the identity of particles are very common

a method to compute statistics of large noise induced perturbations of nonlinear schrodinger solitons we demonstrate in detail the application of importance sampling to the numerical simulation of large noise induced perturbations in soliton based optical transmission systems governed by the nonlinear schrodinger equation the method allows one to concentrate numerical monte carlo simulations around the noise realizations that are most likely to produce the large pulse deformations connected with errors and yields computational speedups of several orders of magnitude over standard monte carlo simulations we demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude frequency and timing fluctuations in a prototypical soliton based communication system

soft decoding based strategies for relay and interference channels analysis and achievable rates using ldpc codes we provide a rigorous mathematical analysis of two communication strategies soft decode and forward soft df for relay channels and soft partial interference cancelation soft ic for interference channels both strategies involve soft estimation which assists the decoding process we consider ldpc codes not because of their practical benefits but because of their analytic tractability which enables an asymptotic analysis similar to random coding methods of information theory unlike some works on the closely related demodulate and forward we assume non memoryless code structure aware estimation with soft df we develop simultaneous density evolution to bound the decoding error probability at the destination this result applies to erasure relay channels in one variant of soft df the relay applies wyner ziv coding to enhance its communication with the destination borrowing from compress and forward to analyze soft ic we adapt existing techniques for iterative multiuser detection and focus on binary input additive white gaussian noise interference channels we prove that optimal point to point codes are unsuitable for soft ic as well as for all strategies that apply partial decoding to improve upon single user detection and multiuser detection including han kobayashi

monotonic optimization framework for the two user miso interference channel resource allocation and transmit optimization for the multiple antenna gaussian interference channel are important but difficult problems the spatial degrees of freedom can be exploited to avoid align or utilize the interference in recent literature the upper boundary of the achievable rate region has been characterized however the resulting programming problems for finding the sum rate proportional fair and minimax egalitarian operating points are non linear and non convex in this paper we develop a non convex optimization framework based on monotonic optimization by outer polyblock approximation first the objective functions are represented in terms of differences of monotonic increasing functions next the problems are reformulated as maximization of increasing functions over normal constraint sets finally the idea to approximate the constraint set by outer polyblocks is explained and the corresponding algorithm is derived numerical examples illustrate the advantages of the proposed framework compared to an exhaustive grid search approach

spider web solutions of the coupled kp equation the coupled kadomtsev petviashvili ckp equation possesses n soliton solutions with more parametric freedom than the solitons of the usual kp equation its solutions can therefore be expected to model far more complex interactions than their kp counterparts the existence of web like structures on a finite scale for ckp solutions isojima s willox r and satsuma j 2002 j phys a math gen 35 6893 6909 is a manifestation of this greater freedom in this paper we propose a new method to analyse the behaviour of solitons which we demonstrate in some examples in addition we discuss essentially three body collisions described by a two soliton solution of the ckp equation

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

design of low density parity check codes for modulation and detection a coding and modulation technique is studied where the coded bits of an irregular low density parity check ldpc code are passed directly to a modulator at the receiver the variable nodes of the ldpc decoder graph are connected to detector nodes and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder the code is optimized by performing a curve fitting on extrinsic information transfer charts design examples are given for additive white gaussian noise channels as well as multiple input multiple output mimo fading channels where the receiver but not the transmitter knows the channel for the mimo channels the technique operates within 1 25 db of capacity for various antenna configurations and thereby outperforms a scheme employing a parallel concatenated turbo code by wide margins when there are more transmit than receive antennas

capacity approaching bandwidth efficient coded modulation schemes based on low density parity check codes we design multilevel coding mlc and bit interleaved coded modulation bicm schemes based on low density parity check ldpc codes the analysis and optimization of the ldpc component codes for the mlc and bicm schemes are complicated because in general the equivalent binary input component channels are not necessarily symmetric to overcome this obstacle we deploy two different approaches one based on independent and identically distributed i i d channel adapters and the other based on coset codes by incorporating i i d channel adapters we can force the symmetry of each binary input component channel by considering coset codes we extend the concentration theorem based on previous work by richardson et al see ibid vol 47 p 599 618 feb 2001 and kavc spl caron ic spl acute et al see ibid vol 49 p 1636 52 july 2003 we also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior next we jointly optimize the code rates and degree distribution pairs of the ldpc component codes for the mlc scheme the optimized irregular ldpc codes at each level of mlc with multistage decoding msd are able to perform well at signal to noise ratios snr very close to the capacity of the additive white gaussian noise awgn channel we also show that the optimized bicm scheme can approach the parallel independent decoding pid capacity as closely as does the mlc pid scheme simulations with very large codeword length verify the accuracy of the analytical results finally we compare the simulated performance of these coded modulation schemes at finite codeword lengths and consider the results from the perspective of a random coding exponent analysis

on a family of solutions of the kadomtsev petviashvili equation which also satisfy the toda lattice hierarchy we describe the interaction pattern in the x y plane for a family of soliton solutions of the kadomtsev petviashvili kp equation the solutions considered also satisfy the finite toda lattice hierarchy we determine completely their asymptotic patterns for y and we show that all the solutions except the 1 soliton solution are of resonant type consisting of arbitrary numbers of line solitons in both asymptotics that is arbitrary n incoming solitons for y interact to form arbitrary n outgoing solitons for y we also discuss the interaction process of those solitons and show that the resonant interaction creates a web like structure having n 1 n 1 holes

statistics of soliton bearing systems with additive noise we present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise even though the noise is weak we are interested in probabilities of large fluctuations generally non gaussian which are beyond perturbation theory our method is a development of the instanton formalism method of optimal fluctuation based on a saddle point approximation in the path integral we first