symmetric capacity of the gaussian interference channel with an out of band relay to within 1 15 bits this paper studies the gaussian interference channel ic with a relay which transmits and receives in a band that is orthogonal to the ic the channel associated with the relay is thus an out of band relay channel obrc the focus is on a symmetric channel model in order to assess the fundamental impact of the obrc on the signal interaction of the ic in the simplest possible setting first the linear deterministic model is investigated and the sum capacity of this channel is established for all possible channel parameters in particular it is observed that the impact of obrc as its links get stronger is similar to that of output feedback for the ic the insights obtained from the deterministic model are then used to design achievable schemes for the gaussian model the interference links are classified as extremely strong very strong strong moderate weak and very weak for strong and moderate interference separate encoding is near optimal for very strong and extremely strong interference the interference links provide side information to the destinations which can help the transmission through the obrc for weak or very weak interference an extension of the han kobayashi scheme for the ic is utilized where the messages are split into common and private to achieve higher rates it is beneficial to further split the common message into two parts and the obrc plays an important role in decoding the common message it is shown that our strategy achieves the symmetric capacity to within 1 14625 bits per channel use with duplexing factor 0 5 and 1 27125 bits per channel use for arbitrary duplexing factors for all channel parameters an important observation from the constant gap result is that strong interference can be beneficial with the presence of an obr

strongly self absorbing c algebras say that a separable unital c algebra v c is strongly self absorbing if there exists an isomorphism v such that lx ai e approximately unitarily equivalent homomorphisms we study this class of algebras which includes the cuntz algebras 2 ooo the uhf algebras of infinite type the jiang su algebra z and tensor products of 00 with uhf algebras of infinite type given a strongly self absorbing c algebra v we characterise when a separable c algebra absorbs v tensorially i e is p stable and prove closure properties for the class of separable testable c algebras finally we compute the possible if groups and prove a number of classification results which suggest that the examples listed above are the only strongly self absorbing c algebras

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

lasalle type theorem and its applications to infinite horizon optimal control of discrete time nonlinear stochastic systems based on discrete martingale theory the lasalle type theorem for general discrete time stochastic systems is obtained and the almost sure stability is in turn discussed as applications infinite horizon nonlinear optimal regulator is investigated and a dynamical programming equation called the hamilton jacobi bellman equation is also derived for discrete time nonlinear stochastic optimal control

on the symmetric k user interference channels with limited feedback in this paper we develop achievability schemes for symmetric k user interference channels with a rate limited feedback from each receiver to the corresponding transmitter we study this problem under two different channel models the linear deterministic model and the gaussian model for the deterministic model the proposed scheme achieves a symmetric rate that is the minimum of the symmetric capacity with infinite feedback and the sum of the symmetric capacity without feedback and the symmetric amount of feedback for the gaussian interference channel we use lattice codes to propose a transmission strategy that incorporates the techniques of han kobayashi message splitting interference decoding and decode and forward this strategy achieves a symmetric rate which is within a constant number of bits to the minimum of the symmetric capacity with infinite feedback and the sum of the symmetric capacity without feedback and the amount of symmetric feedback this constant is obtained as a function of the number of users k we note that for the special case of gaussian ic with k 2 our proposed achievability scheme results in a symmetric rate that is within at most 21 085 bits s hz of the outer bound which is the first constant gap bound despite the constant gap claim in 1 the symmetric achievable rate is used to characterize the achievable generalized degrees of freedom which exhibits a gradual increase from no feedback to perfect feedback in the presence of feedback links with limited capacity

an integrated optimal control algorithm for discrete time nonlinear stochastic system consider a discrete time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable an iterative procedure based on the linear quadratic gaussian optimal control model is developed for solving the optimal control of this stochastic system the optimal state estimate provided by kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm the iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete time nonlinear system despite model reality differences when the convergence is achieved an illustrative example is solved using the method proposed the results obtained show the effectiveness of the algorithm proposed

the degrees of freedom region of the mimo interference channel with shannon feedback the two user multiple input multiple output mimo fast fading interference channel ic with an arbitrary number of antennas at each of the four terminals is studied under the settings of shannon feedback and output feedback wherein channel matrices and outputs or just the channel outputs respectively are available to the transmitters with a delay while for most numbers of antennas at the four terminals the degree of freedom dof regions with shannon feedback are equal to that with just delayed channel state information csit it is shown that for the rest of the mimo ics the dof region with shannon feedback is strictly larger than the dof region with just delayed csit to realize these dof gains with shannon feedback a new interference alignment scheme is obtained wherein transmitter cooperation made possible by output feedback in addition to delayed csit is employed to effect a more efficient form of interference alignment than is feasible with previously known schemes that use just delayed csit the dof region for output only feedback is also obtained for all but a class of mimo ics that satisfy one of two inequalities involving the numbers of antennas moreover the dof region for shannon feedback is shown to be applicable to two limited shannon feedback settings where the transmitters have knowledge only of certain channel matrices and certain outputs with delay

on the symmetric feedback capacity of the k user cyclic z interference channel the k user cyclic z interference channel models a situation in which the kth transmitter causes interference only to the k 1 th receiver in a cyclic manner e g the first transmitter causes interference only to the kth receiver the impact of noiseless feedback on the capacity of this channel is studied by focusing on the gaussian cyclic z interference channel to this end the symmetric feedback capacity of the linear shift deterministic cyclic z interference channel is completely characterized for all interference regimes using insights from the linear deterministic channel model the symmetric feedback capacity of the gaussian cyclic z interference channel is characterized up to within a constant number of bits as a byproduct of the constant gap result the symmetric generalized degrees of freedom with feedback for the gaussian cyclic z interference channel are also characterized these results highlight that the symmetric feedback capacities for both linear and gaussian channel models are in general functions of k the number of users furthermore the capacity gain obtained due to feedback decreases as k increases

dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems an algorithm for solving nonlinear discrete time optimal control problems with model reality differences is presented the technique uses dynamic integrated system optimization and parameter estimation disope which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure a version of the algorithm with a linear quadratic model based problem implemented in the c programming language is developed and applied to illustrative simulation examples an analysis of the optimality and convergence properties of the algorithm is also presented

the two user causal cognitive interference channel novel outer bounds and constant gap result for the symmetric gaussian noise channel in weak interference this paper studies the two user causal cognitive interference channel ccic where two transmitters aim to communicate independent messages to two different receivers via a common channel one source referred to as the cognitive is capable of overhearing the other source referred to as the primary through a noisy in band link and thus can assist in sending the primary s data the authors of this paper recently characterized to within a constant gap the capacity of the symmetric gaussian ccic in 1 the strong interference regime and 2 for a subset of the weak interference regime when the cooperation link is larger than a given threshold this paper characterizes to within a constant gap the capacity for the symmetric gaussian ccic in the regime that was still open to this end two novel outer bounds of the types 2 r mathsf p r mathsf c and r mathsf p 2 r mathsf c are derived for the class of injective semideterministic ccics where the noises at the different source destination pairs are independent these outer bounds as well as an achievable rate region based on gelfand pinsker binning superposition coding and simultaneous decoding at the receivers are then specialized to the gaussian noise case it is shown that the novel outer bounds are necessary to characterize the capacity within a constant gap when the cooperation link is weaker than the direct links that is in this regime unilateral cooperation leaves some system resources underutilized

approximate capacity of fast fading interference channels with no instantaneous csit we develop a characterization of fading models which assigns a number called logarithmic jensen s gap to a given fading model we show that as a consequence of a finite logarithmic jensen s gap an approximate capacity region can be obtained for fast fading interference channels ff ics for several scenarios we illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic jensen s gap first for an ff ic with neither feedback nor instantaneous channel state information at transmitter csit if the fading distribution has finite logarithmic jensen s gap we show that a rate splitting scheme based on the average interference to noise ratio can achieve its approximate capacity second we show that a similar scheme can achieve the approximate capacity of ff ic with feedback and delayed csit if the fading distribution has finite logarithmic jensen s gap third when this condition holds we show that point to point codes can achieve approximate capacity for a class of ff ics with feedback we prove that the logarithmic jensen s gap is finite for common fading models including rayleigh and nakagami fading thereby obtaining the approximate capacity region of ff ic with these fading models

on the capacity of symmetric m user gaussian interference channels with feedback a general time varying feedback coding scheme is proposed for m user fully connected symmetric gaussian interference channels based on the analysis of the general coding scheme we prove a theorem which gives a criterion for designing good time varying feedback codes for gaussian interference channels the proposed scheme improves the suh tse and kramer inner bounds of the channel capacity for the cases of weak and not very strong interference when m 2 this capacity improvement is more significant when the signal to noise ratio snr is not very high in addition our coding scheme can be proved mathematically and numerically to outperform the kramer code for m geq 2 when the snr is equal to the interference to noise ratio inr besides the generalized degrees of freedom gdof of our proposed coding scheme can be proved to be optimal in the all network situations very weak weak strong very strong for any m the numerical results show that our coding scheme can attain better performance than the suh tse coding scheme for m 2 or the mohajer tandon poor lattice coding scheme for m 2 furthermore the simplicity of the encoding decoding algorithms is another strong point of our proposed coding scheme compared with the suh tse coding scheme when m 2 and the mohajer tandon poor lattice coding scheme when m 2 more importantly our results show that an optimal coding scheme for the symmetric gaussian interference channels with feedback can be achieved by only using marginal posterior distributions under a better cooperation strategy between transmitters

nuclear dimension and mathcal z stability simple separable unital monotracial and nuclear mathrm c algebras are shown to have finite nuclear dimension whenever they absorb the jiang su algebra mathcal z tensorially this completes the proof of the toms winter conjecture in the unique trace case

interference and x networks with noisy cooperation and feedback the gaussian k user interference and m times k x channels are investigated with no instantaneous channel state information at transmitters csit first it is assumed that the csi is fed back to all nodes after a finite delay delayed csit and furthermore the transmitters operate in full duplex mode i e they can transmit and receive simultaneously achievable results on the degrees of freedom dofs of these channels under the above assumption are obtained it is observed that in contrast with no csit and full csit models when csit is delayed the achievable dofs for both channels with the full duplex transmitter cooperation are greater than the available achievable results on their dof without transmitter cooperation then k user interference and k times k x channels are considered with output feedback wherein the channel output of each receiver is causally fed back to its corresponding transmitter our achievable results with output feedback demonstrate strict dof improvements over those with the full duplex delayed csit when k 5 in the k user interference channel and k 2 in the k times k x channel next the combination of delayed csit and output feedback known as shannon feedback is studied and strictly higher dofs compared with the output feedback model are achieved in the k user interference channel when k 5 or k 6 and in the k times k x channel when k 2

a rokhlin type theorem for simple c algebras of finite nuclear dimension abstract we study z actions on unital simple separable stably finite c algebras of finite nuclear dimension assuming that the extreme boundary of the trace space is compact and finite dimensional and that the induced action on the trace space is trivial we show that strongly outer z actions have finite rokhlin dimension in the sense of hirshberg winter and zacharias

an achievable rate region for the multiple access channel with feedback an achievable rate region r 1 leq i x 1 y x 2 u r 2 leq i x 2 y x 1 u r 1 r 2 leq i x 1 x 2 y where p u x l x 2 y p u p x l u p x 2 u p y x l x 2 is established for the multiple access channel with feedback time sharing of these achievable rates yields the rate region of this paper this region generally exceeds the achievable rate region without feedback and exceeds the rate point found by gaarder and wolf for the binary erasure multiple access channel with feedback the presence of feedback allows the independent transmitters to understand each other s intended transmissions before the receiver has sufficient information to achieve the desired decoding this allows the transmitters to cooperate in the transmission of information that resolves the residual uncertainty of the receiver at the same time independent information from the transmitters is superimposed on the cooperative correction information the proof involves list codes and block markov encoding

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

equivariant kirchberg phillips type absorption for amenable group actions we show an equivariant kirchberg phillips type absorption theorem for pointwise outer actions of discrete amenable groups on kirchberg algebras with respect to natural model actions on the cuntz algebras mathcal o infty and mathcal o 2 this generalizes results known for finite groups and poly mathbb z groups the model actions are shown to be determined up to strong cocycle conjugacy by natural abstract properties which are verified for some examples of actions arising from tensorial shifts we also show the following homotopy rigidity result which may be understood as a precursor to a general kirchberg phillips type classification theory if two outer actions of an amenable group on a unital kirchberg algebra are equivariantly homotopy equivalent then they are conjugate this marks the first c dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups

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

covering dimension for nuclear c algebras we introduce the completely positive rank a notion of covering dimension for nuclear c algebras and analyze some of its properties the completely positive rank behaves nicely with respect to direct sums quotients ideals and inductive limits for abelian c algebras it coincides with covering dimension of the spectrum and there are similar results for continuous trace algebras as it turns out a c algebra is zero dimensional precisely if it is af we consider various examples particularly of one dimensional c algebras like the irrational rotation algebras the bunce deddens algebras or blackadar s simple unital projectionless c algebra finally we compare the completely positive rank to other concepts of noncommutative covering dimension such as stable or real rank

reinforcement learning for adaptive optimal control of unknown continuous time nonlinear systems with input constraints in this paper an adaptive reinforcement learning based solution is developed for the infinite horizon optimal control problem of constrained input continuous time nonlinear systems in the presence of nonlinearities with unknown structures two different types of neural networks nns are employed to approximate the hamilton jacobi bellman equation that is an recurrent nn is constructed to identify the unknown dynamical system and two feedforward nns are used as the actor and the critic to approximate the optimal control and the optimal cost respectively based on this framework the action nn and the critic nn are tuned simultaneously without the requirement for the knowledge of system drift dynamics moreover by using lyapunov s direct method the weights of the action nn and the critic nn are guaranteed to be uniformly ultimately bounded while keeping the closed loop system stable to demonstrate the effectiveness of the present approach simulation results are illustrated

on the classification problem for nuclear c algebras we exhibit a counterexample to elliott s classification conjecture for simple separable and nuclear c algebras whose construction is elementary and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves the consequences for the program to classify nuclear c algebras are far reaching one has among other things that existing results on the classification of simple unital ah algebras via the elliott invariant of k theoretic data are the best possible and that these cannot be improved by the addition of continuous homotopy invariant functors to the elliott invariant

dependence balance bounds for single output two way channels if in a transmission the inputs of a single output two way channel exhibit some interdependence this dependence must have been created during earlier transmissions the idea that no more dependence can be consumed than is produced is used to obtain new upper bounds to the capacity region of the discrete memoryless single output two way channel with these upper bounds it is shown that c e shannon 1961 inner bound region is the capacity region for channels in a certain class and the zhang berger schalkwijk upper bound 1986 for blackwell s multiplying channel is improved upon

computation in multicast networks function alignment and converse theorems the classical problem in a network coding theory considers communication over multicast networks multiple transmitters send independent messages to multiple receivers that decode the same set of messages in this paper computation over multicast networks is considered each receiver decodes an identical function of the original messages for a countably infinite class of two transmitter two receiver single hop linear deterministic networks the computation capacity is characterized for a linear function modulo 2 sum of bernoulli sources a new upper bound is derived that is tighter than cut set based and genie aided bounds a matching inner bound is established via the development of a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality the decomposition theorem provides a conceptually simple proof of achievability that generalizes to l transmitter l receiver networks

on the feedback capacity of the fully connected k user interference channel the symmetric k user interference channel with fully connected topology is considered in which 1 each receiver suffers interference from all other k 1 transmitters and 2 each transmitter has causal and noiseless feedback from its respective receiver the number of generalized degrees of freedom ssr gdof is characterized in terms of where the interference to noise ratio ssr inr is given by ssr inr ssr snr it is shown that the per user ssr gdof of this network is the same as that of the two user interference channel with feedback except for 1 for which existence of feedback does not help in terms of ssr gdof the coding scheme proposed for this network termed cooperative interference alignment is based on two key ingredients namely interference alignment and interference decoding moreover an approximate characterization is provided for the symmetric feedback capacity of the network when the ssr snr and ssr inr are far apart from each other

z stability and infinite tensor powers of c algebras we prove that under a mild hypothesis the infinite tensor power of a unital separable c algebra absorbs the jiang su algebra z tensorially combining this result with a recent theorem of winter we complete elliott s classification program for strongly self absorbing ash algebras we also give a succinct universal property for z in an ambient category so large that there are no unital separable c algebras without characters that are known to lie outside it this category contains the vast majority of our stock in trade separable amenable c algebras and is closed under passage to quotients and separable superalgebras in particular the category is closed under the formation of unital direct limits unital tensor products and crossed products by countable discrete groups finally we take a significant step toward the confirmation of elliott s classification conjecture for the c algebras of minimal diffeomorphisms

degrees of freedom of the rank deficient interference channel with feedback we study the sum degrees of freedom dofs of the k user rank deficient interference channel with feedback for the two user case we characterize the sum dof by developing an achievable scheme and deriving a matching upper bound for the three user case we develop a new achievable scheme which employs interference alignment to efficiently utilize the dimension of the received signal space in addition we derive an upper bound for the general k user case and show the tightness of the bound when the number of antennas at each node is sufficiently large as a consequence of these results we show that feedback can increase the dof when the number of antennas at each node is large enough as compared with the ranks of channel matrices this finding is in contrast to the full rank interference channel where feedback provides no dof gain the gain comes from using feedback to provide alternative signal paths thereby effectively increasing the ranks of desired channel matrices

the jiang su algebra revisited we give a number of new characterizations of the jiang su algebra z both intrinsic and extrinsic in terms of c algebraic dynamical topological and k theoretic conditions along the way we study divisibility properties of c algebras we give a precise characterization of those unital c algebras of stable rank one that admit a unital embedding of the dimensiondrop c algebra zn n 1 and we prove a cancellation theorem for the cuntz semigroup of c algebras of stable rank one

the rohlin property for automorphisms of the jiang su algebra abstract for projectionless c algebras absorbing the jiang su algebra tensorially we study a kind of the rohlin property for automorphisms we show that the crossed products obtained by automorphisms with this rohlin property also absorb the jiang su algebra tensorially under a mild technical condition on the c algebras in particular for the jiang su algebra we show the uniqueness up to outer conjugacy of the automorphism with this rohlin property

optimal control of a class of discrete continuous non linear systems decomposition and hierarchical structure a technique is derived for solving a non linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form the technique is designed to achieve the correct solution of the original non linear optimal control problem in spite of these simplifications a mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design and it is shown how the global problem can be decomposed into local sub system problems and a co ordinator within a hierarchical framework an analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non separable performance index

interference alignment from degrees of freedom to constant gap capacity approximations interference alignment is a key technique for communication scenarios with multiple interfering links in several such scenarios interference alignment was used to characterize the degrees of freedom of the channel however these degree of freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal to noise ratios snrs the aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap we focus on real time invariant frequency flat x channels the only known solutions achieving the degrees of freedom of this channel are either based on real interference alignment or on layer selection schemes neither of these solutions seems sufficient for a constant gap capacity approximation in this paper we propose a new communication scheme and show that it achieves the capacity of the gaussian x channel to within a constant gap to aid in this process we develop a novel deterministic channel model this deterministic model depends on the 1 2 log snr most significant bits of the channel coefficients rather than only the single most significant bit used in conventional deterministic models the proposed deterministic model admits a wider range of achievable schemes that can be translated to the gaussian channel for this deterministic model we find an approximately optimal communication scheme we then translate this scheme for the deterministic channel to the original gaussian x channel and show that it achieves capacity to within a constant gap this is the first constant gap result for a general fully connected network requiring interference alignment

achievability proof of some multiuser channel coding theorems using backward decoding new and simpler achievability proofs that are based on the backward decoding technique are presented for the well known coding theorems for the multiple access channel mac with perfect feedback and the degraded relay channel a class of macs with different generalized feedback signals is also considered and achievable rate regions that are larger than those previously presented in the literature are established

coding schemes and asymptotic capacity for the gaussian broadcast and interference channels with feedback a coding scheme is proposed for the memoryless gaussian broadcast channel with correlated noises and feedback for all noise correlations other than 1 the gap between the sum rate that the scheme achieves and the full cooperation bound vanishes as the signal to noise ratio tends to infinity when the correlation coefficient is 1 the gains afforded by feedback are unbounded and the prelog is doubled when the correlation coefficient is 1 we demonstrate a dichotomy that if the noise variances are equal then feedback is useless and otherwise feedback affords unbounded rate gains and doubles the prelog the unbounded feedback gains however require perfect noiseless feedback when the feedback links are noisy the feedback gains are bounded unless the feedback noise decays to zero sufficiently fast with the signal to noise ratio extensions to more receivers are also discussed as is the memoryless gaussian interference channel with feedback

when does output feedback enlarge the capacity of the interference channel in this paper the benefits of channel output feedback in the gaussian interference channel g ic are studied under the effect of additive gaussian noise using a linear deterministic ld model the signal to noise ratios snrs in the feedback links beyond which feedback plays a significant role in terms of increasing the individual rates or the sum rate are approximated the relevance of this work lies in the fact that it identifies the feedback snrs for which in any g ic one of the following statements is true a feedback does not enlarge the capacity region b feedback enlarges the capacity region and the sum rate is greater than the largest sum rate without feedback and c feedback enlarges the capacity region but no significant improvement is observed in the sum rate

euclidean information theory of networks in this paper we extend the information theoretic framework that was developed in earlier works to multi hop network settings for a given network we construct a novel deterministic model that quantifies the ability of the network in transmitting private and common messages across users based on this model we formulate a linear optimization problem that explores the throughput of a multi layer network thereby offering the optimal strategy as to what kind of common messages should be generated in the network to maximize the throughput with this deterministic model we also investigate the role of feedback for multi layer networks from which we identify a variety of scenarios in which feedback can improve transmission efficiency our results provide fundamental guidelines as to how to coordinate cooperation between users to enable efficient information exchanges across them

approximate capacity region for the symmetric gaussian interference channel with noisy feedback recent results have shown that feedback can significantly increase the capacity of interference networks this paper considers the impact of noise on such gains due to feedback in particular this paper considers the two user linear deterministic interference channel with noisy feedback as a stepping stone to characterize the approximate capacity region for the two user gaussian interference channel with noisy feedback first the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained it is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l it is found that excluding the regime 1 2 leq alpha leq 2 where alpha is the normalized interference level in which even full feedback does not increase symmetric capacity this threshold l is equal to the per user symmetric capacity without feedback one of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2r 1 r 2 and r 1 2r 2 these results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric gaussian interference channel with noisy feedback the outer bounds are shown to be at most 4 7 b s hz away from the achievable rate region as a corollary the generalized degrees of freedom region which approximates the capacity region of the symmetric gaussian interference channel at high snr is found

central sequence c algebras and tensorial absorption of the jiang su algebra we study properties of the central sequence algebra a a 0 of a c algebra a and we present an alternative approach to a recent result of matui and sato they prove that every unital separable simple nuclear c algebra whose trace simplex is nite dimensional tensorially absorbs the jiang su algebra if and only if it has the strict comparison property we extend their result to the case where the extreme boundary of the trace simplex is closed and of nite topological dimension we are also able to relax the assumption on the c algebra of having the strict com parison property to a weaker property that we call local weak comparison namely we prove that a unital separable simple nuclear c algebra whose trace simplex has nite dimensional closed extreme boundary tensorially absorbs the jiang su algebra if and only if it has the local weak comparison property we can also eliminate the nuclearity assumption if instead we assume the si property of matui and sato and moreover that each ii1 factor representation of the c algebra is a mcdu factor

on the maximum achievable sum rate with successive decoding in interference channels in this paper we investigate the maximum achievable sum rate of the two user gaussian interference channel with gaussian superposition coding and successive decoding we first examine an approximate deterministic formulation of the problem and introduce the complementarity conditions that capture the use of gaussian coding and successive decoding in the deterministic channel problem we find the constrained sum capacity and its achievable schemes with the minimum number of messages first in symmetric channels and then in general asymmetric channels we show that the constrained sum capacity oscillates as a function of the cross link gain parameters between the information theoretic sum capacity and the sum capacity with interference treated as noise furthermore we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum capacity the maximum achievable sum rate drops to that with interference treated as noise we provide two algorithms to translate the optimal schemes in the deterministic channel model to the gaussian channel model we also derive two upper bounds on the maximum achievable sum rate of the gaussian han kobayashi schemes which automatically upper bound the maximum achievable sum rate using successive decoding of gaussian codewords numerical evaluations show that similar to the deterministic channel results the maximum achievable sum rate with successive decoding in the gaussian channels oscillates between that with han kobayashi schemes and that with single message schemes