stochastic precoding for miso interference channels with channel mean feedback this work considers linear precoding strategies for multiple input single out miso interference channels with channel mean feedback at transmitters where the interference at each receiver is treated as additive noise the challenge here is that previous precoder designs with perfect channel state information csi at transmitters do not apply and new approaches are required based on the laplace transform order an altruistic non equilibrium strategy i e the stochastic zero forcing is first proposed under practical assumptions generalizing the traditional zero forcing which requires perfect csi interestingly the precoding matrices here are all rank one beamformers as in the traditional zero forcing the competitive use of the common physical media in miso interference channels is also formulated as a strategic noncooperative game in contrast to the perfect csi case with a unique rank one nash equilibrium with channel mean feedback the nash equilibria here are not necessarily rank one in general nevertheless when achieved by the rank one beamforming the equilibrium is unique and convenient for implementation accordingly the condition for beamforming to achieve the equilibrium is derived comparisons of the above two strategies reveal no overall dominance of one over the other thereby establishing stochastic zero forcing as an alternative to the nash equilibrium designs

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

mesh partitioning a multilevel balancing and refinement algorithm multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem they usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level in this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions we also present a formulation of the kernighan lin partition optimization algorithm which incorporates load balancing the resulting algorithm is tested against a different but related state of the art partitioner and shown to provide improved results

n k user interference channels degrees of freedom this paper analyzes the gains of opportunistic communication in multiuser interference channels consider a fully connected n user gaussian interference channel at each time instance only k n transmitters are allowed to be communicating with their respective receivers and the remaining n k transmitter receiver pairs remain inactive for finite n if the transmitters can acquire the instantaneous channel realizations and if all channel gains are bounded away from zero and infinity the seminal results on interference alignment establish that for any k arbitrary active pairs the total number of spatial degrees of freedom per orthogonal time and frequency domain is k 2 in dense networks n however as the size of the network increases it becomes less likely to sustain the bounding conditions on the channel gains by exploiting this fact we show that when n obeys certain scaling laws by opportunistically and dynamically selecting the k active pairs at each time instance the number of degrees of freedom can exceed k 2 and in fact can be made arbitrarily close to k more specifically for single antenna transmitters and receivers the network size scaling as n snrd d 1 when power allocation is allowed and scaling as n snrd k 1 without power allocation are sufficient conditions for achieving d 1 k degrees of freedom moreover for achieving these degrees of freedom the transmitters do not require the knowledge of the instantaneous channel realizations hence invoking opportunistic communication in the context of interference channels leads to achieving higher degrees of freedom that are not achievable otherwise we extend the results for multi antenna gaussian interference channels

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

asynchronous iterative water filling for gaussian frequency selective interference channels this paper considers the maximization of information rates for the gaussian frequency selective interference channel subject to power and spectral mask constraints on each link to derive decentralized solutions that do not require any cooperation among the users the optimization problem is formulated as a static noncooperative game of complete information to achieve the so called nash equilibria of the game we propose a new distributed algorithm called asynchronous iterative water filling algorithm in this algorithm the users update their power spectral density psd in a completely distributed and asynchronous way some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference the proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water filling algorithms e g sequential and simultaneous versions the main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the unique nash equilibrium of the game

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

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

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

further analysis of the remedian algorithm we present an analysis of the remedian an efficient known algorithm for the approximate median selection problem that is easy to implement the algorithm can be used for data in an array as well as for streaming data in an array it performs in place recursively dividing the candidate values into sets of size b from which exact medians are selected for the next phase on streaming data it performs a filter operation requiring by the time n items are processed the storage of log bn candidate entries the contribution of the article is a precise characterization combinatorial and asymptotic of the accuracy of the algorithm showing explicitly the role of the critical design parameter b in addition we compute the time and space costs of the algorithm and present experimental illustrations of its accuracy

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

selecting the median improving a long standing result of schonhage paterson and pippenger j comput system sci 13 1976 pp 184 199 we show that the median of a set containing n elements can always be found using at most c cdot n comparisons where c 2 95

how good is recursive bisection the most commonly used p way partitioning method is recursive bisection rb it first divides a graph or a mesh into two equal sized pieces by a good bisection algorithm and then recursively divides the two pieces ideally we would like to use an optimal bisection algorithm because the optimal bisection problem that partitions a graph into two equal sized subgraphs to minimize the number of edges cut is np complete practical rb algorithms use more efficient heuristics in place of an optimal bisection algorithm most such heuristics are designed to find the best possible bisection within allowed time we show that the rb method even when an optimal bisection algorithm is assumed may produce a p way partition that is very far way from the optimal one our negative result is complemented by two positive ones first we show that for some important classes of graphs that occur in practical applications such as well shaped finite element and finite difference meshes rb is within a constant factor of the optimal one almost always second we show that if the balance condition is relaxed so that each block in the p way partition is bounded by 2n p where n is the number of vertices of the graph then a modified rb finds an approximately balanced p way partition whose cost is within an o log p factor of the cost of the optimal p way partition

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

mmse of bad codes we examine codes over the additive gaussian noise channel designed for reliable communication at some specific signal to noise ratio snr and constrained by the permitted minimum mean square error mmse at lower snrs the maximum possible rate is below point to point capacity and hence these are nonoptimal codes alternatively referred to as bad codes we show that the maximum possible rate is the one attained by superposition codebooks moreover the mmse and mutual information behavior as a function of snr for any code attaining the maximum rate under the mmse constraint is known for all snr we also provide a lower bound on the mmse for finite length codes as a function of the error probability of the code

is non unique decoding necessary in multiterminal communication systems signals carrying messages meant for different destinations are often observed together at any given destination receiver han and kobayashi proposed a receiving strategy which performs a joint unique decoding of messages of interest along with a subset of messages which are not of interest it is now well known that this provides an achievable region which is in general larger than if the receiver treats all messages not of interest as noise nair and el gamal and chong motani garg and el gamal independently proposed a generalization called indirect or nonunique decoding where the receiver uses the codebook structure of the messages to uniquely decode only its messages of interest nonunique decoding has since been used in various scenarios the main result in this paper is to provide an interpretation and a systematic proof technique for why nonunique decoding in all known cases where it has been employed can be replaced by a particularly designed joint unique decoding strategy without any penalty from a rate region viewpoint

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

new inner and outer bounds for the memoryless cognitive interference channel and some new capacity results the cognitive interference channel is a two user interference channel in which one transmitter is non causally provided with the message of the other transmitter this channel model has been extensively studied in the past years and capacity results have been proved for certain classes of channels this paper presents new inner and outer bounds for the capacity region of the cognitive interference channel as well as new capacity results previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint of their alphabet is known consequently it is not possible to evaluate such outer bounds explicitly for a given channel the outer bound derived in this work is based on an idea originally devised by sato for channels without receiver cooperation and results in an outer bound that does not contain auxiliary random variables thus allowing it to be more easily evaluated the inner bound presented in this work which includes rate splitting superposition coding a broadcast channel like binning scheme and gel fand pinsker coding is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions the novel inner and outer bounds are shown to coincide in certain cases in particular capacity is proved for a class of channels in the so called better cognitive decoding regime which includes the regimes in which capacity was known finally the capacity region of the semi deterministic cognitive interference channel in which the signal at the cognitive receiver is an arbitrary deterministic function of the channel inputs is established

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

system utility maximization with interference processing for cognitive radio networks in spectrum underlay cognitive radio networks secondary users sus are allowed to reuse the spectrum allocated to a primary system the interference between sus actually carries information and can potentially be exploited to improve the network performance through information theoretic interference processing in this paper we design an optimal joint power and rate control algorithm that maximizes the secondary system utility subject to the interference temperature constraints of primary users based on the capacity approaching interference processing scheme called as the han kobayashi scheme the optimal solution is difficult to achieve because the optimization problem is in general non convex to make the optimization problem tractable this paper first transforms the problem into a monotonic optimization problem through exploiting its hidden monotonicity we then devise an effective algorithm to obtain the global optimal solution to the joint power and rate control problem in the han kobayashi scheme the key idea behind the proposed algorithm is to construct a sequence of shrinking polyblocks that approximate the upper boundary of the feasible region with increasing precision numerical results further show that the achieved utility of our scheme significantly outperforms the utility of conventional schemes which treat the interference between sus as the noise

average case selection it is shown that n k o 1 comparisons are necessary on average to find the k th smallest of n numbers k l n 2 this lower bound matches the behavior of the technique of floyd and rivest to within a lower order term 7 n 4 o n comparisons on average are shown to be necessary and sufficient to find the maximum and median of a set an upper bound of 9 n 4 o n and a lower bound of 2 n o n are shown for the max min median problem

fast projection onto the simplex and the pmb l _ mathbf 1 l1 ball a new algorithm is proposed to project exactly and in finite time a vector of arbitrary size onto a simplex or an l 1 l1 norm ball it can be viewed as a gauss seidel like variant of michelot s variable fixing algorithm that is the threshold used to fix the variables is updated after each element is read instead of waiting for a full reading pass over the list of non fixed elements this algorithm is empirically demonstrated to be faster than existing methods

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

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

classical communication over a quantum interference channel calculating the capacity of interference channels is a notorious open problem in classical information theory such channels have two senders and two receivers and each sender would like to communicate with a partner receiver the capacity of such channels is known exactly in the settings of very strong and strong interference while the han kobayashi coding strategy gives the best known achievable rate region in the general case here we introduce and study the quantum interference channel a natural generalization of the interference channel to the setting of quantum information theory we restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results though generalizations of our results to channels with quantum inputs are straightforward we are able to determine the exact classical capacity of this channel in the settings of very strong and strong interference by exploiting winter s successive decoding strategy and a novel two sender quantum simultaneous decoder respectively we provide a proof that a han kobayashi strategy is achievable with holevo information rates up to a conjecture regarding the existence of a three sender quantum simultaneous decoder this conjecture holds for a special class of quantum multiple access channels with average output states that commute and we discuss some other variations of the conjecture that hold finally we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates

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

the discrete memoryless interference channel with one sided generalized feedback we study the interference channel with one sided generalized feedback and secrecy requirements in our model message 1 that is known just to encoder 1 should be decoded by both receivers message 2 known only to encoder 2 should be decoded by decoder 2 and kept as secret as possible from decoder 1 the uncertainty of decoder 1 about message 2 is measured by means of the equivocation rate in addition a noisy feedback is provided to encoder 2 we derive an achievable rate equivocation region for this model and an outer bound for the noisy cribbing regime without secrecy the gap being the markov conditions satisfied by one of the auxiliary random variables furthermore we consider a simplified causal cognitive interference model the interference channel with a cribbing encoder we derive an inner bound on the rate region for this model and prove that when the interference channel is degraded conditionally on the input of encoder 1 our inner bound is tight

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

outer bounds on the capacity of interference channels corresp new outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and gaussian interference channels the bound for discrete channels coincides with the capacity region in special cases the bound for gaussian channels improves previous knowledge when the interference is of medium strength

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

interference alignment based sum capacity bounds for random dense gaussian interference networks we consider a dense k user gaussian interference network formed by paired transmitters and receivers placed independently at random in a fixed spatial region under natural conditions on the node position distributions and signal attenuation we prove convergence in probability of the average per user capacity c k to 1 2e log 1 2snr the achievability result follows directly from results based on an interference alignment scheme presented in recent work of nazer et al our main contribution comes through an upper bound motivated by ideas of bottleneck capacity developed in recent work of jafar by controlling the physical location of transmitter receiver pairs we can match a large proportion of these pairs to form so called e bottleneck links with consequent control of the sum capacity

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

the capacity region of frequency selective gaussian interference channels under strong interference this paper presents the capacity region of frequency selective gaussian interference channels under the condition of strong interference assuming an average power constraint per user first a frequency selective gaussian interference channel is modeled as a set of independent parallel memoryless gaussian interference channels using nonfrequency selective results the capacity region of frequency selective gaussian interference channels under strong interference is expressed mathematically exploiting structures inherent in the problem a dual problem is constructed for each independent memoryless channel in which both mathematical and numerical analysis are performed furthermore three suboptimal methods are compared to the capacity achieving coding and power allocation scheme iterative waterfilling a suboptimal scheme provides close to optimum performance and has a distributed coding and power allocation scheme which are attractive in practice

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

characterization of the pareto boundary for the two user symmetric gaussian interferencechannel we characterize the pareto boundary of the achiev able rate region of the two user symmetric gaussian interference channel when transmitters control their transmission power and receivers have successive interference cancelation capability by identifying the shape of achievable rate region according to the strength of interference channels we find combinations of decod ing and power allocation strategies achieving the pareto boundary we also characterize the pareto boundary of the achievable rate region when time sharing is additionally considered index terms interference channel achievable rate region pareto boundary successive interference cancelation

complete characterization of the pareto boundary for the miso interference channel in this correspondence we study the achievable rate region of the multiple input single output miso interference channel under the assumption that all receivers treat the interference as additive gaussian noise our main result is an explicit parametrization of the pareto boundary for an arbitrary number of users and antennas the parametrization describes the boundary in terms of a low dimensional manifold for the two user case we show that a single real valued parameter per user is sufficient to achieve all points on the pareto boundary and that any point on the pareto boundary corresponds to beamforming vectors that are linear combinations of the zero forcing zf and maximum ratio transmission mrt beamformers we further specialize the results to the miso broadcast channel bc a numerical example illustrates the result

a strong entropy power inequality when one of the random summands is gaussian we sharpen the entropy power inequality epi in terms of the strong data processing function for gaussian channels among other consequences this strong epi generalizes the vector extension of costa s epi to non gaussian channels in a precise sense this leads to a new reverse epi and as a corollary sharpens stam s uncertainty principle relating entropy power and fisher information or equivalently gross logarithmic sobolev inequality applications to network information theory are also given including a short self contained proof of the rate region for the two encoder quadratic gaussian source coding problem and a new outer bound for the one sided gaussian interference channel

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

on floyd and rivest s select algorithm we show that several versions of floyd and rivest s algorithm select for finding the kth smallest of n elements require at most n min k n k o n comparisons on average and with high probability this rectifies the analysis of floyd and rivest and extends it to the case of nondistinct elements our computational results confirm that select may be the best algorithm in practice

the degrees of freedom of isotropic mimo interference channels without state information at the transmitters this paper fully determines the degree of freedom dof region of two user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent or block wise independent fading where the channel state information is available to the receivers but not to the transmitters thus the dof gap between previous upper and lower bounds due to the authors vaze and varanasi and huang jafar shamai and vishwanath is closed the dof result characterizes the capacity region to the first order of the logarithm of the signal to noise ratio snr in the high snr regime the dof region is achievable by using random gaussian codebooks independent of the channel states which implies that it is impossible to increase the dof using beamforming and interference alignment in the absence of channel state information at the transmitters

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

constant gap to capacity and generalized degrees of freedom regions of the mimo mac ic mac the mac ic mac is a class of multiple access interference channels consisting of two multiple access channels macs that are mutually interfering but in which there is interference only from one transmitter of each mac to the receiver of the other mac two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete memoryless semi deterministic mac ic mac were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions in this paper we obtain single distribution and hence explicit inner and outer bounds that characterize the capacity region of the mimo gaussian mac ic mac to within a constant gap we also evaluate and study the generalized degrees of freedom gdof region via multidimensional signal level partitioning for mimo networks through its lens the achievability of the key vertices of the gdof region are examined this analysis as well as the symmetric gdof curve reveal that at high snr when the ratio of the interference to noise to the signal to noise ratios both taken in db is within a certain range non interfering transmitters in that cell can fully occupy the receivers signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone this extends the same finding in the companion paper which established the results of this work for the scalar gaussian mac ic mac

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 remedian a robust averaging method for large data sets abstract it is often assumed that to compute a robust estimator on n data values one needs at least n storage elements contrary to the sample average that may be calculated with an updating mechanism this is one of the main reasons why robust estimators are seldom used for large data sets and why they are not included in most statistical packages we introduce a new estimator that takes up little storage space investigate its statistical properties and provide an example on real time curve averaging in a medical context the remedian with base b proceeds by computing medians of groups of b observations and then medians of these medians until only a single estimate remains this method merely needs k arrays of size b where n bk so the total storage is o log n for fixed b or alternatively o nl k for fixed k its storage economy makes it useful for robust estimation in large data bases for real time engineering applications in which the data themselves are not stored and for resistant

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

the dispersion of nearest neighbor decoding for additive non gaussian channels we study the second order asymptotics of information transmission using random gaussian codebooks and nearest neighbor decoding over a power limited stationary memoryless additive non gaussian noise channel we show that the dispersion term depends on the non gaussian noise only through its second and fourth moments thus complementing the capacity result lapidoth 1996 which depends only on the second moment furthermore we characterize the second order asymptotics of point to point codes over k sender interference networks with non gaussian additive noise specifically we assume that each user s codebook is gaussian and that nn decoding is employed i e that interference from the k 1 unintended users gaussian interfering signals is treated as noise at each decoder we show that while the first order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum this does not hold for the second order term

diversity multiplexing tradeoff for the interference channel with a relay we study the diversity multiplexing tradeoff dmt for the slow fading interference channel with a relay icr we derive four inner bounds on the dmt region the first is based on the compress and forward cf relaying scheme the second is based on the decode and forward df relaying scheme and the last two bounds are based on the half duplex hd and full duplex fd amplify and forward af schemes for the cf and df schemes we find conditions on the channel parameters and the multiplexing gains under which the corresponding inner bound achieves the optimal dmt region we also identify the cases in which the dmt region of the icr corresponds to that of two parallel slow fading relay channels implying that interference does not decrease the dmt for each pair and that a single relay can be dmt optimal for two pairs simultaneously for the hd af scheme we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal dmt for the af based relay channel finally we identify the conditions under which adding a relay strictly enlarges the dmt region relative to the interference channel without a relay

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

interference channels with arbitrarily correlated sources communicating arbitrarily correlated sources over interference channels is considered in this paper a sufficient condition is found for lossless transmission of a pair of correlated sources over a discrete memoryless interference channel with independent sources the sufficient condition reduces to the han kobayashi achievable rate region for interference channels for sources with a special correlation structure the proposed region reduces to the known achievable region for interference channels with common information moreover the proposed coding scheme is optimal for transmitting such set of correlated sources over a class of deterministic interference channels as defined in el gamal and costa 1982

optimal sampling strategies in quicksort and quickselect it is well known that the performance of quicksort can be improved by selecting the median of a sample of elements as the pivot of each partitioning stage for large samples the partitions are better but the amount of additional comparisons and exchanges to find the median of the sample also increases we show in this paper that the optimal sample size to minimize the average total cost of quicksort as a function of the size n of the current subarray size is a cdot sqrt n o sqrt n we give a closed expression for a which depends on the selection algorithm and the costs of elementary comparisons and exchanges moreover we show that selecting the medians of the samples as pivots is not the best strategy when exchanges are much more expensive than comparisons we also apply the same ideas and techniques to the analysis of quickselect and get similar results

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

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

partial interference alignment for k user mimo interference channels in this paper we consider a partial interference alignment and interference detection piaid design for k user quasi static mimo interference channels with discrete constellation inputs each transmitter has m antennas and transmits l independent data streams to the desired receiver with n receive antennas we focus on the case where not all k 1 interfering transmitters can be aligned at every receiver as a result there will be residual interference at each receiver that cannot be aligned each receiver detects and cancels the residual interference based on the constellation map however there is a window of unfavorable interference profile at the receiver for interference detection id in this paper we propose a low complexity partial interference alignment scheme in which we dynamically select the user set for ia so as to create a favorable interference profile for id at each receiver we first derive the average symbol error rate ser by taking into account of the non guassian residual interference due to discrete constellation using graph theory we then devise a low complexity user set selection algorithm for the piaid scheme which minimizes the asymptotically tight bound for the average end to end ser performance moreover we substantially simplify interference detection at the receiver using semi definite relaxation sdr techniques it is shown that the ser performance of the proposed piaid scheme has significant gain compared with various conventional baseline solutions

error exponents of optimum decoding for the interference channel exponential error bounds for the finite alphabet interference channel ifc with two transmitter receiver pairs are investigated under the random coding regime our focus is on optimum decoding as opposed to heuristic decoding rules that have been used in previous works like joint typicality decoding decoding based on interference cancellation and decoding that considers the interference as additional noise indeed the fact that the actual interfering signal is a codeword and not an independent and identically distributed i i d noise process complicates the application of conventional techniques to the performance analysis of the optimum decoder using analytical tools rooted in statistical physics we derive a single letter expression for error exponents achievable under optimum decoding and demonstrate strict improvement over error exponents obtainable using suboptimal decoding rules but which are amenable to more conventional analysis

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

a multilevel approach to the travelling salesman problem we motivate derive and implement a multilevel approach to the travelling salesman problem the resulting algorithm progressively coarsens the problem initialises a tour and then employs either the lin kernighan lk or the chained lin kernighan clk algorithm to refine the solution on each of the coarsened problems in reverse order in experiments on a well established test suite of 80 problem instances we found multilevel configurations that either improved the tour quality by over 25 as compared to the standard clk algorithm using the same amount of execution time or that achieved approximately the same tour quality over seven times more rapidly moreover the multilevel variants seem to optimise far better the more clustered instances with which the lk and clk algorithms have the most difficulties

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

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

breakpoint searching algorithms for the continuous quadratic knapsack problem we give several linear time algorithms for the continuous quadratic knapsack problem in addition we report cycling and wrong convergence examples in a number of existing algorithms and give encouraging computational results for large scale problems

analysis of deterministic binary interference channels via a general outer bound we present a new outer bound for the general two user discrete memoryless interference channel ifc and use it to establish the capacity region of the binary erasure ifc whose determination was left open in we also show that there are essentially two deterministic binary ifcs in addition to the binary erasure ifc whose capacity regions are not obvious from previous results we determine the capacity region of one of these and apply the aforementioned general outer bound to obtain the best available bound on the maximum achievable sum rate for the other we also show that the new general outer bound is tight for one sided deterministic ifcs that belong to the class studied by el gamal and costa

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

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

sum capacity of one sided parallel gaussian interference channels the sum capacity of the one sided parallel gaussian interference channel is shown to be a concave function of user powers exploiting the inherent structure of the problem we construct a numerical algorithm to compute it two suboptimal schemes are compared with the capacity achieving scheme one of the suboptimal schemes namely iterative waterfilling yields close to capacity performance when the cross link gain is small

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

a case where interference does not affect the channel dispersion in 1975 carleial presented a special case of an interference channel called the very strong interference regime in which the interference does not reduce the capacity of the constituent point to point gaussian channels in this paper we show that in the strictly very strong interference regime the dispersions are similarly unaffected more precisely in this paper we characterize the second order coding rates of the gaussian interference channel in the strictly very strong interference regime in other words we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the rectangular capacity region these second order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the single user gaussian channel this allows us to conclude that the dispersions are unaffected by interference in this channel model