interference alignment with asymmetric complex signaling settling the host madsen nosratinia conjecture it has been conjectured by ho madsen and nosratinia that complex gaussian interference channels with constant channel coefficients have only one degree of freedom regardless of the number of users while several examples are known of constant channels that achieve more than 1 degree of freedom these special cases only span a subset of measure zero in other words for almost all channel coefficient values it is not known if more than 1 degree of freedom is achievable in this paper we settle the host madsen nosratinia conjecture in the negative we show that at least 1 2 degrees of freedom are achievable for all values of complex channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper it is also shown that 1 2 is the maximum number of degrees of freedom achievable on the complex gaussian 3 user interference channel with constant channel coefficients for almost all values of channel coefficients to establish the achievability of 1 2 degrees of freedom we use the novel idea of asymmetric complex signaling i e the inputs are chosen to be complex but not circularly symmetric it is shown that unlike gaussian point to point multiple access and broadcast channels where circularly symmetric complex gaussian inputs are optimal for interference channels optimal inputs are in general asymmetric with asymmetric complex signaling we also show that the 2 user complex gaussian x channel with constant channel coefficients achieves the outer bound of 4 3 degrees of freedom i e the assumption of time variations frequency selectivity used in prior work to establish the same result is not needed

generalized degrees of freedom of the symmetric gaussian k user interference channel we characterize the generalized degrees of freedom of the k user symmetric gaussian interference channel where all desired links have the same signal to noise ratio snr and all undesired links carrying interference have the same interference to noise ratio inr snr we find that the number of generalized degrees of freedom per user d does not depend on the number of users so that the characterization is identical to the 2 user interference channel with the exception of a singularity at 1 where d 1 1 k the achievable schemes use multilevel coding with a nested lattice structure that opens the possibility that the sum of interfering signals can be decoded at a receiver even though the messages carried by the interfering signals are not decodable

near optimal quantization and linear network coding for relay networks we introduce a discrete network corresponding to any gaussian wireless network that is obtained by simply quantizing the received signals and restricting the transmitted signals to a finite precision since signals in the discrete network are obtained from those of a gaussian network the gaussian network can be operated on the quantization based digital interface defined by the discrete network we prove that this digital interface is near optimal for gaussian relay networks and the capacities of the gaussian and the discrete networks are within a bounded gap of o m2 bits where m is the number of nodes we also prove that any near optimal coding strategy for the discrete network can be naturally transformed into a near optimal coding strategy for the gaussian network merely by quantization we exploit this property by designing a linear coding strategy for the case of layered discrete relay networks the linear coding strategy is near optimal and achieves all rates within o m2 bits of the capacity independent of channel gains or signal to noise ratio the linear code is therefore a near optimal strategy for layered gaussian relay networks and can be used as on the gaussian network after simply quantizing the signals the relays in the linear code need not know the channel gains on either the incoming or the outgoing links the transmit and receive signals at all relays are simply quantized to binary tuples of the same length n which is all that the nodes need to know the linear network code is a particularly simple scheme and requires all the relay nodes to collect the received binary tuples into a long binary vector and apply a linear transformation on the long vector the resulting binary vector is split into smaller binary tuples for transmission by the relays the quantization requirements of the linear network code are completely defined by the parameter n which therefore also determines the resolution of the analog to digital and digital to analog converters that are required for operating the network within a bounded gap of the network s capacity as evident from the description the linear network code explicitly connects network coding for wireline networks with codes for gaussian networks

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

on the capacity of the finite field counterparts of wireless interference networks this paper explores how degrees of freedom dof results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications the main insight is that scalar siso finite field channels over mathbb f p n are analogous to n times n vector mimo channels in the wireless setting but with an important distinction there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n making these channels similar to diagonal channels in the wireless setting within the limits imposed by the channel structure the dof optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts this is shown through the study of capacity of the 2 user x channel and linear capacity of the 3 user interference channel besides bringing the insights from wireless networks into network coding applications the study of finite field networks over mathbb f p n also touches upon important open problems in wireless networks finite snr finite diversity scenarios through interesting parallels between p and snr and n and diversity

topological interference management through index coding this paper studies linear interference networks both wired and wireless with no channel state information at the transmitters except a coarse knowledge of the end to end one hop topology of the network that only allows a distinction between weak zero and significant nonzero channels and no further knowledge of the channel coefficients realizations the network capacity wired and degrees of freedom dof wireless are found to be bounded above by the capacity of an index coding problem for which the antidote graph is the complement of the given interference graph the problems are shown to be equivalent under linear solutions an interference alignment perspective is then used to translate the existing index coding solutions into the wired network capacity and wireless network dof solutions as well as to find new and unified solutions to different classes of all three problems

a modified log rank test for competing risks with missing failure type summary we propose a modified log rank test for the analysis of competing risks survival data when failure type is missing for some individuals the proposed test reduces to a standard log rank test when all failure types are known the test arises from a partial likelihood constructed under semiparametric assumptions on the relationship between cause specific hazards

a unified theory of multiple access and interference channels via approximate capacity regions for the mac ic mac approximate capacity regions are established for a class of interfering multiple access channels consisting of two multiple access channels macs each with an arbitrary number of transmitters with one transmitter in each mac causing interference to the receiver of the other mac a channel we refer to henceforth as the mac ic mac for the discrete memory less dm mac ic mac two inner bounds are obtained that are generalizations of prior inner bounds for the two user dm interference channel ic due to chong et al for the semi deterministic mac ic mac it is shown that single user coding at the non interfering transmitters and superposition coding at the interfering transmitter of each mac achieves a rate region that is within a quantifiable gap of the capacity region thereby extending such a result for the two user semi deterministic ic by telatar and tse for the gaussian mac ic mac an approximate capacity region that is within a constant gap of the capacity region is obtained generalizing such a result for the two user gaussian ic by etkin et al on contrary to the aforementioned approximate capacity results for the two user ic whose achievability requires the union of all admissible input distributions our gap results on the semi deterministic and the gaussian mac ic mac are achievable by only a subset and one of all admissible coding distributions respectively the symmetric generalized degrees of freedom gdofs of the symmetric gaussian mac ic mac with more than one user per cell which is a function of the interference strength the ratio of inr to snr at high snr both expressed in db and the numbers of users in each cell are v shaped with flat shoulders an analysis based on signal level partitions shows that the non interfering transmitters utilize the signal level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters due to the restriction of superposition coding thereby improving the sum symmetric gdof of up to one degree of freedom per cell under a range of sinr exponent levels which in turn becomes wider as the number of transmitters in each cell increases consequently time sharing between interfering and non interfering transmitters is gdof suboptimal in general as is time sharing between the two embedded mac z macs

feasibility of interference alignment for the mimo interference channel we study vector space interference alignment for the multiple input multiple output interference channel with no time or frequency diversity and no symbol extensions we prove both necessary and sufficient conditions for alignment in particular we characterize the feasibility of alignment for the symmetric three user channel where all users transmit along d dimensions all transmitters have m antennas and all receivers have n antennas as well as feasibility of alignment for the fully symmetric m n channel with an arbitrary number of users an implication of our results is that the total degrees of freedom available in a k user interference channel using only spatial diversity from the multiple antennas is at most 2 this is in sharp contrast to the k 2 degrees of freedom shown to be possible by cadambe and jafar with arbitrarily large time or frequency diversity moving beyond the question of feasibility we additionally discuss computation of the number of solutions using schubert calculus in cases where there are a finite number of solutions

a network information theory for wireless communication scaling laws and optimal operation how much information can be carried over a wireless network with a multiplicity of nodes and how should the nodes cooperate to transfer information to study these questions we formulate a model of wireless networks that particularly takes into account the distances between nodes and the resulting attenuation of radio signals and study a performance measure that weights information by the distance over which it is transported consider a network with the following features i n nodes located on a plane with minimum separation distance spl rho sub min 0 ii a simplistic model of signal attenuation e sup spl gamma spl rho spl rho sup spl delta over a distance spl rho where spl gamma spl ges 0 is the absorption constant usually positive unless over a vacuum and spl delta 0 is the path loss exponent iii all receptions subject to additive gaussian noise of variance spl sigma sup 2 the performance measure we mainly but not exclusively study is the transport capacity c sub t sup spl sigma on sub spl lscr 1 sup m r sub spl lscr spl middot spl rho sub spl lscr where the supremum is taken over m and vectors r sub 1 r sub 2 r sub m of feasible rates for m source destination pairs and spl rho sub spl lscr is the distance between the spl lscr th source and its destination it is the supremum distance weighted sum of rates that the wireless network can deliver we show that there is a dichotomy between the cases of relatively high and relatively low attenuation when spl gamma 0 or spl delta 3 the relatively high attenuation case the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network however when spl gamma 0 and spl delta 3 2 the low attenuation case we show that there exist networks that can provide unbounded transport capacity for fixed total power yielding zero energy priced communication examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low these results are established by developing a coding scheme and an achievable rate for gaussian multiple relay channels a result that may be of interest in its own right

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

spatial distribution of avalanches in invasion percolation their role in fingering for two decades invasion percolation ip has provided a simple model of drainage where a non wetting fluid is injected into a porous media saturated with a wetting fluid in the limit where capillary forces dominate and viscous forces are negligible ip produces a characteristic fingering with a fractal dimension close to that of ordinary critical percolation avalanches also called bursts or haines jumps have been observed in this paper we focus on the practical issues relating to the causes of the fingering and of the low saturations of injected fluid we show that the saturation and the average position of the injected fluid exhibit standard fractal scaling behavior however the fractional flow of the injected fluid does not allow an average analysis because of the noise arising from the avalanches even for the million site systems investigated in this paper in studying the spatial distribution of these avalanches we find a size cutoff depending upon the position of the avalanches this is characteristic of the finite size of the system and signals that the systems have not achieved self organized criticality furthermore we show that the average size of these avalanches sa increases with their average distance x from the outlet as sa x 1 1 as a result larger avalanches will tend to occur at the end of longer fingers causing preferential growth of the long fingers at the expense of the shorter fingers

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

fractal dimension and avalanches of invasion percolation the effect of aspect ratio abstract troubled by unreliable estimates of the fractal dimension from straightforward box counting applied to invasion percolation in million site short wide systems i e the length in the average flow direction is the smaller dimension we undertook a study of the effect of aspect ratio on fractal dimension determinations and on avalanche structure in box counting we found evidence of a competition between the different singular behaviors associated with the bulk and the external hull interface which was most noticeable for the short wide systems with a long external hull modifying the box counting to exclude those boxes covering the external hull provides results for the short wide systems which are consistent with results from the literature and from straightforward box counting on long narrow systems not surprisingly we found that the avalanche size distribution was cut off by the length in the short wide systems however we also found that the distribution was cut off by the width in the long narrow systems therefore the smaller dimension served as a cut off length for the distribution of avalanche sizes so that in the long narrow systems the distribution of avalanche sizes collapses long before the injected fluid reaches the outlet this results in fingering patterns in the long narrow systems that are different from those in the short wide systems where the avalanche size distribution is maintained all the way to the outlet determining the fractal dimension from the power law dependence of mass upon a typical length scale was found to be unaffected by the length of the external hull providing the standard literature values of fractal dimension for the problematic short wide systems

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

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

the degrees of freedom of compute and forward we analyze the asymptotic behavior of compute and forward relay networks in the regime of high signal to noise ratios we consider a section of such a network consisting of k transmitters and k relays the aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters an upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays transforming the network into a k k multiple input multiple output mimo channel the number of degrees of freedom of compute and forward is hence at most k in this paper we analyze the degrees of freedom achieved by the lattice coding implementation of compute and forward proposed recently by nazer and gastpar we show that this lattice implementation achieves at most 2 1 1 k 2 degrees of freedom thus exhibiting a very different asymptotic behavior than the mimo upper bound this raises the question if this gap of the lattice implementation to the mimo upper bound is inherent to compute and forward in general we answer this question in the negative by proposing a novel compute and forward implementation achieving k degrees of freedom

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 as noise friend or foe this paper shows that for the two user gaussian interference channel g ic treating interference as noise without time sharing tinnots achieves the closure of the capacity region to within either a constant gap or to within a gap of the order o log ln min mathsf s mathsf i gamma up to a set of lebesgue measure gamma in 0 1 where mathsf s is the largest signal to noise ratio on the direct links and mathsf i is the largest interference to noise ratio on the cross links as a consequence tinnots is optimal from a generalized degrees of freedom gdof perspective for all channel gains except for a subset of zero measure tinnots with gaussian inputs is known to be optimal within 1 2 bit for a subset of the weak interference regime rather surprisingly this paper shows that tinnots is gdof optimal in all parameter regimes even in the strong and very strong interference regimes where joint decoding of gaussian inputs is optimal for approximate optimality of tinnots in all parameter regimes it is critical to use non gaussian inputs this paper thus proposes to use mixed inputs as channel inputs for the g ic where a mixed input is the sum of a discrete and a gaussian random variable interestingly with reference to the han kobayashi achievable scheme the discrete part of a mixed input is shown to effectively behave as a common message in the sense that although treated as noise its effect on the achievable rate region is as if it were jointly decoded together with the desired messages at a non intended receiver the practical implication is that a discrete interfering input is a friend while an gaussian interfering input is in general a foe this paper also discusses other practical implications of the proposed tinnots scheme with mixed inputs since tinnots requires neither explicit joint decoding nor time sharing the results of this paper are applicable to a variety of oblivious or asynchronous channels such as the block asynchronous g ic which is not an information stable channel and the g ic with partial codebook knowledge at one or more receivers

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

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

quasi structured codes for multi terminal communications a new class of structured codes called quasi group codes qgcs is introduced a qgc is a subset of a group code in contrast with the group codes qgcs are not closed under group addition the parameters of the qgc can be chosen such that the size of mathcal c mathcal c is equal to any number between mathcal c and mathcal c 2 we analyze the performance of a specific class of qgcs this class of qgcs is constructed by assigning single letter distributions to the indices of the codewords in a group code then the qgc is defined as the set of codewords whose index is in the typical set corresponding to these single letter distributions the asymptotic performance limits of this class of qgcs are characterized using single letter information quantities corresponding covering and packing bounds are derived it is shown that the point to point channel capacity and optimal rate distortion function are achievable using qgcs coding strategies based on qgcs are introduced for three fundamental multi terminal problems the korner marton problem for modulo prime power sums computation over the multiple access channel mac and mac with distributed states for each problem a single letter achievable rate region is derived it is shown through examples that the coding strategies improve upon the previous strategies based on the unstructured codes linear codes and group codes

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

on the robustness of lattice interference alignment a static constant channel gains real k user interference channel is considered where all interference cross channel gains are integers for such channels previous results demonstrate that the number of degrees of freedom is very sensitive to slight variations in the direct channel gains in this paper we derive an achievable rate region for such channels that is valid for finite snr at moderate values of snr the derived rate region is robust to slight variations in the direct channel gains at asymptotic high snr conditions known results on the degrees of freedom are recovered the new rate region is based on lattice interference alignment the result is established via a new coding theorem for the two user gaussian multiple access channel where both users use a single linear code

new achievable rates for gaussian partially cognitive interference channels with multiple cognitive pairs this paper characterizes achievable rate regions for the gaussian partially cognitive interference channel with multiple cognitive pairs k pcifc where the cognitive transmitters know one part of the primary transmitter s message we explore a novel methodology using the deterministic discrete superposition model dsm we find codes and their achievable rate regions in the dsm and we show that they yield achievable rate regions in the gaussian model our coding scheme in the dsm can be applied in general scenarios we devise an achievable rate region for the k pcifc which is within a constant gap to known outer bounds for k 2 in the weak interference regime from our expressions we derive guidelines for designing the cognitive link between the primary transmitter and the cognitive transmitters furthermore we show that the gain from cognition diminishes for increasing k

an achievable rate region for the three user interference channel based on coset codes we consider the problem of communication over a three user discrete memoryless interference channel 3 ic the current known coding techniques for communicating over an arbitrary 3 ic are based on message splitting superposition coding and binning using independent and identically distributed i i d random codebooks in this paper we propose a new ensemble of codes partitioned coset codes pccs that possess an appropriate mix of empirical and algebraic closure properties we develop coding techniques that exploit the algebraic closure property of pcc to enable interference alignment over general 3 ic we analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete 3 ic additive and non additive examples are identified for which the derived achievable rate region is the capacity moreover strictly larger than the current known largest achievable rate regions based on the i i d random codebooks

degrees of freedom region of the mimo x channel we provide achievability as well as converse results for the degrees of freedom region of a multiple input multiple output mimo x channel i e a system with two transmitters two receivers each equipped with multiple antennas where independent messages need to be conveyed over fixed channels from each transmitter to each receiver the inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message with m 1 antennas at each node we find that the total sum rate degrees of freedom are bounded above and below as 1 les eta x les 4 3 if m 1 and channel matrices are nondegenerate then the precise degrees of freedom eta x 4 3 m thus the mimo x channel has noninteger degrees of freedom when m is not a multiple of 3 simple zero forcing without dirty paper encoding or successive decoding suffices to achieve the 4 3 m degrees of freedom if the channels vary with time frequency then the channel with single antennas m 1 at all nodes has exactly 4 3 degrees of freedom the key idea for the achievability of the degrees of freedom is interference alignment i e signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired we also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio

temporal development of invasion percolation the authors consider the dynamics of invasion percolation for different models this process exhibits scaling behaviours which in the simplest case can be related to some critical static properties of usual percolation in particular the concept of bursts is shown to be of fundamental importance the critical exponents they derive are checked numerically on a case of invasion percolation where growth is restricted to the hull of the existing cluster

nonparametric prevalence and mortality estimators for animal experiments with incomplete cause of death data abstract age specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished this article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the animals dying with the disease the proposed analysis makes no assumptions about the degree of disease lethality data from sacrificed animals can be incorporated easily although sacrifices are not necessary if a certain representativeness assumption holds no restrictions are imposed on the distribution of survival times but the prevalence function is held constant over time intervals for stabilization purposes variances are estimated by inverting the observed information matrix an em algorithm simplifies the analysis when the

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

on the optimality of treating interference as noise general message sets in a k user gaussian interference channel it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all values in decibel scale then treating interference as noise tin is optimal from the perspective of generalized degrees of freedom gdof and achieves the entire channel capacity region to within a constant gap in this paper we show that for such tin optimal interference channels even if the message set is expanded to include an independent message from each transmitter to each receiver operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap furthermore we extend the result to the sum gdof optimality of tin in the general setting of x channels with arbitrary numbers of transmitters and receivers

approximate ergodic capacity of a class of fading two user two hop networks the fading awgn two user two hop network is considered where the channel coefficients are independent and identically distributed i i d according to a continuous distribution and vary over time for a broad class of channel distributions the ergodic sum capacity is characterized to within a constant number of bits second hertz independent of the signal to noise ratio the achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into m pairs and interference is neutralized separately by each pair of relays when m 1 the proposed ergodic interference neutralization characterizes the ergodic sum capacity to within 4 bits sec hz for i i d uniform phase fading and approximately 4 7 bits sec hz for i i d rayleigh fading it is further shown that this gap can be tightened to 4 log 4 bits sec hz approximately 2 6 for i i d uniform phase fading and 4 4 log 3 8 bits sec hz approximately 3 1 for i i d rayleigh fading in the limit of large m1

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

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

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 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

a note on a test for competing risks with missing failure type summary the modified log rank test for competing risks with missing failure type suggested by goetghebeur ryan 1990 is derived from a partial likelihood which leaves out some information this extra information is incorporated to give a new partial likelihood and hence a new test statistic

on the sum rate of the gaussian mimo z channel and the gaussian mimo x channel in this paper we study the gaussian mimo z channel and the gaussian mimo x channel the mimo x channel xc consists of two multiple antenna transmit receive pairs where each transmitter communicates with both receivers the mimo z channel zc is obtained from the mimo x channel by eliminating one of the links and its corresponding message first we derive a sum rate upper bound for the mimo z channel and compare it with an existing bound in literature next we consider the mimo x channel and propose a new sum rate upper bound by utilizing the sum rate upper bound for the mimo zc subsequently we derive another upper bound for the mimo xc by assuming receiver cooperation and deriving the worst noise covariance matrix for the resulting two user mac we compare the above two upper bounds for the mimo xc with the maddahali motahari khandani mmk scheme then we consider some consequences of the above results for the mimo interference channel finally we present some numerical results the numerical results suggest that the proposed sum rate capacity upper bounds are tighter than existing bounds

on the gaussian many to one x channel in this paper the gaussian many to one x channel xc which is a special case of general multiuser xc is studied in the gaussian many to one xc communication links exist between all transmitters and one of the receivers along with a communication link between each transmitter and its corresponding receiver as per the xc assumption transmission of messages is allowed on all the links of the channel this communication model is different from the corresponding many to one interference channel ic transmission strategies which involve using gaussian codebooks and treating interference from a subset of transmitters as noise are formulated for the above channel sum rate is used as the criterion of optimality for evaluating the strategies initially a 3 times 3 many to one xc is considered and three transmission strategies are analyzed the first two strategies are shown to achieve sum rate capacity under certain channel conditions for the third strategy a sum rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized these results are later extended to the k times k case next a region in which the many to one xc can be operated as a many to one ic without the loss of sum rate is identified furthermore in the above region it is shown that using gaussian codebooks and treating interference as noise achieve a rate point that is within k 2 1 bits from the sum rate capacity subsequently some implications of the above results to the gaussian many to one ic are discussed transmission strategies for the many to one ic are formulated and channel conditions under which the strategies achieve sum rate capacity are obtained a region where the sum rate capacity can be characterized to within k 2 1 bits is also identified finally the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 times 3 many to one xc and the corresponding many to one ic

on the optimality of treating interference as noise for k user parallel gaussian interference networks it has been recently shown by geng et al that in a k user gaussian interference network if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user all signal strengths measured in db scale then power control and treating interference as noise tin is sufficient to achieve the entire generalized degrees of freedom gdof region motivated by the intuition that the deterministic model of avestimehr et al avestimehr diggavi tse deterministic model is particularly suited for exploring the optimality of tin the results of geng et al are first re visited under the adt deterministic model and are shown to directly translate between the gaussian and deterministic settings next we focus on the extension of these results to parallel interference networks from a sum capacity sum gdof perspective to this end we interpret the explicit characterization of the sum capacity sum gdof of a tin optimal network without parallel channels as a minimum weighted matching problem in combinatorial optimization and obtain a simple characterization in terms of a partition of the interference network into vertex disjoint cycles aided by insights from the cyclic partition the sum capacity optimality of tin for k user parallel interference networks is characterized for the adt deterministic model leading ultimately to the corresponding gdof results for the gaussian setting in both the cases subject to a mild invertibility condition the optimality of tin is shown to extend to parallel networks in a separable fashion

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

approximately achieving gaussian relay network capacity with lattice based qmf codes recently a new relaying strategy quantize map and forward qmf scheme has been demonstrated to approximately achieve within an additive constant number of bits the gaussian relay network capacity universally i e for arbitrary topologies channel gains and snrs this was established using gaussian codebooks for transmission and random mappings at the relays in this paper we develop structured lattice codes that implement the qmf strategy the main result of this paper is that such structured lattice codes can approximately achieve the gaussian relay network capacity universally again within an additive constant in addition we establish a similar result for half duplex networks where we demonstrate that one can approximately achieve the capacity using fixed transmit receive tx rx schedules for the relays with no transmit power optimization across the different tx rx states of the network

survival with competing risks and masked causes of failures consider a life testing situation in which systems are subject to failure from independent competing risks the hazards of various risks are proportional to each other when a failure occurs immediate i e stage 1 procedures are used in an attempt to reach a definitive diagnosis if a diagnosis is not reached this phenomenon is called masking stage 2 procedures such as failure analysis or autopsy provide definitive diagnosis for a small sample of the masked cases this paper shows how stage 1 and stage 2 information can be combined to provide statistical inference about a survival functions of the individual risks b the proportions of failures associated with individual risks and c probability for a specified masked case that each of the masked competing risks is responsible for the failure