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

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

an improved strength pareto evolutionary algorithm 2 with application to the optimization of distributed generations this paper presents an improved strength pareto evolutionary algorithm 2 ispea2 which introduces a penalty factor in objective function constraints uses adaptive crossover and a mutation operator in the evolutionary process and combines simulated annealing iterative process over spea2 the testing result of ispea2 by authoritative testing functions meets the requirement of petro optimum fronts the case study result shows that the proposed algorithm provides a rapid convergence in obtaining pareto optimal solutions during the calculation process of evolution based on the fuzzy set theory ispea2 is able to solve the multi objective problems in the ieee 33 bus system and its validity and practicality are demonstrated by the utilization on dg s economic dispatch and optimal operation in the field of power industry

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

aligned image sets under channel uncertainty settling conjectures on the collapse of degrees of freedom under finite precision csit a conjecture made by lapidoth et al at allerton 2005 also an open problem presented at ita 2006 states that the degrees of freedom dof of a two user broadcast channel where the transmitter is equipped with two antennas and each user is equipped with one antenna must collapse under finite precision channel state information at the transmitter csit that this conjecture which predates interference alignment has remained unresolved is emblematic of a pervasive lack of understanding of the dof of wireless networks including interference and x networks under channel uncertainty at the transmitter s in this paper we prove that the conjecture is true in all non degenerate settings e g where the probability density function of unknown channel coefficients exists and is bounded the dof collapse even when perfect channel knowledge for one user is available to the transmitter this also settles a related recent conjecture by tandon et al the key to our proof is a bound on the number of codewords that can cast the same image within noise distortion at the undesired receiver whose channel is subject to finite precision csit while remaining resolvable at the desired receiver whose channel is precisely known by the transmitter we are also able to generalize the result along two directions first if the peak of the probability density function is allowed to scale as o sqrt p alpha representing the concentration of probability density improving csit due to e g quantized feedback at rate alpha 2 log p then the dof is bounded above by 1 alpha which is also achievable under quantized feedback second we generalize the result to arbitrary number of antennas at the transmitter arbitrary number of single antenna users and complex channels the generalization directly implies a collapse of dof to unity under non degenerate channel uncertainty for the general k user interference and m times n user x networks as well

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

asymptotic interference alignment for optimal repair of mds codes in distributed storage the high repair bandwidth cost of n k maximum distance separable mds erasure codes has motivated a new class of codes that can reduce repair bandwidth over that of conventional mds codes in this paper we address n k d exact repair mds codes which allow for any single failed node to be repaired exactly with access to any arbitrary set of d survivor nodes we show the existence of exact repair mds codes that achieve minimum repair bandwidth matching the cut set lower bound for arbitrary admissible n k d i e k d n 1 moreover we extend our results to show the optimality of our codes for multiple node failure scenarios in which an arbitrary set of r n k failed nodes needs to repaired our approach is based on asymptotic interference alignment proposed by cadambe and jafar as a byproduct we also characterize the capacity of a class of multisource nonmulticast networks

on feasibility of interference alignment in mimo interference networks we explore the feasibility of interference alignment in signal vector space based only on beamforming for k user mimo interference channels our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry it is well known e g from bezout s theorem that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables following this intuition we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables rigorous connections between feasible and proper systems are made through bernshtein s theorem for the case where each transmitter uses only one beamforming vector the multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems in this case we show that the connection between feasible and proper systems can be further strengthened since the equivalency between feasible and proper systems does not always hold by including standard information theoretic outer bounds in the feasibility analysis

rank matching for multihop multiflow we study the degrees of freedom dof of the layered 2 times 2 times 2 multiple input multiple output mimo interference channel where each node is equipped with arbitrary number of antennas the channels between the nodes have arbitrary rank constraints and subject to the rank constraints the channel coefficients can take arbitrary values the dof outer bounds reveal a fundamental rank matching phenomenon reminiscent of impedance matching in circuit theory it is well known that the maximum power transfer in a circuit is achieved not for the maximum or minimum load impedance but for the load impedance that matches the source impedance similarly the maximum dof in the rank constrained 2 times 2 times 2 mimo interference network is achieved not for the maximum or minimum ranks of the destination hop but when the ranks of the destination hop match the ranks of the source hop in fact for mismatched settings of interest the outer bounds identify a dof loss penalty that is precisely equal to the rank mismatch between the two hops for symmetric settings we also provide achievability results to show that along with the min cut max flow bounds the rank mismatch bounds are the best possible i e they hold for all channels that satisfy the rank constraints and are tight for almost all channels that satisfy the rank constraints limited extensions from sum dof to dof region from 2 unicasts to x message sets from 2 hops to more than 2 hops and from 2 nodes per layer to more than 2 nodes per layer are considered to illustrate how the insights generalize beyond the elemental 2 times 2 times 2 channel model

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

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

subspace alignment chains and the degrees of freedom of the three user mimo interference channel we show that the three user mt mr multiple input multiple output mimo interference channel where each transmitter is equipped with mt antennas and each receiver is equipped with mr antennas has m d m n min m 2 1 n 2 1 degrees of freedom dof normalized by time frequency and space dimensions where min mt mr n max mt mr m n m while the dof outer bound of d m n is established for every mt mr value the achievability of d m n dof is established in general subject to a normalization with respect to spatial extensions i e the scaling of the number of antennas at all nodes in particular we show that qd m n dof are achievable for the three user qmt qmr mimo interference channel for some positive integer q which may be seen as a spatial extension factor q is the scaling factor needed to make the value qd m n an integer given spatial extensions the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency in the absence of spatial extensions it is shown through examples how essentially the same interference alignment scheme may be applied over time extensions over either constant or time varying channels the central new insight to emerge from this paper is the notion of subspace alignment chains as the dof bottlenecks the subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the dof outer bound as well as in the construction of the optimal interference alignment schemes the dof value d m n is a piecewise linear function of m n with either m or n being the bottleneck within each linear segment whereas the other value contains some redundancy i e it can be reduced without reducing the dof the corner points of these piecewise linear segments correspond to two sets a 1 2 2 3 3 4 and b 1 3 3 5 5 7 the set a contains all those values of m n and only those values of m n for which there is redundancy in both m and n i e either can be reduced without reducing the dof the set b contains all those values of m n and only those values of m n for which there is no redundancy in either m or n i e neither can be reduced without reducing the dof because a and b represent settings with maximum and minimum redundancy essentially they are the basis for the dof outer bounds and inner bounds respectively our results settle the question of feasibility of linear interference alignment introduced previously by cenk et al for the three user mt mr mimo interference channel completely for all values of mt mr in particular we show that the linear interference alignment problem mt mr d 3 as defined in previous paper by cenk et al is feasible if and only if d d m n with the exception of the values m n b and only with that exception we show that for every m n value there are proper systems as defined by cenk et al that are not feasible evidently the redundancy contained in all other values of m n manifests itself as superfluous variables that are not discounted in the definition of proper systems thus creating a discrepancy between proper and feasible systems our results show that m n a are the only values for which there is no dof benefit of joint processing among co located antennas at the transmitters or receivers this may also be seen as a consequence of the maximum redundancy in the m n a settings

index coding an interference alignment perspective author s maleki h cadambe vr jafar sa abstract the index coding problem is studied from an interference alignment perspective providing new results as well as new insights into and generalizations of previously known results an equivalence is established between the capacity of multiple unicast index coding where each message is desired by exactly one receiver and groupcast index coding where a message can be desired by multiple receivers which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints and generalizations to feasibility of rate 1 l 1 per message when each destination desires at least l messages are similarly obtained finally capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks the solutions are based on vector linear coding 1963 2012 ieee

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

on the degrees of freedom of finite state compound wireless networks we explore the degrees of freedom dof of three classes of finite state compound wireless networks in this paper first we study the multiple input single output miso finite state compound broadcast channel bc with arbitrary number of users and antennas at the transmitter in prior work weingarten have found inner and outer bounds on the dof with 2 users the bounds have a different character while the inner bound collapses to unity as the number of states increases the outer bound does not diminish with the increasing number of states beyond a threshold value it has been conjectured that the outer bound is loose and the inner bound represents the actual dof in the complex setting all signals noise and channel coefficients are complex variables we solve a few cases to find that the outer bound and not the inner bound of weingarten is tight for the real setting all signals noise and channel coefficients are real variables we completely characterize the dof once again proving that the outer bound of weingarten is tight we also extend the results to arbitrary number of users second we characterize the dof of finite state scalar single antenna nodes compound x networks with arbitrary number of users in the real setting third we characterize the dof of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting the key finding is that scalar interference networks and real x networks do not lose any dof due to channel uncertainty at the transmitter in the finite state compound setting the finite state compound miso bc does lose dof relative to the perfect csit scenario however what is lost is only the dof benefit of joint processing at transmit antennas without which the miso bc reduces to an x network

interlinked cycles for index coding generalizing cycles and cliques we consider a graphical approach to index coding as cycles have been shown to provide coding gain cycles and cliques a specific type of overlapping cycles have been exploited in an existing literature in this paper we define a more general form of overlapping cycles called the interlinked cycle mathsf ic structure that generalizes cycles and cliques we propose a scheme called the interlinked cycle cover mathsf icc scheme that leverages mathsf ic structures in digraphs to construct scalar linear index codes we characterize a class of infinitely many digraphs where our proposed scheme is optimal over all linear and non linear index codes consequently for this class of digraphs we indirectly prove that scalar linear index codes are optimal furthermore we show that the mathsf icc scheme can outperform all the existing graph based schemes including partial clique cover and fractional local chromatic number schemes and a random coding scheme namely composite coding for certain graphs

nonintersecting subspaces based on finite alphabets two subspaces of a vector space are here called nonintersecting if they meet only in the zero vector motivated by the design of noncoherent multiple antenna communications systems we consider the following question how many pairwise nonintersecting m sub t dimensional subspaces of an m dimensional vector space v over a field f can be found if the generator matrices for the subspaces may contain only symbols from a given finite alphabet a spl sube f the most important case is when f is the field of complex numbers c then m sub t is the number of antennas if a f gf q it is shown that the number of nonintersecting subspaces is at most q sup m 1 q sup mt 1 and that this bound can be attained if and only if m is divisible by m sub t furthermore these subspaces remain nonintersecting when lifted to the complex field it follows that the finite field case is essentially completely solved in the case when f c only the case m sub t 2 is considered it is shown that if a is a psk configuration consisting of the 2 sup r complex roots of unity the number of nonintersecting planes is at least 2 sup r m 2 and at most 2 sup r m 1 1 the lower bound may in fact be the best that can be achieved

an efficient solution to multi objective control problems with lmi objectives we revisit a technique for solving multi objective control problems through affinely parameterizing the closed loop system with the youla parameterization and confining the search of the youla parameter to finite dimensional subspaces it is pretty well known how to solve such problems if the closed loop specifications are formulated in terms of the solvability of linear matrix inequalities however all approaches proposed so far suffer from a substantial inflation of size of the resulting optimization problems if improving the approximation accuracy on the basis of a novel state space approach to solving static output feedback control problems by convex optimization for a specific class of plants we reveal how the growth of the size of the optimization problems can be considerably reduced to arrive at more efficient algorithms as an additional ingredient we discuss how to use the so called mixed controller as a starting point for a genuine multi objective design in order to improve the algorithms

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

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

the ergodic capacity of phase fading interference networks we identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a k user phase fading interference network i e an interference network where the fading process is restricted primarily to independent and uniform phase variations while the channel magnitudes are held fixed across time it is shown that even though there are k k 1 cross links only about k 2 disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels this scenario is called a minimal bottleneck state it is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state the results are applied to large networks it is shown that large networks are close to bottleneck states with a high probability so that ergodic interference alignment is close to optimal for large networks limitations of the notion of bottleneck states are also highlighted for channels where both the phase and the magnitudes vary with time it is shown through an example that for these channels joint coding across different bottleneck states makes it possible to circumvent the capacity bottlenecks

research on quality performance conceptual design based on spea2 in order to solve the multi objective performance optimal problems spea2 is used to realize the performance design of injection molding machine the optimization objectives are constructed to maximize mould control power maximize injection quantity and minimize injection power the mathematical model is found to optimize the problem a solution is extracted to eliminate the imprecise nature of preference through the pareto optimal set based on fuzzy set theory compared with nsga ii and spea2 spea2 could acquire the pareto front with better distribution and smaller distance with the optimum solutions finally the case illustration of htg1000x3y injection molding machine is taken as an example to demonstrate that such method is effective and practical effective references could be provided to decision makers for objectives tradeoff at the performance conceptual design stage of injection molding machine

mapping class group and a global torelli theorem for hyperkahler manifolds a mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies we compute a mapping class group of a hyperkahler manifold m showing that it is commensurable to an arithmetic lattice in so 3 b2 3 a teichmuller space of m is a space of complex structures on m up to isotopies we define a birational teichmuller space by identifying certain points corresponding to bimeromorphically equivalent manifolds we show that the period map gives the isomorphism between connected components of the birational teichmuller space and the corresponding period space so b2 3 3 so 2 so b2 3 1 we use this result to obtain a torelli theorem identifying each connected component of the birational moduli space with a quotient of a period space by an arithmetic group when m is a hilbert scheme of n points on a k3 surface with n 1 a prime power our torelli theorem implies the usual hodge theoretic birational torelli theorem for other examples of hyperkahler manifolds the hodge theoretic torelli theorem is known to be false

topological interference management with reconfigurable antennas we study the symmetric degrees of freedom dof of partially connected interference networks under linear coding strategies without channel state information at the transmitters beyond topology we assume that the receivers are equipped with reconfigurable antennas that can switch among their preset modes in such a network setting we characterize the class of network topologies in which half linear symmetric dof is achievable moreover we derive two general upper bounds on the linear symmetric dof for arbitrary network topologies we also demonstrate the tightness of our bounds for the class of network topologies in which all the transmitters in the network have at most two co interferers

on the synergistic benefits of alternating csit for the miso broadcast channel the degrees of freedom dofs of the two user multiple input single output miso broadcast channel bc are studied under the assumption that the form ii i 1 2 of the channel state information at the transmitter csit for each user s channel can be either perfect p delayed d or not available n i e i1 i2 p n d and therefore the overall csit can alternate between the nine resulting states i1i2 the fraction of time associated with csit state i1i2 is denoted by the parameter i1i2 and it is assumed throughout that i1i2 i2i1 i e pn np pd dp dn nd under this assumption of symmetry the main contribution of this paper is a complete characterization of the dof region of the two user miso bc with alternating csit surprisingly the dof region is found to depend only on the marginal probabilities p d n i2 pi2 i2 di2 i2 ni2 i2 p d n which represent the fraction of time that any given user e g user 1 is associated with perfect delayed or no csit respectively as a consequence the dof region with all nine csit states d i1i2 i1 i2 p d n is the same as the dof region with only three csit states d pp dd nn under the same marginal distribution of csit states i e pp dd nn p d n the sum dof value can be expressed as dof min 4 2 p 3 1 p d from which one can uniquely identify the minimum required marginal csit fractions to achieve any target dof value as p d min 3 2 dof 2 1 1 2 dof when dof 4 3 2 and p d min 0 dof 1 when dof 0 4 3 the results highlight the synergistic benefits of alternating csit and the tradeoffs between various forms of csit for any given dof value partial results are also presented for the multiuser miso bc with m transmit antennas and k single antenna users for this problem the minimum amount of perfect csit required per user to achieve the maximum dofs of min m k is characterized by the minimum amount of csit per user we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous csit from a user through a novel converse proof and an achievable scheme it is shown that the minimum fraction of time perfect csit is required per user in order to achieve the dof of min m k is given by min m k k

a theory of network equivalence part i point to point channels a family of equivalence tools for bounding network capacities is introduced given a network n with node set v the capacity of n is a set of non negative vectors with elements corresponding to all possible multicast connections in n a vector is in the capacity region for n if and only if it is possible to simultaneously and reliably establish all multicast connections across n at the given rates any other demand type with independent messages is a special case of this multiple multicast problem and is therefore included in the given rate region in part i we show that the capacity of a network n is unchanged if any independent memoryless point to point channel in n is replaced by a noiseless bit pipe with throughput equal to the removed channel s capacity it follows that the capacity of a network comprised entirely of such point to point channels equals the capacity of an error free network that replaces each channel by a noiseless bit pipe of the corresponding capacity a related separation result was known previously for a single multicast connection over an acyclic network of independent memoryless point to point channels our result treats general connections e g a collection of simultaneous unicasts and allows cyclic or acyclic networks

an equivalence between network coding and index coding we show that the network coding and index coding problems are equivalent this equivalence holds in the general setting which includes linear and nonlinear codes specifically we present a reduction that maps a network coding instance to an index coding instance while preserving feasibility i e the network coding instance has a feasible solution if and only if the corresponding index coding instance is feasible in addition we show that one can determine the capacity region of a given network coding instance with colocated sources by studying the capacity region of a corresponding index coding instance previous connections between network and index coding were restricted to the linear case

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

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

on the index coding problem and its relation to network coding and matroid theory the index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks an instance of the index coding problem includes a sender that holds a set of information messages x x1 xk and a set of receivers r each receiver x h in r needs to obtain a message x x and has prior side information consisting of a subset h of x the sender uses a noiseless communication channel to broadcast encoding of messages in x to all clients the objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers in this paper we analyze the relation between the index coding problem the more general network coding problem and the problem of finding a linear representation of a matroid in particular we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem specifically we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions

topological interference management with transmitter cooperation interference networks with no channel state information at the transmitter except for the knowledge of the connectivity graph have been recently studied under the topological interference management framework in this paper we consider a similar problem with topological knowledge but in a distributed broadcast channel setting i e a network where transmitter cooperation is enabled we show that the topological information can also be exploited in this case to strictly improve the degrees of freedom dof as long as the network is not fully connected which is a reasonable assumption in practice achievability schemes from graph theoretic and interference alignment perspectives are proposed together with outer bounds built upon generator sequence the concept of compound channel settings and the relation to index coding we characterize the symmetric dof for the so called regular networks with constant number of interfering links and identify the sufficient and or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric dof

index coding with side information motivated by a problem of transmitting supplemental data over broadcast channels birk and kol infocom 1998 we study the following coding problem a sender communicates with n receivers r1 rn he holds an input x 0 01l n and wishes to broadcast a single message so that each receiver ri can recover the bit xi each ri has prior side information about x induced by a directed graph grain nodes ri knows the bits of a in the positions j i j is an edge of g g is known to the sender and to the receivers we call encoding schemes that achieve this goal indexcodes for 0 1 n with side information graph g in this paper we identify a measure on graphs the minrank which exactly characterizes the minimum length of linear and certain types of nonlinear index codes we show that for natural classes of side information graphs including directed acyclic graphs perfect graphs odd holes and odd anti holes minrank is the optimal length of arbitrary index codes for arbitrary index codes and arbitrary graphs we obtain a lower bound in terms of the size of the maximum acyclic induced subgraph this bound holds even for randomized codes but has been shown not to be tight

interference networks with no csit impact of topology we consider partially connected k user interference networks where the transmitters have no knowledge about the channel gain values but they are aware of network topology we introduce several linear algebraic and graph theoretic concepts to derive new topology based outer bounds and inner bounds on the symmetric degrees of freedom of these networks we evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes quantify the gain of our inner bounds over benchmark interference management strategies and illustrate the effect of network topology on these gains