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

examples of non algebraic classes in the brown peterson tower for every n ge 0 we construct classes in the brown peterson cohomology bp langle n rangle of smooth projective complex algebraic varieties which are not in the image of the cycle map from the corresponding motivic brown peterson cohomology this generalizes the examples of atiyah and hirzebruch to all finite levels in the brown peterson tower

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

torsion cohomology classes and algebraic cycles on complex projective manifolds abstract atiyah and hirzebruch gave examples of even degree torsion classes in the singular cohomology of a smooth complex projective manifold which are not poincare dual to an algebraic cycle we notice that the order of these classes must be small compared to the dimension of the manifold however building upon a construction of kollar one can provide such examples with arbitrary high prime order the dimension being fixed this method also provides examples of torsion algebraic cycles which are non trivial in the griffiths group and lie in a arbitrary high level of the h saito filtration on chow groups

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

mimo interference alignment over correlated channels with imperfect csi interference alignment ia given uncorrelated channel components and perfect channel state information obtains the maximum degrees of freedom in an interference channel little is known however about how the sum rate of ia behaves at finite transmit power with imperfect channel state information or antenna correlation this paper provides an approximate closed form signal to interference plus noise ratio sinr expression for ia over multiple input multiple output mimo channels with imperfect channel state information and transmit antenna correlation assuming linear processing at the transmitters and zero forcing receivers random matrix theory tools are utilized to derive an approximation for the postprocessing sinr distribution of each stream for each user perfect channel knowledge and i i d channel coefficients constitute special cases this sinr distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate but also permits a realistic comparison of ia with other transmission techniques more specifically ia is compared with spatial multiplexing and beamforming and it is shown that ia may not be optimal for some performance criteria

hyperbolic boundary value problems for symmetric systems with variable multiplicities abstract we extend the kreiss majda theory of stability of hyperbolic initial boundary value and shock problems to a class of systems notably including the equations of magnetohydrodynamics mhd for which majda s block structure condition does not hold namely simultaneously symmetrizable systems with characteristics of variable multiplicity satisfying at points of variable multiplicity either a totally nonglancing or a nonglancing and linearly splitting condition at the same time we give a simple characterization of the block structure condition as geometric regularity of characteristics defined as analyticity of associated eigenprojections the totally nonglancing or nonglancing and linearly splitting conditions are generically satisfied in the simplest case of crossings of two characteristics and likewise for our main physical examples of mhd or maxwell equations for a crystal together with previous analyses of spectral stability carried out by gardner kruskal and blokhin trakhinin this yields immediately a number of new results of nonlinear inviscid stability of shock waves in mhd in the cases of parallel or transverse magnetic field and recovers the sole previous nonlinear result obtained by blokhin trakhinin by direct dissipative integral methods of stability in the zero magnetic field limit we also discuss extensions to the viscous case

from algebraic cobordism to motivic cohomology let s be an essentially smooth scheme over a eld of characteristic exponent c we prove that there is a canonical equivalence of motivic spectra over s mgl a1 a2 1 c hz 1 c where hz is the motivic cohomology spectrum mgl is the algebraic cobordism spectrum and the elements an are generators of the lazard ring we discuss several applications including the computation of the slices of z 1 c local landweber exact motivic spectra and the convergence of the associated slice spectral sequences

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

emergence of unstable modes for classical shock waves in isothermal ideal mhd abstract this note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity for this mathematically prototypical material it identifies mainly numerically two critical manifolds in parameter space across which slow resp fast mhd shock waves undergo emergence of a complex conjugate pair of unstable transverse modes for slow shocks this emergence occurs in a particularly interesting way already in the parallel case in which it happens at the spectral value 0 and the critical manifold possesses a simple explicit algebraic representation results of refined numerical treatment show that within the set of non parallel slow shocks the unstable mode pair emerges from two generically different spectral values i for fast shocks the critical manifold does not intersect the parallel regime and the emergence within the set of non parallel fast shocks again starts from two generically different spectral values

spectra of linear relations _ series and cohomology of eilenberg mac lane spaces on brown peterson cohomology groups of a space we introduce a natural inherent topology bp topology which is always complete hausdorff for any space we then construct a spectra map which calculates infinite bp linear sums convergent with respect to the bp topology and a spectrum which describes infinite sum bp linear relations in bp cohomology the mod p cohomology of this spectrum is a cyclic module over the steenrod algebra with relations generated by products of exactly two milnor primitives we show a close relationship between bp linear relations in bp cohomology and the action of the milnor primitives on mod p cohomology we prove main relations in the bp cohomology of eilenberg mac lane spaces these are infinite sum bp linear relations convergent with respect to the bp topology using bp fundamental classes we define v series which are v analogues of the p series finally we show that the above main relations come from the vn series

torsion algebraic cycles and etale cobordism we prove that the classical integral cycle class map from algebraic cycles to etale cohomology factors through a quotient of l adic etale cobordism over an algebraically closed field of positive characteristic this shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of atiyah hirzebruch and totaro also work in positive characteristic

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

structural stability of shock waves in 2d compressible elastodynamics we study the two dimensional structural stability of shock waves in a compressible isentropic inviscid elastic material in the sense of the local in time existence and uniqueness of discontinuous shock front solutions of the equations of compressible elastodynamics in two space dimensions by the energy method based on a symmetrization of the wave equation and giving an a priori estimate without loss of derivatives for solutions of the constant coefficients linearized problem we find a condition sufficient for the uniform stability of rectilinear shock waves comparing this condition with that for the uniform stability of shock waves in isentropic gas dynamics we make the conclusion that the elastic force plays stabilizing role in particular we show that as in isentropic gas dynamics all compressive shock waves are uniformly stable for convex equations of state moreover for some particular deformations and general equations of state by the direct test of the uniform kreiss lopatinski condition we show that the stability condition found by the energy method is not only sufficient but also necessary for uniform stability as is known uniform stability implies structural stability of corresponding curved shock waves

a complete 2d stability analysis of fast mhd shocks in an ideal gas an algorithm of numerical testing of the uniform lopatinski condition for linearized stability problems for 1 shocks is suggested the algorithm is used for finding the domains of uniform stability neutral stability and instability of planar fast mhd shocks a complete stability analysis of fast mhd shock waves is first carried out in two space dimensions for the case of an ideal gas main results are given for the adiabatic constant 5 3 mono atomic gas that is most natural for the mhd model the cases 7 5 two atomic gas and 5 3 are briefly discussed not only the domains of instability and linear in the usual sense stability but also the domains of uniform stability for which a corresponding linearized stability problem satisfies the uniform lopatinski condition are numerically found for different given angles of inclination of the magnetic field behind the shock to the planar shock front as is known uniform linearized stability implies the nonlinear stability that is local existence of discontinuous shock front solutions of a quasilinear system of hyperbolic conservation laws

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

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

on the cohomology of elementary abelian groups the structure of the bp cohomology of elementary abelian p groups is studied obtaining a presentation expressed in terms of bp cohomology and mod p singular cohomology using the milnor derivations the arguments are based on a result on multi koszul complexes which is related to margolis s criterion for freeness of a graded module over an exterior algebra

mimo minimum total mse transceiver design with imperfect csi at both ends this paper presents new results on joint linear transceiver design under the minimum total mean square error mse criterion with channel mean as well as both transmit and receive correlation information at both ends of a multiple input multiple output mimo link the joint design is formulated into an optimization problem the optimum closed form precoder and decoder are derived compared to the case with perfect channel state information csi linear filters are added at both ends to balance the suppression of channel noise and the noise from imperfect channel estimation the impact of channel estimation error as well as channel correlation on system performance is assessed based on analytical and simulation results

one dimensional stability of parallel shock layers in isentropic magnetohydrodynamics abstract extending investigations of barker humpherys lafitte rudd and zumbrun for compressible gas dynamics and freistuhler and trakhinin for compressible magnetohydrodynamics we study by a combination of asymptotic ode estimates and numerical evans function computations the one dimensional stability of parallel isentropic magnetohydrodynamic shock layers over the full range of physical parameters shock amplitude strength of imposed magnetic field viscosity magnetic permeability and electrical resistivity for a law gas with 1 3 other values may be treated similarly but were not checked numerically depending on magnetic field strength these shocks may be of fast lax intermediate overcompressive or slow lax type however the shock layer is independent of magnetic field consisting of a purely gas dynamical profile in each case our results indicate stability interesting features of the analysis are the need to renormalize the evans function in order to pass continuously across parameter values where the shock changes type or toward the large amplitude limit at frequency 0 and the systematic use of winding number computations on riemann surfaces

least squares approach to joint beam design for interference alignment in multiuser multi input multi output interference channels in this correspondence the problem of interference alignment for k user time invariant multi input multi output interference channels is considered the necessary and sufficient conditions for interference alignment are converted to a system of linear equations that have dummy variables based on this linear system a new algorithm for beam design for interference alignment is proposed by minimizing the overall interference misalignment the proposed algorithm consists of solving a least squares problem iteratively the convergence of the proposed algorithm is established and its complexity is analyzed the performance of the proposed algorithm is also evaluated numerically it is shown that the proposed algorithm has faster convergence and lower complexity than the previous method with a comparable sum rate performance in the most practical case of two receive antennas

torsion algebraic cycles and complex cobordism atiyah and hirzebruch gave the first counterexamples to the hodge conjecture with integral coefficients 3 that conjecture predicted that every integral cohomology class of hodge type p p on a smooth projective variety should be the class of an algebraic cycle but atiyah and hirzebruch found additional topological properties which must be satisfied by the integral cohomology class of an algebraic cycle here we provide a more systematic explanation for their results by showing that the classical cycle map from algebraic cycles modulo algebraic equivalence to integral cohomology factors naturally through a topologically defined ring which is richer than integral cohomology the new ring is based on complex cobordism a well developed topological theory which has been used only rarely in algebraic geometry since hirzebruch used it to prove the riemann roch theorem 17 this factorization of the classical cycle map implies the topological restrictions on algebraic cycles found by atiyah and hirzebruch it goes beyond their work by giving a topological method to show that the classical cycle map can be noninjective as well as nonsurjective the kernel of the classical cycle map is called the griffiths group and the topological proof here that the griffiths group can be nonzero is the first proof of this fact which does not use hodge theory the proof here gives nonzero torsion elements in the griffiths group whereas griffiths s hodge theoretic proof gives nontorsion elements 13 this topological argument also gives examples of algebraic cycles in the kernel of various related cycle maps where few or no examples were known before thus answering some questions posed by colliot thelene and schoen 8 p 14 37 p 13 colliot thelene asked in particular whether the map ch2 x n h4 x z n is injective for all smooth complex projective varieties x here ch x is the group of codimension i algebraic cycles modulo rational equivalence the first examples where colliot thelene s map is not injective were found by kollar and van geemen see 4 p 135 very recently bloch and esnault found examples defined over number fields 7 over nonalgebraically closed fields k there are other examples of smooth projective varieties xk with ch2 xk n hg4t xk z n not injective due to colliot thelene and sansuc as reinterpreted by salberger see 9 and 8 remark 7 6 1 and parimala and suresh 31 these elements of ch2 xk n are not shown to remain nonzero in ch2 xc n however here our topological method