on optimal gaussian signaling in mimo relay channels with partial decode and forward for gaussian multiple input multiple output mimo relay channels with partial decode and forward the optimal type of input distribution is still an open question in general recent research has revealed that in some other scenarios with unknown optimal input distributions e g interference channels improper i e noncircular gaussian distributions can outperform proper circular gaussian distributions in this paper we show that this is not the case for partial decode and forward in the gaussian mimo relay channel with gaussian transmit signals i e we show that a proper gaussian input distribution is the optimal one among all gaussian distributions in order to prove this property an innovation covariance matrix is introduced and a decomposition is performed by considering the optimization over this matrix as an outer problem a key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two user mimo broadcast channel under a sum covariance constraint for which the optimality of proper signals can be shown

exponential codimension growth of pi algebras an exact estimate abstract letabe an associative pi algebra over a fieldfof characteristic zero by studying the exponential behavior of the sequence of codimensions cn a ofa we prove thatinv a limn c n a always exists and is an integer we also give an explicit way for computing such integer letbbe a finite dimensionalz2 graded algebra whose grassmann envelopeg b satisfies the same identities ofa theninv a inv g b dim c 0 dim c 1 wherec 0 c 1 is a suitablez2 graded semisimple subalgebra ofb

the freiheitssatz for poisson algebras abstract we prove the freiheitssatz for poisson algebras in characteristic zero we also give a new proof of the tameness of automorphisms for two generated free poisson algebras and show that an analogue of the commutator test theorem is equivalent to the two dimensional classical jacobian conjecture

the capacity of the semideterministic relay channel corresp the capacity of the class of relay channels with sender x 1 a relay sender x 2 a relay receiver y 1 f x 1 x 2 and ultimate receiver y is proved to be c max min p x 1 x 2 i x 1 x 2 y h y 1 x 2 i x 1 y x 2 y 1

bilayer low density parity check codes for decode and forward in relay channels this paper describes an efficient implementation of binning for decode and forward df in relay channels using low density parity check ldpc codes bilayer ldpc codes are devised to approach the theoretically promised rate of the df relaying strategy by incorporating relay generated parity bits in specially designed bilayer graphical code structures while conventional ldpc codes are sensitively tuned to operate efficiently at a certain channel parameter the proposed bilayer ldpc codes are capable of working at two different channel parameters and two different rates that at the relay and at the destination to analyze the performance of bilayer ldpc codes bilayer density evolution is devised as an extension of the standard density evolution algorithm based on bilayer density evolution a design methodology is developed for the bilayer codes in which the degree distribution is iteratively improved using linear programming further in order to approach to the theoretical df rate for a wide range of channel parameters this paper proposes two different forms of bilayer codes the bilayer expurgated and bilayer lengthened codes it is demonstrated that the rate of a properly designed bilayer ldpc code can closely approach the theoretical df limit finally it is shown that a generalized version of the proposed bilayer code construction is applicable to relay networks with multiple relays

transient and self similar dynamics in thin film coarsening abstract we study coarsening in a simplified model of one dimensional thin films of viscous fluids on hydrophobic substrates lubrication theory shows that such films are unstable and dewet to form droplets that then aggregate over long timescales the masses and positions of the droplets can be described by a coarsening dynamical system cds consisting of odes and deletion rules we develop discrete and continuous mean field models that reproduce the well known n t o t 2 5 long time statistical power law for the number of drops a lifshitz slyozov wagner type lsw continuous model predicts the self similar distribution of drop masses matching with histograms produced by cds simulations and the discrete mean field model we also describe the distribution of drops following homogeneous versus heterogeneous dewetting and use these as initial conditions for the cds simulations that yield characteristic staircasing transients transients can also include recurring spike formation behavior in the mass distribution for idealized initial conditions we show that the transient dynamics can span the full coarsening process bypassing the power law regime entirely

gaussian orthogonal relay channels optimal resource allocation and capacity a gaussian orthogonal relay model is investigated where the source transmits to the relay and destination in channel 1 and the relay transmits to the destination in channel 2 with channels 1 and 2 being orthogonalized in the time frequency plane in order to satisfy practical constraints the total available channel resource time and bandwidth is split into the two orthogonal channels and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized the main focus of the analysis is on the case where the source to relay link is better than the source to destination link which is the usual scenario encountered in practice a lower bound on the capacity achievable rate is derived and optimized over the parameter spl theta which represents the fraction of the resource assigned to channel 1 it is shown that the lower bound achieves the max flow min cut upper bound at the optimizing spl theta the common value thus being the capacity of the channel at the optimizing spl theta furthermore it is shown that when the relay to destination signal to noise ratio snr is less than a certain threshold the capacity at the optimizing spl theta is also the maximum capacity of the channel over all possible resource allocation parameters spl theta finally the achievable rates for optimal and equal resource allocations are compared and it is shown that optimizing the resource allocation yields significant performance gains

bifurcation diagram for compartmentalized granular gases the bifurcation diagram for a vibrofluidized granular gas in n connected compartments is constructed and discussed at vigorous driving the uniform distribution in which the gas is equi partitioned over the compartments is stable but when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state for the simplest case n52 this transition takes place via a pitchfork bifurcation but for all n 2 the transition involves saddle node bifurcations the associated hysteresis becomes more and more pronounced for growing n in the bifurcation diagram apart from the uniform and the one peaked distributions also a number of multipeaked solutions occur these are transient states their physical relevance is discussed in the context of a stability analysis

a discrete model for an ill posed nonlinear parabolic pde we study a finite difference discretization of an ill posed nonlinear parabolic partial differential equation the pde is the one dimensional version of a simplified two dimensional model for the formation of shear bands via anti plane shear of a granular medium for the discretized initial value problem we derive analytically and observed numerically a two stage evolution leading to a steady state i an initial growth of grid scale instabilities and ii coarsening dynamics elaborating the second phase at any fixed time the solution has a piecewise linear profile with a finite number of shear bands in this coarsening phase one shear band after another collapses until a steady state with just one jump discontinuity is achieved the amplitude of this steady state shear band is derived analytically but due to the ill posedness of the underlying problem its position exhibits sensitive dependence analyzing data from the simulations we observe that the number of shear bands at time t decays like t 1 3 from this scaling law we show that the time scale of the coarsening phase in the evolution of this model for granular media critically depends on the discreteness of the model our analysis also has implications to related ill posed nonlinear pdes for the one dimensional perona malik equation in image processing and to models for clustering instabilities in granular materials 2001 elsevier science b v all rights reserved

decorrelation of neutral vector variables theory and applications in this paper we propose novel strategies for neutral vector variable decorrelation two fundamental invertible transformations namely serial nonlinear transformation and parallel nonlinear transformation are proposed to carry out the decorrelation for a neutral vector variable which is not multivariate gaussian distributed the conventional principal component analysis cannot yield mutually independent scalar variables with the two proposed transformations a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom we also evaluate the decorrelation performances for the vectors generated from a single dirichlet distribution and a mixture of dirichlet distributions the mutual independence is verified with the distance correlation measurement the advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

bounds on capacity and minimum energy per bit for awgn relay channels upper and lower bounds on the capacity and minimum energy per bit for general additive white gaussian noise awgn and frequency division awgn fd awgn relay channel models are established first the max flow min cut bound and the generalized block markov coding scheme are used to derive upper and lower bounds on capacity these bounds are never tight for the general awgn model and are tight only under certain conditions for the fd awgn model two coding schemes that do not require the relay to decode any part of the message are then investigated first it is shown that the side information coding scheme can outperform the block markov coding scheme it is also shown that the achievable rate of the side information coding scheme can be improved via time sharing in the second scheme the relaying functions are restricted to be linear the problem is reduced to a single letter nonconvex optimization problem for the fd awgn model the paper also establishes a relationship between the minimum energy per bit and capacity of the awgn relay channel this relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy per bit that do not differ by more than a factor of 1 45 for the fd awgn relay channel model and 1 7 for the general awgn model

iterative decoding threshold analysis for ldpc convolutional codes an iterative decoding threshold analysis for terminated regular ldpc convolutional ldpcc codes is presented using density evolution techniques the convergence behavior of an iterative belief propagation decoder is analyzed for the binary erasure channel and the awgn channel with binary inputs it is shown that for a terminated ldpcc code ensemble the thresholds are better than for corresponding regular and irregular ldpc block codes

bilayer ldpc convolutional codes for decode and forward relaying in this paper we present bilayer ldpc convolutional codes for half duplex relay channels two types of codes bilayer expurgated ldpc convolutional codes and bilayer lengthened ldpc convolutional codes are proposed for decode and forward df relaying in the case of the binary erasure relay channel we prove analytically that both code constructions achieve the capacities of the source relay link and the source destination link simultaneously provided that the channel conditions are known when designing the codes meanwhile both codes enable the highest transmission rate possible with df relaying for a wide range of channel parameters in addition the regular degree distributions can easily be computed from the channel parameters which significantly simplifies the code optimization the code construction and performance analysis are extended to the general binary memoryless symmetric channel where a capacity achieving performance is conjectured numerical results are provided for both types of codes with finite node degrees over binary erasure channels and binary input additive white gaussian noise channels which verify the aforementioned theoretical analysis

poisson pi algebras we study poisson algebras satisfying polynomial identities in particular such algebras satisfy customary identities farkas 1998 1999 our main result is that the growth of the corresponding codimensions of a poisson algebra with a nontrivial identity is exponential with an integer exponent we apply this result to prove that the tensor product of poisson pi algebras is a pi algebra we also determine the growth of the poisson grassmann algebra and of the hamiltonian algebras

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

coarsening of sand ripples in mass transfer models coarsening of sand ripples is studied in a one dimensional stochastic model where neighboring ripples exchange mass with algebraic rates ensuremath gamma m ensuremath sim m ensuremath gamma and ripples of zero mass are removed from the system for ensuremath gamma l0 ripples vanish through rare fluctuations and the average ripple mass grows as m t ensuremath sim ensuremath ensuremath gamma ensuremath 1 mathrm ln t temporal correlations decay as t ensuremath 1 2 or t ensuremath 2 3 depending on the symmetry of the mass transfer and asymptotically the system is characterized by a product measure the stationary ripple mass distribution is obtained exactly for ensuremath gamma g0 ripple evolution is linearly unstable and the noise in the dynamics is irrelevant for ensuremath gamma 1 the problem is solved on the mean field level but the mean field theory does not adequately describe the full behavior of the coarsening in particular it fails to account for the numerically observed universality with respect to the initial ripple size distribution the results are not restricted to sand ripple evolution since the model can be mapped to zero range processes urn models exclusion processes and cluster cluster aggregation

transmit signal and bandwidth optimization in multiple antenna relay channels in a multiple antenna relay channel the full duplex cut set capacity upper bound and decode and forward rate are formulated as convex optimization problems for half duplex relaying bandwidth allocation and transmit signals are optimized jointly moreover achievable rates based on the compress and forward strategy are presented using rate distortion and wyner ziv compression schemes

the rate loss in the wyner ziv problem the rate distortion function for source coding with side information at the decoder the wyner ziv problem is given in terms of an auxiliary random variable which forms a markov chain with the source and the side information this markov chain structure typical to the solution of multiterminal source coding problems corresponds to a loss in coding rate with respect to the conditional rate distortion function i e to the case where the encoder is fully informed we show that for difference or balanced distortion measures this loss is bounded by a universal constant which is the minimax capacity of a suitable additive noise channel furthermore in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise test channel for example the loss in the wyner ziv problem is less than 0 5 bit sample in the squared error distortion case and it is less than 0 22 bit for a binary source with hamming distance these results have implications also in universal quantization with side information and in more general multiterminal source coding problems

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec convolutional low density parity check ldpc ensembles introduced by felstrom and zigangirov have excellent thresholds and these thresholds are rapidly increasing functions of the average degree several variations on the basic theme have been proposed to date all of which share the good performance characteristics of convolutional ldpc ensembles we describe the fundamental mechanism that explains why convolutional like or spatially coupled codes perform so well in essence the spatial coupling of individual codes increases the belief propagation bp threshold of the new ensemble to its maximum possible value namely the maximum a posteriori map threshold of the underlying ensemble for this reason we call this phenomenon threshold saturation this gives an entirely new way of approaching capacity one significant advantage of this construction is that one can create capacity approaching ensembles with an error correcting radius that is increasing in the blocklength although we prove the threshold saturation only for a specific ensemble and for the binary erasure channel bec empirically the phenomenon occurs for a wide class of ensembles and channels more generally we conjecture that for a large range of graphical systems a similar saturation of the dynamical threshold occurs once individual components are coupled sufficiently strongly this might give rise to improved algorithms and new techniques for analysis

lie structure of truncated symmetric poisson algebras abstract the paper naturally continues series of works on identical relations of group rings enveloping algebras and other related algebraic structures let l be a lie algebra over a field of characteristic p 0 consider its symmetric algebra s l n 0 u n u n 1 which is isomorphic to a polynomial ring it also has a structure of a poisson algebra where the lie product is traditionally denoted by this bracket naturally induces the structure of a poisson algebra on the ring s l s l x p x l which we call a truncated symmetric poisson algebra we study lie identical relations of s l namely we determine necessary and sufficient conditions for l under which s l is lie nilpotent strongly lie nilpotent solvable and strongly solvable where we assume that p 2 to specify the solvability we compute the strong lie nilpotency class of s l also we prove that the lie nilpotency class coincides with the strong lie nilpotency class in case p 3 shestakov proved that the symmetric algebra s l of an arbitrary lie algebra l satisfies the identity x y z 0 if and only if l is abelian we extend this result for the strong lie nilpotency and the strong solvability of s l we show that the solvability of s l and s l in case char k 2 is different from other characteristics namely we construct examples of such algebras which are solvable but not strongly solvable we use delta sets for lie algebras and the theory of identical relations of poisson algebras also we study filtrations in poisson algebras and prove results on products of terms of the lower central series for poisson algebras

filter and forward relay design for mimo ofdm systems in this paper the filter and forward ff relay design for multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated due to the considered mimo structure the ff relay design is investigated in the framework of joint design together with the linear mimo transceiver as the design criterion first the minimization of weighted sum mean square error mse is considered the joint design in this case is approached based on alternating optimization that iterates between the optimal design of the ff relay for given mimo precoding and decoding matrices and the optimal design of mimo precoding and decoding matrices for a given ff relay filter second a more advanced problem of joint design for rate maximization is considered the second problem is approached based on the obtained result regarding the first problem of weighted sum mse minimization and the existing result regarding the relationship between weighted mse minimization and rate maximization numerical results show the effectiveness of the proposed ff relay design method and significant performance improvement by the proposed ff relay over widely considered simple af relays for mimo ofdm systems

hook young diagrams with applications to combinatorics and to representations of lie superalgebras definition et etude des tableaux k l semi standards applications a la combinatoire et aux representations des superalgebres de lie des diagrammes de young a crochets