the poisson multiple access channel the poisson multiple access channel mac models many to one optical communication through an optical fiber or in free space for this model we compute the capacity region for the two user case as a function of the allowed peak power focusing on the maximum throughput we generalize our results to the case where the users are subjected to an additional average power constraint and to the many users case we show that contrary to the gaussian mac in the poisson mac the maximum throughput is bounded in the number of users we quantify the loss that is incurred when time division multiple access tdma is employed and show that while in the two user case and in the absence of dark current the penalty is rather mild the penalty can be quite severe in the many users case in the presence of large dark current we introduce a generalized tdma technique that mitigates this loss to a large extent

rotational surfaces in mathbb l 3 and solutions of the nonlinear sigma model the gauss map of non degenerate surfaces in the three dimensional minkowski space are viewed as dynamical fields of the two dimensional o 2 1 nonlinear sigma model in this setting the moduli space of solutions with rotational symmetry is completely determined essentially the solutions are warped products of orbits of the 1 dimensional groups of isometries and elastic curves in either a de sitter plane a hyperbolic plane or an anti de sitter plane the main tools are the equivalence of the two dimensional o 2 1 nonlinear sigma model and the willmore problem and the description of the surfaces with rotational symmetry a complete classification of such surfaces is obtained in this paper indeed a huge new family of lorentzian rotational surfaces with a space like axis is presented the description of this new class of surfaces is based on a technique of surgery and a gluing process which is illustrated by an algorithm

multipliers and dual operator algebras abstract in a previous paper we showed how the main theorems characterizing operator algebras and operator modules fit neatly into the framework of the noncommutative shilov boundary and more particularly via the left multiplier operator algebra of an operator space as well as giving new characterization theorems the approach of that paper allowed many of the hypotheses of the earlier theorems to be eliminated recent progress of the author with effros and zarikian now enables weak versions of these characterization theorems for example we prove a result analogous to sakai s famous characterization of von neumann algebras as the c algebras with predual namely that the weakly closed unital not necessarily selfadjoint subalgebras of b h for a hilbert space h are exactly the unital operator algebras which possess an operator space predual this removes one of the hypotheses from an earlier characterization due to le merdy we also show that the multiplier operator algebras of dual operator spaces are dual operator algebras using this we refine several known results characterizing dual operator modules

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

randomized resource allocation in decentralized wireless networks in this paper we consider a decentralized wireless communication network with a fixed number u of frequency subbands to be shared among n transmitter receiver pairs it is assumed that the number of active users is a realization of a random variable with a given probability mass function moreover users are unaware of each other s codebooks and hence no multiuser detection is possible we propose a randomized frequency hopping fh scheme in which each transmitter randomly hops over a subset of u subbands from transmission slot to transmission slot assuming all users transmit gaussian signals the distribution of the noise plus interference is mixed gaussian which makes calculation of the mutual information between the transmitted and received signals of each user intractable we derive lower and upper bounds on the mutual information of each user and demonstrate that for large signal to noise ratio snr values the two bounds coincide this observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity we compare the performance of the fh system to that of the frequency division fd system in terms of the following performance measures average sum multiplexing gain 1 and average minimum multiplexing gain per user 2 we show that depending on the probability mass function of the number of active users the fh system can offer a significant improvement in terms of 1 and 2 implying a more efficient usage of the spectrum in the sequel we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains developing a new upper bound on the differential entropy of a mixed gaussian random vector and using entropy power inequality we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given snr level we demonstrate that the so called outage capacity can be considerably higher in the fh scheme than in the fd scenario for reasonable distributions on the number of active users this guarantees a higher spectral efficiency in fh compared to fd

random sequence multisets for synchronous code division multiple access channels the effect of using randomly selected sequence multisets for the uplink of a synchronous code division multiple access channel is considered a tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given for large systems the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as the number of users becomes large compared to the sequence length

asymptotically optimal multiple access communication via distributed rate splitting we consider the multiple access communication problem in a distributed setting for both the additive white gaussian noise channel and the discrete memoryless channel we propose a scheme called distributed rate splitting to achieve the optimal rates allowed by information theory in a distributed manner in this scheme each real user creates a number of virtual users via a power rate splitting mechanism in the m user gaussian channel or via a random switching mechanism in the m user discrete memoryless channel at the receiver all virtual users are successively decoded compared with other multiple access techniques distributed rate splitting drs can be implemented with lower complexity and less coordination furthermore in a symmetric setting we show that the rate tuple achieved by this scheme converges to the maximum equal rate point allowed by the information theoretic bound as the number of virtual users per real user tends to infinity when the capacity regions are asymmetric we show that a point on the dominant face can be achieved asymptotically finally when there is an unequal number of virtual users per real user we show that differential user rate requirements can be accommodated in a distributed fashion

asynchronous communication exact synchronization universality and dispersion recently tchamkerten and coworkers proposed a novel variation of the problem of joint synchronization and error correction this paper considers a strengthened formulation that requires the decoder to estimate both the message and the location of the codeword exactly such a scheme allows for transmitting data bits in the synchronization phase of the communication thereby improving bandwidth and energy efficiencies it is shown that the capacity region remains unchanged under the exact synchronization requirement furthermore asynchronous capacity can be achieved by universal channel independent codes comparisons with earlier results on another delay compensated definition of rate are made the finite blocklength regime is investigated and it is demonstrated that even for moderate blocklengths it is possible to construct capacity achieving codes that tolerate exponential level of asynchronism and experience only a rather small loss in rate compared to the perfectly synchronized setting in particular the channel dispersion does not suffer any degradation due to asynchronism for the binary symmetric channel a translation coset of a good linear code is shown to achieve the capacity synchronization tradeoff

symmetric capacity and signal design for l out of k symbol synchronous cdma gaussian channels we consider the symbol synchronous gaussian l out of k code division multiaccess channel and obtain the capacity region and the upper and lower bounds to the symmetric capacity the capacity region is found to be the same with or without frame synchronism the lower bound depends on the signature waveforms through the eigenvalues of the snr weighted crosscorrelation matrix we find a sufficient condition for the signature waveform set to maximize this lower bound and give an algorithm to construct a set of signature waveforms satisfying the sufficient condition

a formulation of the channel capacity of multiple access channel the necessary and sufficient condition of the channel capacity is rigorously formulated for the n user discrete memoryless multiple access channel mac the essence is to invoke an elementary mac where sizes of input alphabets are not greater than the size of output alphabet the main objective is to demonstrate that the channel capacity of an mac is achieved by an elementary mac included in the original mac the proof is quite straightforward by the very definition of the elementary mac the second objective is to prove that the kuhn tucker conditions of the elementary mac are sufficient obviously necessary for the channel capacity the latter proof requires two distinctive properties of the mac every solution of the kuhn tucker conditions is a local maximum on the domain of all possible input probability distributions ipds and then particularly for the elementary mac a set of ipds for which the value of the mutual information is not smaller than the arbitrary positive number is connected on the domain as a result in respect of the channel capacity the mac in general can be regarded as an aggregate of a finite number of elementary macs

duality and operator algebras automatic weak continuity and applications abstract we investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras and give several applications of the surprising fact that certain maps are always weak continuous on dual spaces in particular if x is a subspace of a c algebra a and if a a satisfies ax x then we show that the function x ax on x is automatically weak continuous if either a x is a dual operator space or b a x x and x is a dual banach space these results hinge on a generalization to banach modules of tomiyama s famous theorem on contractive projections onto a c subalgebra applications include a new characterization of the weakly closed possibly nonunital and nonselfadjoint operator algebras and a generalization of the theory of w modules to the framework of modules over such algebras we also give a banach module characterization of weakly closed spaces of operators which are invariant under the action of a von neumann algebra

stably isomorphic dual operator algebras we prove that two unital dual operator algebras a b are stably isomorphic if and only if they are equivalent eleftherakis in j pure appl algebra arxiv math oa 0607489v4 2007 if and only if they have completely isometric normal representations on hilbert spaces h k respectively and there exists a ternary ring of operators mathcal m subset b h k such that alpha a mathcal m beta b mathcal m w and beta b mathcal m alpha a mathcal m w

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

quickest sequence phase detection a phase detection sequence is a length n cyclic sequence such that the location of any length k contiguous subsequence can be determined from a noisy observation of that subsequence in this paper we derive bounds on the minimal possible k in the limit of n to infty and describe some sequence constructions we further consider multiple phase detection sequences where the location of any length k contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences we study the optimal trade offs between the lengths of the sequences and describe some sequence constructions we compare these phase detection problems to their natural channel coding counterparts and show a strict separation between the fundamental limits in the multiple sequence case both adversarial and probabilistic noise models are addressed

on lorentzian surfaces with h2 k in minkowski 3 space abstract a well known classical result classifies the surfaces in 3 space r 3 with the mean curvatures h and the gauss curvatures k satisfying h 2 k as pieces of planes or two spheres corresponding results are given here for lorentzian surfaces in minkowski 3 space this work is done by proving that all the lorentzian surfaces with h 2 k in minkowski 3 space are null scrolls locally and can be classified into three cases two of which have no counterparts in euclidean space

an operator space characterization of dual operator algebras this paper is devoted to dual algebras that is w closed algebras of bounded operators on hilbert space we give abstract characterizations of unital dual algebras resp dual algebras up to w homeomorphic unital complete isometry resp complete isomorphism the results we obtain are natural w versions of analogous characterizations due to blecher ruan sinclair and blecher respectively in the category of operator algebras

the capacity region of the totally asynchronous multiple access channel it is shown that the capacity region of the asynchronous multiple access channel differs from that of the synchronous channel only by the lack of a convex hull operation

on the structure of the capacity region of asynchronous memoryless multiple access channels the asynchronous capacity region of memoryless multiple access channels is the union of certain polytopes it is well known that vertices of such polytopes may be approached via a technique called successive decoding it is also known that an extension of successive decoding applies to the dominant face of such polytopes the extension consists of forming groups of users in such a way that users within a group are decoded jointly whereas groups are decoded successively this paper goes one step further it is shown that successive decoding extends to every face of the aforementioned polytopes the group composition as well as the decoding order for all rates on a face of interest is obtained from a label assigned to that face from the label one can extract a number of structural properties such as the dimension of the corresponding face and whether or not two faces intersect expressions for the number of faces of any given dimension are also derived from the labels

logmodularity and isometries of operator algebras we generalize some facts about function algebras to operator algebras using the noncommutative shilov boundary or c envelope first considered by arveson in the first part we study and characterize complete isometries between operator algebras in the second part we introduce and study a notion of logmodularity for operator algebras we also give a result on conditional expectations many miscellaneous applications are provided

totally asynchronous slepian wolf data compression it is proved that the slepian wolf data compression theorem still holds when both encoders are operating totally asynchronously in addition it is shown that in this case the wyner ahlswede korner source coding theorem holds

rate splitting multiple access for discrete memoryless channels it is shown that the encoding decoding problem for any asynchronous m user discrete memoryless multiple access channel can be reduced to corresponding problems for at most 2m 1 single user discrete memoryless channels this result which extends a similar result for gaussian channels reduces the seemingly hard task of finding good multiple access codes to the much better understood task of finding good codes for single user channels as a by product some interesting properties of the capacity region of m user asynchronous discrete memoryless channels are derived

bjorling problem for timelike surfaces in the lorentz minkowski space abstract we solve the bjorling problem for timelike surfaces in the lorentz minkowski space through a split complex representation formula obtained for this kind of surface our approach uses the split complex numbers and natural split holomorphic extensions as applications we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate bjorling problems in the lorentz minkowski space

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces

multiple access channels with memory with and without frame synchronism the capacity region of frame synchronous and frame asynchronous discrete two user multiple access channels with finite memory is obtained frame synchronism refers to the ability of the transmitters to send their code words in unison the absence of frame synchronism in memoryless multiple access channels is known to result in the removal of the convex hull operation from the expression of the capacity region it is shown that when the channel has memory frame asynchronism rules out nonstationary inputs to achieve any point in the capacity region thereby allowing only coding strategies that involve cooperation in the frequency domain but not in the time domain this restriction drastically reduces the capacity region of some multiple access channels with memory and in particular the total capacity of the channel which is invariant to frame asynchronism for memoryless channels

helicoidal surfaces with h2 k in minkowski 3 space in this paper we prove that any helicoidal surface with h2 k in minkowski 3 space is locally a generalized umbilical surface i e a surface with the shape operator having the minimal polynomial x a 2 where a is constant we also give the representation formulas for these helicoidal surfaces

null scrolls as solutions of a sigma model the two dimensional o 2 1 nonlinear sigma model with boundary is considered we calibrate the size of its space of field configurations by exhibiting new and wide classes of solutions we first construct solutions by evolving under a certain group of transformations free elastic curves in any surface either riemannian or lorentzian of constant curvature furthermore we show that any null scroll can provide a solution of this sigma model this surprising phenomenon which obviously has no euclidean counterpart guarantees the existence of an ample class of solutions which are generated by null or lightlike curves evolving through null ruling flows

capacity region of the asynchronous gaussian vector multiple access channel in this paper we derive explicit expressions for the capacity region of the two user symbol asynchronous gaussian vector multiple access channel verdu considered the case where each user linearly modulates a fixed waveform in each symbol period where the symbol periods for the users are not perfectly aligned at the receiver he derived explicit capacity region expressions for the case where the transmitters have knowledge of the mutual offset and also for the case where the transmitters have no knowledge of the mutual offset in this paper we extend verdu s results to allow each user to linearly modulate a set of orthonormal waveforms instead of a single waveform in each symbol period and with no restrictions imposed on the waveforms we consider group power constraints which include individual sum power constraints as orthonormal waveforms assigned to each user may come from different frequency bands with different power constraints similar to the case where each user is allowed to linearly modulate only a single waveform our results hold regardless of whether or not the transmitters are frame synchronous in addition we present some results that are necessary to numerically compute the capacity region expressions with general purpose convex optimization algorithms next we simplify the capacity region expression when there are only individual sum power constraints and when the transmitters know the mutual offset we also prove a sufficient condition for a similar simplification to hold when the transmitters have no knowledge of the mutual offset finally we consider a specialized algorithm to numerically compute the simplified capacity region expression when the transmitters know the mutual offset