oblivious communication channels and their capacity let be c x1 xn sub 0 1 n be an n n binary error correcting code not necessarily linear let e 0 1 n be an error vector a codeword xepsic is said to be disturbed by the error e if the closest codeword to xopluse is no longer x let ae be the subset of codewords in c that are disturbed by e in this work we study the size of ae in random codes c i e codes in which each codeword is chosen uniformly and independently at random from 0 1 n using recent results of vu random structures and algorithms vol 20 no 3 pp 262 316 2002 on the concentration of non lipschitz functions we show that ae is strongly concentrated for a wide range of values of n and e we apply this result in the study of communication channels we refer to as oblivious roughly speaking a channel w y x is said to be oblivious if the error distribution imposed by the channel is independent of the transmitted codeword x a family of channels psi is said to be oblivious if every member w of the family is oblivious in this work we define oblivious and partially oblivious families of not necessarily memoryless channels and analyze their capacity when considering the capacity of a family of channels psi one must address the design of error correcting codes which allow communication under the uncertainty of which channel wepsipsi is actually used the oblivious channels we define have connections to arbitrarily varying channels with state constraints

exponential error bounds for random codes in the arbitrarily varying channel random codes for the arbitrarily varying channel are investigated the code ensemble is restricted to increase only exponentially with codeword length a quantity called key rate is used as a measure of the rate of increase the reliability function for such codes is related to the reliability function for codes with unlimited key rate explicit results are obtained in some examples of practical interest

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

bounds for a nonparametric t table summary a simple inequality for bounding the tail probabilities of normalized sums of independent symmetric random variables is used to produce bounds on the tail probabilities of the usual student t statistic under the same hypothesis the relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero as an example a table of upper 0 025 cutoff bounds is given and compared to the usual bounds some key word8 nonparametric test permutation test student t test the following theorem is based on an approach first introduced by fisher 1935 and may be used to facilitate the application of the sign permutation test he introduced since the theorem provides bounds on tail probabilities of normalized sums of independent symmetric random variables it may prove useful in a theoretical context as well

distribution free bounds for serial correlation coefficients in heteroskedastic symmetric time series abstract we consider the problem of testing whether the observations x 1 x n of a time series are independent with unspecified possibly nonidentical distributions symmetric about a common known median various bounds on the distributions of serial correlation coefficients are proposed exponential bounds eaton type bounds chebyshev bounds and berry esseen zolotarev bounds the bounds are exact in finite samples distribution free and easy to compute the performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment the procedures proposed are applied to u s data on interest rates commercial paper rate

arbitrarily varying channels with constrained inputs and states random coding theorems are proved for discrete memoryless arbitrarily varying channels avcs with constraints on the transmitted codewords and channel state sequences two types of constraints are considered peak i e required for each n length sequence almost surely and average over the message set or over an ensemble for peak constraints on the codewords and on the channel state sequences the avc is shown to have a strong random coding capacity if the codewords and or the channel state sequences are constrained in the average sense the avcs do not possess strong capacities only epsilon capacities are shown to exist

arbitrarily small amounts of correlation for arbitrarily varying quantum channels as our main result show that in order to achieve the randomness assisted message and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share asymptotically perfect common randomness rather it is sufficient that they each have access to an unlimited amount of uses of one part of a correlated bipartite source this access might be restricted to an arbitrary small nonzero fraction per channel use without changing the main result we investigate the notion of common randomness it turns out that this is a very costly resource generically it cannot be obtained just by local processing of a bipartite source this result underlines the importance of our main result also the asymptotic equivalence of the maximal and average error criterion for classical message transmission over finite arbitrarily varying quantum channels is proven at last we prove a simplified symmetrizability condition for finite arbitrarily varying quantum channels

arbitrarily varying channels with general alphabets and states previous results of csiszar and narayan 1988 1989 1991 on the capacity of discrete arbitrarily varying channels with input and state constraints are extended to the case of arbitrary alphabets and state sets for channels with scalar or vector inputs and additive interference consisting of a deterministic part and noise both arbitrarily varying subject to power constraints the capacity for deterministic codes is shown to be equal to the random coding capacity if the input power exceeds the power of the deterministic interference and zero otherwise explicit capacity formulas are also given

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

the common randomness capacity of a pair of independent discrete memoryless channels we study the following problem two agents alice and bob are connected to each other by independent discrete memoryless channels they wish to generate common randomness i e agree on a common random variable by communicating interactively over the two channels assuming that alice and bob are allowed access to independent external random sources at rates in bits per step of communication of h sub a and h sub b respectively we show that they can generate common randomness at a rate of max min h sub a h w q i p v min h sub b h v p i q w bits per step by exploiting the noise on the two channels here v is the channel from alice to bob and w is the channel from bob to alice the maximum is over all probability distributions p and q on the input alphabets of v and w respectively we also prove a strong converse which establishes the above rate as the highest attainable in this situation

the quantization conjecture revisited a strong version of the quantization conjecture of guillemin and sternberg is proved for a reductive group action on a smooth compact polarized variety x l the cohomologies of l over the git quotient x g equal the invariant part of the cohomologies over x this generalizes the theorem of gs on global sections and strengthens its subsequent extensions jk li to riemannroch numbers remarkable by products are the invariance of cohomology of vector bundles over x g under a small change in the defining polarization or under shift desingularization as well as a new proof of boutot s theorem also studied are equivariant holomorphic forms and the equivariant hodgeto de rham spectral sequences for x and its strata whose collapse is shown one application is a new proof of the borel weil bott theorem of ti for the moduli stack of c bundles over a curve and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures collapse of the hodge to de rham sequences for these stacks is also shown

on error exponents for arbitrarily varying channels the minimum probability of error achievable by random codes on the arbitrarily varying channel avc is investigated new exponential error bounds are found and applied to the avc with and without input and state constraints also considered is a simple subclass of random codes called randomly modulated codes in which encoding and decoding operations are separate from code randomization a universal coding theorem is proved which shows the existence of randomly modulated codes that achieve the same error bounds as fully random codes for all avcs

microlocalization of rational cherednik algebras we construct a microlocalization of the rational cherednik algebras h of type sn this is achieved by a quantization of the hilbert scheme hilb c2 of n points in c2 we then prove the equivalence of the category of h modules and that of modules over its microlocalization under certain conditions on the parameter

the capacity of a vector gaussian arbitrarily varying channel the random coding capacity of a vector gaussian arbitrarily varying channel vgavc is determined along with a simple general method for computing this capacity the vgavc is a discrete time memoryless vector channel with an input power constraint and additive gaussian noise that is further corrupted by an additive jamming signal the statistics of this jamming signal are unknown and can be arbitrary subject only to a power constraint

capacity and decoding rules for classes of arbitrarily varying channels the capacity of an arbitrarily varying channel avc is considered for deterministic codes with the average probability of error criterion and typically subject to at state constraint first sufficient conditions are provided that enable relatively simple decoding rules such as typicality maximum mutual information and minimum distance to attain capacity then the possibly noisy or channels and group adder channels are studied in detail for the former the capacity is explicitly determined and shown to be attainable by minimum distance decoding next for a large class of addictive avcs in addition to providing an intuitively suggestive simplification of the general avc capacity formula it is proven that capacity can be attained by a universal decoding rule finally the effect of random state selections on capacity is studied the merits and limitations of a previous mutual information game approach are also discussed

on the deterministic code capacity region of an arbitrarily varying multiple access channel under list decoding we study the capacity region cl of an arbitrarily varying multiple access channel avmac for deterministic codes with decoding into a list of a fixed size l and for the average error probability criterion motivated by known results in the study of fixed size list decoding for a point to point arbitrarily varying channel we define for every avmac whose capacity region for random codes has a nonempty interior a nonnegative integer called its symmetrizability it is shown that for every l cl has an empty interior and for every l 1 2 cl equals the nondegenerate capacity region of the avmac for random codes with a known single letter characterization for a binary avmac with a nondegenerate random code capacity region it is shown that the symmetrizability is always finite

the common randomness capacity of a network of discrete memoryless channels we generalize our previous results on generating common randomness at two terminals to a situation where any finite number of agents interconnected by an arbitrary network of independent point to point discrete memoryless channels wish to generate common randomness by interactive communication over the network our main result is an exact characterization of the common randomness capacity of such a network i e the maximum number of bits of randomness that all the agents can agree on per step of communication as a by product we also obtain a purely combinatorial result viz a characterization of the incidence vectors of the spanning arborescences rooted at a specified vertex in a digraph and having exactly one edge exiting the root as precisely the extreme points of a certain unbounded convex polyhedron described by a system of linear inequalities

exact inequalities for sums of asymmetric random variables with applications let rm bs 1 dots rm bs n be independent identically distributed random variables each having the standardized bernoulli distribution with parameter p in 0 1 let m p 1 p 2 p 2 2 sqrt p p 2 4 p 2 if 0 p le frac12 and m p 1 if frac12 le p 1 let m ge m p let f be such a function that f and f are nondecreasing and convex then it is proved that for all nonnegative numbers c 1 dots c n one has the inequality mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n le mathsf e f big s m mathrm b s 1 dots mathrm bs n big where s m big frac1n sum i 1 n c i 2m big frac1 2m the lower bound m p on m is exact for each p in 0 1 moreover operatorname mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n is schur concave in c 1 2m ldots c n 2m

common randomness in information theory and cryptography ii cr capacity for pt i see ibid vol 39 p 1121 1993 the common randomness cr capacity of a two terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model we determine cr capacity for several models including those whose statistics depend on unknown parameters the cr capacity is shown to be achievable robustly by common randomness of nearly uniform distribution no matter what the unknown parameters are our cr capacity results are relevant for the problem of identification capacity and also yield a new result on the regular transmission capacity of arbitrarily varying channels with feedback

the capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

communication over individual channels a communication problem in considered where no mathematical model is specified for the channel the achievable rates are determined as a function of the channel input and output sequences known a posteriori without assuming any a priori relation between them for discrete channels the empirical mutual information between the input and output sequences is shown to be achievable while for continuous channels the achievable rate is based on the empirical correlation between the sequences a rate adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability without prior knowledge of the channel behavior is presented

an inequality of optimal order for the tail probabilities of the t statistic under symmetry abstract an inequality for the tail probabilites of the t statistic under the hypotheses of independence and symmetry is presented and is shown to yield bounds for the upper quantiles that approach those of the normal and hence the smallest of such bounds possible as the corresponding upper tail area tends to 0

improved eaton bounds for linear combinations of bounded random variables with statistical applications abstract the problem of evaluating tail probabilities for linear combinations of independent possibly nonidentically distributed bounded random variables arises in various statistical contexts mainly connected with nonparametric inference a remarkable inequality on such tail probabilities has been established by eaton the significance of eaton s inequality is substantiated by a recent result of pinelis showing that the minimum b ep of eaton s bound b e and a traditional chebyshev bound yields an inequality that is optimal within a fairly general class of bounds eaton s bound however is not directly operational because it is not explicit apparently it never has been studied numerically and its many potential statistical applications have not yet been considered a simpler inequality recently proposed by edelman for linear combinations of iid bernoulli variables is also considered but it appears considerably less tight than eaton s original bound this article has three main objectives first

list decoding for arbitrarily varying multiple access channel revisited list configuration and symmetrizability in a recent work s nitinawarat obtained a lower bound and an upper bound for the minimum list size in list decoding for an arbitrarily varying multiple access channel avmac for which the interior of the capacity region of deterministic list codes is nonempty in the same paper he proved that for a binary avmac the minimum list size is finite if and only if the interior of the capacity region of random correlated codes is nonempty the goal of this paper is to close the gap between the two bounds for the minimum list size we find a necessary and sufficient condition for the list codes for an avmac to have a capacity region with a nonempty interior in terms of bipartite graphs therefore we determine the minimum list size moreover we prove that for any avmac the minimum list size is finite if and only if the interior of the capacity region of random correlated codes is nonempty

rational cherednik algebras and hilbert schemes let h c be the rational cherednik algebra of type a n 1 with spherical subalgebra u c e h c e then u c is filtered by order of differential operators with associated graded ring mbox gr u c mathbb c mathfrak h oplus mathfrak h where w is the n th symmetric group we construct a filtered mathbb z algebra b such that under mild conditions on c the category b qgr of graded noetherian b modules modulo torsion is equivalent to u c mod the associated graded mathbb z algebra mbox gr b has mbox gr b lqgr simeq coh hilb n this can be regarded as saying that u c simultaneously gives a non commutative deformation of mathfrak h oplus mathfrak h w and of its resolution of singularities hilb n rightarrow mathfrak h oplus mathfrak h as we show elsewhere this result is a powerful tool for studying the representation theory of h c and its relationship to hilb n

on the capacity region of the discrete additive multiple access arbitrarily varying channel the discrete additive multiple access arbitrarily varying channel avc with two senders and one receiver is considered necessary and sufficient conditions are given for its deterministic code average probability of error capacity region under a state constraint to have a nonempty interior in the case that no state constraint is present the capacity region is characterized exactly in the case of the noiseless mod 2 adder avc using state constraint function l s s and subject to a state constraint l less than or equal to 0 13616917 the capacity region is shown to be a 45 degree triangle whose legs have length 1 h l where h denotes the binary entropy function

universal communication over arbitrarily varying channels consider the problem of universally communicating over an arbitrarily varying channel i e a channel comprised of an unknown arbitrary sequence of memoryless channels it is shown that there is a communication system using feedback and common randomness that asymptotically attains with high probability the capacity of the time averaged channel universally for every sequence of channels this attainable rate is optimal under certain conditions while no prior knowledge of the channel sequence is assumed the capacity of the time averaged channel meets or exceeds the traditional arbitrarily varying channel avc capacity for every memoryless avc defined over the same alphabets and therefore the system universally attains the random code avc capacity without knowledge of the avc parameters the presented system combines rateless coding with a universal prediction scheme for the input prior distribution from which the codebook is randomly drawn because at each point in time the future of the channel sequence is unknown to the communicators the adaptation of the input behavior by universally predicting the prior plays a major role in the result

correlated sources help transmission over an arbitrarily varying channel it is well known that the deterministic code capacity for the average error probability criterion of an arbitrarily varying channel avc either equals its random code capacity or zero here it is shown that if two components of a correlated source are additionally available to the sender and receiver respectively the capacity always equals its random code capacity

permutational extreme values of autocorrelation coefficients and a pitman test against serial dependence somewhat more difficult this problem which is shown to reduce to a particular case of the well known travelling salesman problem is explicitly solved here for the autocorrelation coefficient of order one allowing for a simple computation of permutational critical values for pitman tests against serial dependence the case of higher order autocorrelations is however of a different nature and requires another approach

on the capacity of channels with unknown interference the process of communicating in the presence of interference that is unknown or hostile is modeled as a two person zero sum game with the communicator and the jammer as the players the objective function considered is the rate of reliable communication the communicator s strategies are encoders and distributions on a set of quantizers the jammer s strategies are distributions on the noise power subject to certain constraints various conditions are considered on the jammer s strategy set and on the communicator s knowledge for the case where the decoder is uninformed of the actual quantizer chosen it is shown that from the communicator s perspective the worst case jamming strategy is a distribution concentrated on a finite number of points thereby converting a functional optimization problem into a nonlinear programming problem moreover the worst case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify for the case where the decoder is informed of the actual quantizer chosen the existence of saddle point strategies is demonstrated the analysis is also seen to be valid for a number of situations where the jammer is adaptive

rateless codes for avc models the arbitrarily varying channel avc is a channel model whose state is selected maliciously by an adversary fixed blocklength coding assumes a worst case bound on the adversary s capabilities which leads to pessimistic results this paper defines a variable length perspective on this problem for which achievable rates are shown that depend on the realized actions of the adversary specifically rateless codes are constructed which require a limited amount of common randomness these codes are constructed for two kinds of avc models in the first the channel state cannot depend on the channel input and in the second it can as a by product the randomized coding capacity of the avc with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness the results for this model are proved using a randomized strategy based on list decoding

list decoding for the arbitrarily varying channel under state constraints list decoding for arbitrarily varying channels avcs under state constraints is investigated it is shown that rates within of the randomized coding capacity of avcs with input dependent state can be achieved under maximal error with list decoding using lists of size o 1 under the average error criterion an achievable rate and converse bound are given for lists of size l these bounds are based on two different notions of symmetrizability and do not coincide in general an example is given which shows that for list size l the capacity may be positive but strictly smaller than the randomized coding capacity in contrast to the situation without constraints

rational cherednik algebras and hilbert schemes ii representations and sheaves let h c be the rational cherednik algebra of type a n 1 with spherical subalgebra u c e h c e then u c is filtered by order of differential operators with associated graded ring gr u c mathbb c mathfrac h mathfrac h w where is the n th symmetric group using the z algebra construction from gs it is also possible to associate to a filtered h c or u c module hat m on the hilbert scheme hilb n using this technique we study the representation theory of u c and h c and we relate it to hilb n and to the resolution of singularities hilb n mathfrac h mathfrac h w for example we prove the following if c 1 n so that l c triv is the unique one dimensional simple h c module then hat e l c triv mathcal o z n where z n 1 0 is the punctual hilbert scheme if c 1 n k for k in mathbb n then under a canonical filtration on the finite dimensional module l c triv gr e l c triv has a natural bigraded structure that coincides with that on h 0 z n mathscr l k where mathscr l mathcal o hilb n 1 this confirms conjectures of berest etingof and ginzburg beg2 conjectures 7 2 7 3 under mild restrictions on c the characteristic cycle of hat e c equals sum k z where k are kostka numbers and the z are known irreducible components of 1 mathfrak h w

upper bounds on the capacity of binary channels with causal adversaries in this paper we consider the communication of information in the presence of a causal adversarial jammer in the setting under study a sender wishes to communicate a message to a receiver by transmitting a codeword x x1 xn bit by bit over a communication channel the sender and the receiver do not share common randomness the adversarial jammer can view the transmitted bits xi one at a time and can change up to a p fraction of them however the decisions of the jammer must be made in a causal manner namely for each bit xi the jammer s decision on whether to corrupt it or not must depend only on xj for j i this is in contrast to the classical adversarial jamming situations in which the jammer has no knowledge of x or knows x completely in this study we present upper bounds that hold under both the average and maximal probability of error criteria on the capacity which hold for both deterministic and stochastic encoding schemes

polytope codes against adversaries in networks this paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location this problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network in that linear codes are insufficient to solve the node problem the class of polytope codes is introduced polytope codes are constant composition codes operating over bounded polytopes in integer vector fields the polytope structure creates additional complexity but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network it is shown that polytope codes achieve a cut set bound for a class of planar networks it is also shown that this cut set bound is not always tight and a tighter bound is given for an example network

a channel under simultaneous jamming and eavesdropping attack correlated random coding capacities under strong secrecy criteria we give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels avwcs we apply two alternative strong secrecy criteria which both lead to the same multi letter formula the difference of these criteria lies in the treatment of correlated randomness they coincide in the case of uncorrelated codes on the basis of the derived formula we show that the correlated random coding secrecy capacity is continuous as a function of the avwc in contrast to the discontinuous uncorrelated coding secrecy capacity in the proof of the secrecy capacity formula for correlated random codes we apply an auxiliary channel which is compound from the sender to the intended receiver and arbitrarily varying from the sender to the eavesdropper

identification without randomization in the theory of identification via noisy channels randomization in the encoding has a dramatic effect on the optimal code size namely it grows double exponentially in the blocklength whereas in the theory of transmission it has the familiar exponential growth we consider now instead of the discrete memoryless channel dmc more robust channels such as the familiar compound cc and arbitrarily varying channels avc they can be viewed as models for jamming situations we make the pessimistic assumption that the jammer knows the input sequence before he acts this forces communicators to use the maximal error concept and also makes randomization in the encoding superfluous now for a dmc w by a simple observation made by ahlswede and dueck 1989 in the absence of randomization the identification capacity say c sub nri w equals the logarithm of the number of different row vectors in w we generalize this to compound channels a formidable problem arises if the dmc w is replaced by the avc w in fact for 0 1 matrices only in w we are exactly as for transmission led to the equivalent zero error capacity of shannon but for general w the identification capacity c sub nri w is quite different from the transmission capacity c w an observation is that the separation codes of ahlswede 1989 are also relevant here we present a lower bound on c sub nri w it implies for instance for w sub 0 1 sup 1 0 sub spl delta 1 spl delta 1 0 spl delta spl isin 0 1 2 that c sub nri w 1 which is obviously tight it exceeds c w which is known to exceed 1 h spl delta where h is the binary entropy function we observe that a separation code with worst case average list size l which we call an nra code can be partitioned into l 2 sup ne transmission codes this gives a nonsingle letter characterization of the capacity of avc with maximal probability of error in terms of the capacity of codes with list decoding we also prove that randomization in the decoding does not increase c sub i w and c sub nri w finally we draw attention to related work on source coding

classical capacity of classical quantum arbitrarily varying channels we prove that the average error classical capacity c w of a classicalquantum arbitrarily varying channel cq avc w equals 0 or else the random code capacity c ahlswede s dichotomy we also establish a necessary and sufficient condition for c w 0

deformation quantization in algebraic geometry abstract we study deformation quantizations of the structure sheaf o x of a smooth algebraic variety x in characteristic 0 our main result is that when x is d affine any formal poisson structure on x determines a deformation quantization of o x canonically up to gauge equivalence this is an algebro geometric analogue of kontsevich s celebrated result

twisted deformation quantization of algebraic varieties abstract let x be a smooth algebraic variety over a field k containing the real numbers we introduce the notion of twisted associative resp poisson deformation of the structure sheaf o x these are stack like versions of usual deformations we prove that there is a twisted quantization operation from twisted poisson deformations to twisted associative deformations which is canonical and bijective on gauge equivalence classes this result extends work of kontsevich and our own earlier work on deformation quantization of algebraic varieties

isomorphisms of quantizations via quantization of resolutions abstract in this paper we prove the existence of isomorphisms between certain non commutative algebras that are interesting from the representation theoretic perspective and arise as quantizations of certain poisson algebras we show that quantizations of kleinian singularities obtained by three different constructions are isomorphic to each other the constructions are via symplectic reflection algebras quantum hamiltonian reduction and w algebras next we prove that parabolic w algebras in type a are isomorphic to quantum hamiltonian reductions associated to quivers of type a finally we show that the symplectic reflection algebras for wreath products of the symmetric group and a kleinian group are isomorphic to certain quantum hamiltonian reductions our results involving w algebras are new while for those dealing with symplectic reflection algebras we just find new proofs a key ingredient in our proofs is the study of quantizations of symplectic resolutions of appropriate poisson varieties

on the deterministic code capacity of the two user discrete memoryless arbitrarily varying general broadcast channel with degraded message sets an inner bound on the deterministic code capacity region of the two user discrete memoryless arbitrarily varying general broadcast channel avgbc was characterized by jahn assuming that the common message capacity is nonzero however he did not indicate how one could decide whether the latter capacity is positive csiszaacuter and narayan s result for the single user arbitrarily varying channel avc establishes the missing part in jahn s characterization nevertheless being based on ahlswede s elimination technique jahn s characterization is not applicable for symmetrizable channels under state constraint here the various notions of symmetrizability for the two user broadcast avc are defined sufficient non symmetrizability condition that renders the common message capacity of the avgbc positive is identified using an approach different from jahn s the decoding rules we use establish an achievable region under state and input constraints for the family of degraded message sets codes over the avgbc

universal quantum state merging we determine the optimal entanglement rate of quantum state merging when assuming that the state is unknown except for its membership in a certain set of states we find that merging is possible at the lowest rate allowed by the individual states additionally we establish a lower bound for the classical cost of state merging under state uncertainty to this end we give an elementary proof for the cost in case of a perfectly known state which makes no use of the resource framework as applications of our main result we determine the capacity for one way entanglement distillation if the source is not perfectly known moreover we give another achievability proof for the entanglement generation capacity over compound quantum channels