subblock constrained codes for real time simultaneous energy and information transfer consider an energy harvesting receiver that uses the same received signal both for decoding information and for harvesting energy which is employed to power its circuitry in the scenario where the receiver has limited battery size a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy in this paper we analyze subblock energy constrained codes seccs which ensure that sufficient energy is carried within every subblock duration we consider discrete memoryless channels and characterize the secc capacity and the secc error exponent and provide useful bounds for these values we also study constant subblock composition codes csccs which are a subclass of seccs where all the subblocks in every codeword have the same fixed composition and this subblock composition is chosen to maximize the rate of information transfer while meeting the energy requirement compared with constant composition codes cccs we show that csccs incur a rate loss and that the error exponent for csccs is also related to the error exponent for cccs by the same rate loss term we exploit the symmetry in csccs to obtain a necessary and sufficient condition on the subblock length for avoiding power outage at the receiver furthermore for cscc sequences we present a tight lower bound on the average energy per symbol within a sliding time window we provide numerical examples highlighting the tradeoff between the delivery of sufficient energy to the receiver and achieving high information transfer rates it is observed that the ability to use energy in real time imposes less of penalty compared with the ability to use information in real time

extended nonlinear schrodinger equation with higher order odd and even terms and its rogue wave solutions a a and n a acknowledge the support of the australian research council discovery project dp110102068 and also thank the volkswagen foundation for financial support

a tight upper bound on the second order coding rate of the parallel gaussian channel with feedback this paper investigates the asymptotic expansion for the maximum rate of fixed length codes over a parallel gaussian channel with feedback under the following setting a peak power constraint is imposed on every transmitted codeword and the average error probabilities of decoding the transmitted message are non vanishing as the blocklength increases the main contribution of this paper is a self contained proof of an upper bound on the first and second order asymptotics of the parallel gaussian channel with feedback the proof techniques involve developing an information spectrum bound followed by using curtiss theorem to show that a sum of dependent random variables associated with the information spectrum bound converges in distribution to a sum of independent random variables thus facilitating the use of the usual central limit theorem combined with existing achievability results our result implies that the presence of feedback does not improve the first and second order asymptotics

common message broadcast channels with feedback in the nonasymptotic regime full feedback we investigate the maximum coding rate for a given average blocklength and error probability over a k user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable length stop feedback codes for the point to point case polyanskiy et al 2011 demonstrated that variable length coding combined with stop feedback significantly increases the speed of convergence of the maximum coding rate to capacity this speed up manifests itself in the absence of a square root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths i e zero dispersion in this paper we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common message k user discrete memoryless broadcast channel which strengthen and generalize the ones reported in trillingsgaard et al 2015 for the two user case an asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common message broadcast channels e g the binary symmetric broadcast channel furthermore we identify conditions under which our converse and achievability bounds are tight up to the second order through numerical evaluations we illustrate that our second order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point to point case

a hierarchy of information quantities for finite block length analysis of quantum tasks we consider two fundamental tasks in quantum information theory data compression with quantum side information as well as randomness extraction against quantum side information we characterize these tasks for general sources using so called one shot entropies these characterizations in contrast to earlier results enable us to derive tight second order asymptotics for these tasks in the i i d limit more generally our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain the one shot entropies most accurately describe an operational quantity yet they tend to be difficult to calculate for large systems we show that they asymptotically agree up to logarithmic terms with entropies related to the quantum and classical information spectrum which are easier to calculate in the i i d limit our technique also naturally yields bounds on operational quantities for finite block lengths

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

first and second order coding theorems for mixed memoryless channels with general mixture this paper investigates the first and second order maximum achievable rates of codes with without cost constraints for mixed channels whose channel law is characterized by a general mixture of at most uncountably many stationary and memoryless discrete channels these channels are referred to as mixed memoryless channels with general mixture and include the class of mixed memoryless channels of finitely or countably memoryless channels as a special case for the mixed memoryless channels with general mixture the first order coding theorem which gives a formula for the varepsilon capacity is established and then a direct part of the second order coding theorem is provided a subclass of mixed memoryless channels whose component channels can be ordered according to their capacity is introduced and the first and second order coding theorems are established it is shown that the established formulas reduce to several known formulas for restricted scenarios

finite dimensional infinite constellations in the setting of a gaussian channel without power constraints proposed by poltyrev in 1994 the codewords are points in an n dimensional euclidean space an infinite constellation and the tradeoff between their density and the error probability is considered the normalized log density nld plays the role of the communication rate and capacity as well as error exponent bounds for this setting are known this paper considers the infinite constellation setting in the finite block length dimension regime a simplified expression for poltyrev s achievability bound is found and it is shown to be closely related to the sphere converse bound and to a recently proposed achievability bound based on point processes the bounds are then analyzed asymptotically for growing n for fixed nld the bounds turn out to be extremely tight compared to previous error exponent analysis for fixed error probability e it is shown that the gap of the highest achievable nld to the optimal nld poltyrev s capacity is approximately 1 2n q 1 e where q is the standard complementary gaussian cumulative distribution function thus extending the channel dispersion analysis to infinite constellations connections to the error exponent of the power constrained gaussian channel and to the volume to noise ratio as a figure of merit are discussed finally the new tight bounds are compared to state of the art coding schemes

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

moderate deviation analysis for classical quantum channels and quantum hypothesis testing in this paper we study the tradeoffs between the error probabilities of classical quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate lower than 1 sqrt n a research topic known as moderate deviation analysis we show that the optimal error probability vanishes under this rate convergence our main technical contributions are a tight quantum sphere packing bound obtained via chaganty and sethuraman s concentration inequality in strong large deviation theory and asymptotic expansions of error exponent functions moderate deviation analysis for quantum hypothesis testing is also established the converse directly follows from our channel coding result while the achievability relies on a martingale inequality

concurrent zero knowledge concurrent executions of a zero knowledge protocol by a single prover with one or more verifiers may leak information and may not be zero knowledge in toto in this article we study the problem of maintaining zero knowledge we introduce the notion of an timing constraint for any two processors p1 and p2 if p1 measures elapsed time on its local clock and p2 measures elapsed time on its local clock and p2 starts after p1 does then p2 will finish after p1 does we show that if the adversary is constrained by an assumption then there exist four round almost concurrent zero knowledge interactive proofs and perfect concurrent zero knowledge arguments for every language in np we also address the more specific problem of deniable authentication for which we propose several particularly efficient solutions deniable authentication is of independent interest even in the sequential case our concurrent solutions yield sequential solutions without recourse to timing that is in the standard model

unequal message protection asymptotic and non asymptotic tradeoffs we study a form of unequal error protection that we term unequal message protection ump the message set of a ump code is a union of m disjoint message classes each class has its own error protection requirement with some classes needing better error protection than others we analyze the tradeoff between rates of message classes and the levels of error protection our analysis reveals new tradeoffs which were not captured by prior works on ump codes to obtain our results we generalize finite block length achievability and converse bounds due to polyanskiy poor verdu we evaluate our bounds for the binary symmetric and binary erasure channels and analyze the asymptotic characteristic of the bounds in the fixed error and moderate deviations regimes in addition we consider two questions related to the practical construction of ump codes first we study a header construction that prefixes the message class into a header followed by data protection using a standard homogeneous classical code we show that in general this construction is not optimal at finite block lengths we further demonstrate that our main ump achievability bound can be obtained using coset codes which suggests a path to implementation of tractable ump codes

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

a tight upper bound for the third order asymptotics for most discrete memoryless channels this paper shows that the logarithm of the e error capacity average error probability for n uses of a discrete memoryless channel dmc is upper bounded by the normal approximation plus a third order term that does not exceed 1 2 logn o 1 if the e dispersion of the channel is positive this matches a lower bound by y polyanskiy 2010 for dmcs with positive reverse dispersion if the e dispersion vanishes the logarithm of the e error capacity is upper bounded by n times the capacity plus a constant term except for a small class of dmcs and e 1 2

strong large deviation and local limit theorems abstract an event is loosely called a large deviation event if the dominant term in the probability of that event goes to zero exponentially most papers give asymptotic expressions only to the algorithm of the probability of a large deviation event this paper obtains strong deviation results which give asymptotic expressions to the actual probability of a large deviation event based on an arbitrary sequence of random variables under some conditions on the moment generating functions the proof of these results depends on local limit theorems which also are proved in this paper by imposing some conditions on the characteristic functions a local limit theorem states that the pseudo densities of random variables converge which is stronger than the convergence of these random variables in distribution

second and third order asymptotics of the continuous time poisson channel the paper derives the optimal second order coding rate for the continuous time poisson channel we also obtain bounds on the third order coding rate this is the first instance of a second order result for a continuous time channel the converse proof hinges on a novel construction of an output distribution induced by wyner s discretized channel and the construction of an appropriate epsilon net of the input probability simplex while the achievability proof follows the general program to prove the third order term for non singular discrete memoryless channels put forth by polyanskiy several non standard techniques such as new definitions and bounds on the probabilities of typical sets using logarithmic sobolev inequalities are employed to handle the continuous nature of the channel

f divergence inequalities this paper develops systematic approaches to obtain f divergence inequalities dealing with pairs of probability measures defined on arbitrary alphabets functional domination is one such approach where special emphasis is placed on finding the best possible constant upper bounding a ratio of f divergences another approach used for the derivation of bounds among f divergences relies on moment inequalities and the logarithmic convexity property which results in tight bounds on the relative entropy and bhattacharyya distance in terms of chi 2 divergences a rich variety of bounds are shown to hold under boundedness assumptions on the relative information special attention is devoted to the total variation distance and its relation to the relative information and relative entropy including reverse pinsker inequalities as well as on the e gamma divergence which generalizes the total variation distance pinsker s inequality is extended for this type of f divergence a result which leads to an inequality linking the relative entropy and relative information spectrum integral expressions of the renyi divergence in terms of the relative information spectrum are derived leading to bounds on the renyi divergence in terms of either the variational distance or relative entropy

operational interpretation of renyi information measures via composite hypothesis testing against product and markov distributions we revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis we introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms in this case we find the threshold rate the optimal error and strong converse exponents at large deviations from the threshold and the second order asymptotics at small deviations from the threshold we apply our results to find the operational interpretations of various renyi information measures in case the alternative hypothesis is comprised of bipartite product distributions we find that the optimal error and strong converse exponents are determined by the variations of renyi mutual information in case the alternative hypothesis consists of tripartite distributions satisfying the markov property we find that the optimal exponents are determined by the variations of renyi conditional mutual information in either case the relevant notion of renyi mutual information depends on the precise choice of the alternative hypothesis as such this paper also strengthens the view that different definitions of renyi mutual information conditional entropy and conditional mutual information are adequate depending on the context in which the measures are used

context tree estimation for not necessarily finite memory processes via bic and mdl the concept of context tree usually defined for finite memory processes is extended to arbitrary stationary ergodic processes with finite alphabet these context trees are not necessarily complete and may be of infinite depth the familiar bayesian information criterion bic and minimum description length mdl principles are shown to provide strongly consistent estimators of the context tree via optimization of a criterion for hypothetical context trees of finite depth allowed to grow with the sample size n as o logn algorithms are provided to compute these estimators in o n time and to compute them on line for all i les n in o nlogn time

information spectrum approach to second order coding rate in channel coding in this paper second order coding rate of channel coding is discussed for general sequence of channels the optimum second order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method we apply this result to the discrete memoryless case the discrete memoryless case with a cost constraint the additive markovian case and the gaussian channel case with an energy constraint we also clarify that the gallager bound does not give the optimum evaluation in the second order coding rate

moderate deviation analysis for classical communication over quantum channels we analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases to characterise the fundamental tradeoff between decoding error code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by alt g and wagner as well as polyanskiy and verdu we derive such a tradeoff for classical quantum as well as image additive channels in terms of the channel capacity and the channel dispersion giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data to derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime due to the central importance of the latter task we expect that our techniques will find further applications in the analysis of other quantum information processing tasks

saddle point in the minimax converse for channel coding a minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis in this paper it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound in the course of the proof a number of auxiliary results of separate interest are obtained in particular it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations as a consequence it is demonstrated that in the latter cases the multiletter input distribution in information spectrum verdu han converse bound can be taken to be a memoryless product of single letter ones a tight converse for the binary erasure channel is rederived by computing the optimal nonproduct output distribution for discrete memoryless channels a conjecture of poor and verdu regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative concept of the channel symmetry group is established and relations with the definitions of symmetry by gallager and dobrushin are investigated