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

secret key and private key constructions for simple multiterminal source models we propose an approach for constructing secret and private keys based on the long known slepian wolf code due to wyner for correlated sources connected by a virtual additive noise channel our work is motivated by results of csiszar and narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and slepian wolf near lossless data compression explicit procedures for such constructions and their substantiation are provided the performance of low density parity check channel codes in devising a new class of secret keys is examined

uniform random number generation from markov chains non asymptotic and asymptotic analyses in this paper we derive non asymptotic achievability and converse bounds on the random number generation with without side information our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length we also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds which implies that our bounds are asymptotically tight in those regimes we also show the second order rates of those problems and derive single letter forms of the variances characterizing the second order rates furthermore we address the relative entropy rate and the modified mutual information rate for these problems

communication with imperfectly shared randomness communication complexity investigates the amount of communication needed for two or more players to determine some joint function of their private inputs for many interesting functions the communication complexity can be much smaller than basic information theoretic measures associated with the players inputs such as the input length the entropy or even the conditional entropy communication complexity of many functions reduces further when the players share randomness classical works studied the communication complexity of functions when the interacting players share randomness perfectly i e they get identical copies of randomness from a common source this paper considers the variant of this question when the players share randomness imperfectly i e when they get noisy copies of the randomness produced by some common source our main result shows that any function that can be computed by a k bit protocol in the perfect sharing model has a 2 k bit protocol in the setting of imperfectly shared randomness and such an exponential growth is necessary our upper bound relies on ideas from locality sensitive hashing while lower bounds rely on hypercontractivity and a new invariance principle tailored for communication protocols

enhanced mass conserving closure scheme for lattice boltzmann equation hydrodynamics we derive and demonstrate a practical and accurate algorithm designed to impose dirichlet boundary conditions specified boundary velocity on the edge nodes of a lattice boltzmann fluid simulation space the current algorithm models the lattice fluid on boundary and bulk nodes to identical accuracy and in a demonstrably equivalent manner whilst this new method applies to rectangular geometries it adds to our previous method 2 i the condition of mass conservation and ii the ability to treat with unimpaired accuracy both internal and external corners

application of lattice boltzmann method to sensitivity analysis via complex differentiation sensitivity analysis of flows computed by lattice boltzmann method via complex differentiation is proposed the theoretical work is illustrated and the proposed method assessed considering the d2q9 scheme along with the differentiation of the lattice boltzmann equation boundary condition implementation is also detailed some examples illustrate the capability of the proposed method

wiretap channel with causal state information and secure rate limited feedback in this paper we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate limited feedback in this scenario the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver in addition the legitimate receiver can send secure feedback to the transmitter at a limited rate r f we derive upper and lower bounds on the secrecy capacity and show that when the channel to the eavesdropper is degraded the bounds are tight and the secrecy capacity is completely characterized the capacity achieving scheme is based on wyner csiszar and korner wiretap coding and two steps of shared key generation one from the state information and one via the noiseless feedback the upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback we conclude the paper by showing that a few interesting known results can be seen as special cases of the above as well as discussing the case where the source of local randomness at the encoder is limited

security analysis of varepsilon almost dual universal 2 hash functions smoothing of min entropy versus smoothing of renyi entropy of order 2 recently varepsilon almost dual universal2 hash functions have been proposed as a new and wider class of hash functions using this class of hash functions several efficient hash functions were proposed this paper evaluates the security performance when we apply this kind of hash functions we evaluate the security in several kinds of setting based on the l 1 distinguishability criterion and the modified mutual information criterion the obtained evaluation is based on smoothing of renyi entropy of order 2 and or min entropy we clarify the difference between these two methods

large deviation analysis for quantum security via smoothing of renyi entropy of order 2 it is known that the security evaluation can be done by smoothing of renyi entropy of order 2 in the classical and quantum settings when we apply universal 2 hash functions using the smoothing of renyi entropy of order 2 we derive security bounds for l 1 distinguishability and modified mutual information criterion under the classical and quantum setting and have derived these exponential decreasing rates these results are extended to the case when we apply e almost dual universal 2 hash functions furthermore we apply this analysis to the secret key generation with error correction

applications of ldpc codes to the wiretap channel with the advent of quantum key distribution qkd systems perfect i e information theoretic security can now be achieved for distribution of a cryptographic key qkd systems and similar protocols use classical error correcting codes for both error correction for the honest parties to correct errors and privacy amplification to make an eavesdropper fully ignorant from a coding perspective a good model that corresponds to such a setting is the wire tap channel introduced by wyner in 1975 in this correspondence we study fundamental limits and coding methods for wire tap channels we provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel we also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes in some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity for the special case of a noiseless main channel and binary erasure channel we consider encoder and decoder design for codes achieving secrecy on the wiretap channel we show that it is possible to construct linear time decodable secrecy codes based on low density parity check ldpc codes that achieve secrecy

lattice boltzmann model for exterior flows with an annealing preconditioning method in this paper we propose a highly efficient and stable lattice boltzmann method for solving low reynolds number exterior flows using a preconditioning technique the present method is based on replacing the constant preconditioning parameter gamma within uniform grids guo phys rev e 70 066706 2004 by a space and time dependent one in a nested mesh refined domain to do this for the transition from a fine to the neighboring coarser grid gamma has been divided by a factor k which is large initially and anneals stepwise to a small value after some iterations with this technique more than one order of magnitude larger convergence rate can be achieved and several orders of magnitude larger system size can be treated

secret key agreement by public discussion from common information the problem of generating a shared secret key s by two parties knowing dependent random variables x and y respectively but not sharing a secret key initially is considered an enemy who knows the random variable z jointly distributed with x and y according to some probability distribution p sub xyz can also receive all messages exchanged by the two parties over a public channel the goal of a protocol is that the enemy obtains at most a negligible amount of information about s upper bounds on h s as a function of p sub xyz are presented lower bounds on the rate h s n as n to infinity are derived for the case in which x x sub 1 x sub n y y sub 1 y sub n and z z sub 1 z sub n result from n independent executions of a random experiment generating x sub i y sub i and z sub i for i 1 n it is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels even when the enemy s channel is superior to the other two channels

application of the lattice bhatnagar gross krook method to the simulation of internal pressure driven flow abstract recent modifications to the two speed two dimensional lattice bhatnagar gross krook method eliminate compressibility errors from the simulation of macroscopic fluids governed by the steady state navier stokes equation we describe the means by which this modified scheme makes it possible to compute both pressure drops and flow fields bringing internal pressure driven isothermal flows within the scope of the method the scheme is applied to the simulation of flow of a viscous incompressible fluid past a sudden expansion in an infinite aspect ratio duct back facing step geometry results are presented and compared with experiment and theory over a range of reynolds number

information theoretic key agreement of multiple terminals part i we study the problem of information theoretically secure secret key agreement under the well known source model and channel model in both of these models multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper the terminals have access to a noiseless public communication channel and an additional resource that depends on the model in the source model the resource is an external source that repeatedly beams correlated randomness to the terminals whereas in the channel model the resource is a secure but noisy discrete memoryless broadcast channel we derive new lower and upper bounds on the secret key capacity under both the source model and the channel model the technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which applied to the joint distribution of the source will imply that they dominate the secret key capacity and then prove the bound by a verification argument a similar technique is used for the channel model finally we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement this generalizes an earlier result of csiszar and narayan

a knudsen layer theory for lattice gases abstract a knudsen layer theory is presented for lattice gases with arbitrary boundary conditions analytical results are obtained for two special orientations these exhibit anisotropic knudsen layers provided suitable conditions are satisfied however the standard boundary conditions used in previous simulations are shown to be isotropic the bulk steady state extending everywhere in the gas this theory allows a more accurate localization of the obstacle with respect to the lattice nodes these results are in good agreement with the numerical simulations

secrecy capacity analysis over kappa mu fading channels theory and applications in this paper we consider the transmission of confidential information over a kappa mu fading channel in the presence of an eavesdropper who also experiences kappa mu fading in particular we obtain novel analytical solutions for the probability of strictly positive secrecy capacity spsc and a lower bound of secure outage probability sop l for independent and non identically distributed channel coefficients without parameter constraints we also provide a closed form expression for the probability of spsc when the mu parameter is assumed to take positive integer values monte carlo simulations are performed to verify the derived results the versatility of the kappa mu fading model means that the results presented in this paper can be used to determine the probability of spsc and sop l for a large number of other fading scenarios such as rayleigh rice nakagami n nakagami m one sided gaussian and mixtures of these common fading models in addition due to the duality of the analysis of secrecy capacity and co channel interference cci the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by cci and background noise bn to demonstrate the efficacy of the novel formulations proposed here we use the derived equations to provide a useful insight into the probability of spsc and sop l for a range of emerging wireless applications such as cellular device to device peer to peer vehicle to vehicle and body centric communications using data obtained from real channel measurements

a lossy source coding interpretation of wyner s common information wyner s common information was originally defined for a pair of dependent discrete random variables its significance is largely reflected in and also confined to several existing interpretations in various source coding problems this paper attempts to expand its practical significance by providing a new operational interpretation in the context of the gray wyner network it is established that wyner s common information has a new lossy source coding interpretation specifically it is established that under suitable conditions wyner s common information equals to the smallest common message rate when the total rate is arbitrarily close to the rate distortion function with joint decoding for the gray wyner network a surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are within some distortion region the new lossy source coding interpretation provides the first meaningful justification for defining wyner s common information for continuous random variables and the result can also be extended to that of multiple variables examples are given for characterizing the rate distortion region for the gray wyner lossy source coding problem and for identifying conditions under which wyner s common information equals that of the smallest common rate as a by product the explicit expression for the common information between a pair of gaussian random variables is obtained

analytical solutions of the lattice boltzmann bgk model analytical solutions of the two dimensional triangular and square lattice boltzmann bgk models have been obtained for the plane poiseuille flow and the plane couette flow the analytical solutions are written in terms of the characteristic velocity of the flow the single relaxation time and the lattice spacing the analytic solutions are the exact representation of these two flows without any approximation using the analytical solution it is shown that in poiseuille flow the bounce back boundary condition introduces an error of first order in the lattice spacing the boundary condition used by kadanoffet al in lattice gas automata to simulate poiseuille flow is also considered for the triangular lattice boltzmann bgk model an analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing

drazin moore penrose invertibility in rings abstract characterizations are given for elements in an arbitrary ring with involution having a group inverse and a moore penrose inverse that are equal and the difference between these elements and ep elements is explained the results are also generalized to elements for which a power has a moore penrose inverse and a group inverse that are equal as an application we consider the ring of square matrices of order m over a projective free ring r with involution such that r m is a module of finite length providing a new characterization for range hermitian matrices over the complexes

computational complexity of continuous variable quantum key distribution the continuous variable quantum key distribution has been considered to have the potential to provide high secret key rate however in present experimental demonstrations the secret key can be distilled only under very small loss rates here by calculating explicitly the computational complexity with the channel transmission we show that under high loss rate it is hard to distill the secret key in present continuous variable scheme and one of its advantages the potential of providing high secret key rate may therefore be limited

change of multivariate mutual information from local to global we study the change of multivariate mutual information among a set of random variables when some common randomness is added to or removed from a subset of the random variables this is formulated more precisely as two new multiterminal secret key agreement problems that respectively ask how one can increase the secrecy capacity efficiently by adding common randomness to a small subset of users and how one can simplify the source model by removing redundant common randomness that does not contribute to the secrecy capacity characterizations and strongly polynomial time computations are derived for the rates of change maximum usable increment and redundancy these results can be applied to study the communication complexity for secret key agreement

oriented ordering parameters for free energy lattice boltzmann methods using the bounce back boundary condition we evaluate the lattice boltzmann model that combines the free energy approach for multiphase flow with the bounce back boundary condition this method requires a virtual ordering parameter to be assigned to the wall nodes existing literature has assigned a single ordering parameter for the entire wall node but this is too coarse to give accurate simulations since it allows for a spurious interaction of different phases through the wall nodes the consequences are illustrated by examining rough and hydrophobic surfaces where contact angles can be predicted using the cassie baxter equation it is found that the single value approach gives a large systemic error in the measured contact angles considerable improvement can be obtained by assigning different values of the ordering parameter to each side of the wall node

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

perfect omniscience perfect secrecy and steiner tree packing we consider perfect secret key generation for a pairwise independent network model in which every pair of terminals share a random binary string with the strings shared by distinct terminal pairs being mutually independent the terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity all the terminals as well as an eavesdropper observe this communication the objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible and concealed from the eavesdropper first we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity second a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal steiner tree packing this algorithm attains capacity when all the terminals seek to share a key and in general attains at least half the capacity third when a single helper terminal assists the remaining user terminals in generating a perfect secret key we give necessary and sufficient conditions for the optimality of the algorithm also a weak helper is shown to be sufficient for optimality

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

the commitment capacity of the gaussian channel is infinite we prove that the commitment capacity of the power constrained gaussian channel i e the optimal rate at which this channel can be used for implementing commitment schemes is infinite

tight exponential analysis of universally composable privacy amplification and its applications motivated by the desirability of universal composability we analyze in terms of l1 distinguishability the task of secret key generation from a joint random variable under this secrecy criterion using the renyi entropy of order 1 s for s 0 1 we derive a new upper bound of eve s distinguishability under the application of the universal2 hash functions it is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions the result is applied to the wiretap channel model and to secret key generation distillation by public discussion

on generalized inverses and green s relations we study generalized inverses on semigroups by means of green s relations we first define the notion of inverse along an element and study its properties then we show that the classical generalized inverses group inverse drazin inverse and moore penrose inverse belong to this class

secret key generation for correlated gaussian sources secret key generation by multiple terminals is considered based on their observations of jointly distributed gaussian signals followed by public communication among themselves exploiting an inherent connection between secrecy generation and lossy data compression two main contributions are made the first is a characterization of strong secret key capacity and entails a converse proof technique that is valid for real valued and not necessarily gaussian as well as finite valued signals the capacity formula acquires a simple form when the terminals observe symmetrically correlated jointly gaussian signals for the latter setup with two terminals considering schemes that involve quantization at one terminal the best rate of an achievable secret key is characterized as a function of quantization rate secret key capacity is attained as the quantization rate tends to infinity structured codes are shown to attain the optimum tradeoff between secret key rate and quantization rate constituting our second main contribution

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

strong secrecy from channel resolvability we analyze physical layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability instead of considering capacity based constructions which associate to each message a subcode that operates just below the capacity of the eavesdropper s channel we consider channel resolvability based constructions which associate to each message a subcode that operates just above the resolvability of the eavesdropper s channel building upon the work of csiszar and hayashi we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels specifically we show that at least for symmetric wiretap channels random capacity based constructions fail to achieve the strong secrecy capacity while channel resolvability based constructions achieve it we then leverage channel resolvability to establish the secrecy capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics finally we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information csi mixed channels and compound channels with receiver csi as well as the secret key capacity of source models for secret key agreement by tying secrecy to channel resolvability we obtain achievable rates for strong secrecy metrics with simple proofs

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

secure multiplex coding attaining channel capacity in wiretap channels it is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so called secrecy capacity cs which is usually smaller than the channel capacity c in order to remove the loss c cs we propose a multiplex coding scheme with plural independent messages in this paper it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information spectral methods by extending hayashi s proof in which the coding of the channel resolvability is applied to wiretap channels furthermore the exact region for deterministic coding is determined for stationary memoryless full rank wiretap channels

wiretap channel with causal state information a lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and the decoder is established the lower bound is shown to be strictly larger than that for the noncausal case by liu and chen achievability is proved using block markov coding shannon strategy and key generation from common state information the state sequence available at the end of each block is used to generate a key to enhance the transmission rate of the confidential message in the following block an upper bound on the secrecy capacity when the state is available noncausally at the encoder and the decoder is established and is shown to coincide with the aforementioned lower bound for several classes of wiretap channels with state

moore penrose invertibility of differences and products of projections in rings with involution abstract this article concerns the mp inverse of the differences and the products of projections in a ring r with involution some equivalent conditions are obtained as applications the mp invertibility of the commutator p q q p and the anti commutator p q q p are characterized where p and q are projections in r some related known results in c algebra are generalized

an enhanced lattice bhatnagar gross krook method for boussinesq flow abstract we derive by the established method of chapman enskog expansion a simple thermal lattice bhatnagar gross krook fluid algorithm with adjustable prandtl number specifically adapted to the simulation of flows in the boussinesq approximation where there is negligible coupling between internal and translational kinetic energy we consider implementation aspects of the model and apply it to the solution of flow in a uniformly heated duct and find the results of our simulations to be in good agreement with theory

analytical solution of axi symmetrical lattice boltzmann model for cylindrical couette flows abstract analytical solution for the axi symmetrical lattice boltzmann model is obtained for the low mach number cylindrical couette flows in the hydrodynamic limit the present solution is in excellent agreement with the result of the navier stokes equation since the kinetic boundary condition is used the present analytical solution using nine discrete velocities can describe flows with the knudsen number up to 0 1 meanwhile the comparison with the simulation data obtained by the direct simulation monte carlo method shows that higher order lattice boltzmann models with more discrete velocities are needed for highly rarefied flows

exact random coding secrecy exponents for the wiretap channel we analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in wyner s wiretap channel setting using wiretap channel codes constructed from both i i d and constant composition random codes our analysis for those sampled from i i d random coding ensemble shows that the previously known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble furthermore our analysis on wiretap channel codes constructed from the ensemble of constant composition random codes leads to an exponent which in addition to being the exact exponent for an average code is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i i d random coding ensemble we show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant composition codes is larger than that of those constructed from i i d random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i i d random codes is larger than that of those constructed from constant composition random codes we hence conclude that unlike the error correction problem there is no general ordering between the two random coding ensembles in terms of their secrecy exponent

key generation algorithms for pairwise independent networks based on graphical models we consider two secret key generation problems under a pairwise independent network model and propose low complexity key generation schemes in a framework that connects our problems to network flow problems in graphs our schemes have two components 1 local key generation and 2 global key propagation in the local key generation we use point to point source coding with side information to establish pairwise keys from which we construct a graph with the capacity of each edge being the key rate of the corresponding point to point local key in the global key propagation depending on the particular problem secret keys are delivered to users in the network using various network flow algorithms in particular in the first problem in which one is required to generate a group key for a group of users in the network we propose a network coding based global key propagation approach this approach has a low complexity and has a better performance than the existing approach in the second problem in which one is required to generate multiple keys simultaneously for different pairs of users we propose a multicommodity flow based global key propagation approach we show that the proposed approach is optimal for the case of generating two keys for the general case of generating more than two keys we show that the sum rate of the proposed scheme is larger than an upper bound characterized in this paper divided by a constant

coding theorems for a 2 2 threshold scheme with detectability of impersonation attacks coding theorems on a 2 2 threshold scheme with an opponent are discussed in an asymptotic setup where the opponent tries to impersonate one of the two participants a situation is considered where n secrets s n from a memoryless source is blockwisely encoded to two shares and the two shares are decoded to s n with permitting negligible decoding error we introduce correlation level of the two shares and characterize the minimum attainable rates of the shares and a uniform random number for realizing a 2 2 threshold scheme that is secure against the impersonation attack by the opponent it is shown that if the correlation level between the two shares equals to ell geq 0 the minimum attainable rates coincide with h s ell where h s denotes the entropy of the source and the maximum attainable exponent of the success probability of the impersonation attack equals to ell it is also shown that a simple scheme using an ordinary 2 2 threshold scheme attains all the bounds as well

feedback based collaborative secrecy encoding over binary symmetric channels in this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties over an eavesdropped communication link relative to wyner s traditional encoding scheme our feedback based encoding often yields larger rate equivocation regions and achievable secrecy rates more importantly by exploiting the channel randomness inherent in the feedback channels our scheme achieves a strictly positive secrecy rate even when the eavesdropper s channel is less noisy than the legitimate receiver s channel all channels are modeled as binary and symmetric we demonstrate the versatility of our feedback based encoding method by using it in three different configurations the stand alone configuration the mixed configuration when it combines with wyner s scheme and the reversed configuration depending on the channel conditions significant improvements over wyner s secrecy capacity can be observed in all configurations

the moore penrose inverses of products and differences of projections in a c algebra abstract for two given projections p and q in a c algebra we investigate how to express moore penrose inverses of products pq and differences p q and pq qp moreover it is shown that pq qp is moore penrose invertible if and only if pq and p q are moore penrose invertible in addition some related topics are considered

common randomness and distributed control a counterexample when agents collaborate to perform a control task it is of interest to characterize the set of joint probability distributions they can achieve on their joint action space when they are passively provided with external common randomness we give a simple counterexample to a natural conjecture about this class of joint distributions