coding schemes for user cooperation in low power regimes we consider the design of cooperation coding schemes for a two user multiaccess channel mac in particular we consider two block markov coding schemes namely the multiplexed coding and the superposition coding although the fully multiplexed fmp coding outperforms the superposition coding in theory it is difficult to implement with practical error correction codes we therefore introduce a partially multiplexed pmp coding scheme for code rate r 0 5 and propose a simplified superposition coding scheme the outage analysis shows that these cooperation schemes provide significant gains over the non cooperative mac in the low power regime when the bandwidth w rarr infin we then propose a pmp code design using irregular repeat accumulate ira codes the design method can be extended to build the low rate pmp codes using irregular repeat zigzag hadamard irzh codes a new class of capacity achieving low rate codes simulation results demonstrate that the block markov multiplexed coding using pmp ira codes outperforms the practical superposition coding by 2 db at 10 2 fer and it provides a 10 db gain over the noncooperative mac the multiplex coding using pmp irzh codes offers 1 db gain over the superposition coding and a 9 5 db gain over noncooperative mac at 10 2 fer moreover the pmp irzh coding performs only 0 5 db away from the outage capacity of multiplexed coding in the low power regime

error bounds in approximating the riemann stieltjes integral of c n 1 class integrands and nonsmooth integrators in the present paper we investigate the problem of approximating the riemann stieltjes integral a b f du in the case when the integrand f is n 1 time differentiable n 0 and the derivative f n 1 is continuous on a b while the integrator u is riemann integrable on a b a priory error bounds for different classes of functions are provided

statistical physics of random binning we consider the model of random binning and finite temperature decoding for slepian wolf codes from a statistical mechanical perspective while ordinary random channel coding is intimately related to the random energy model a statistical mechanical model of disordered magnetic materials it turns out that random binning for slepian wolf coding is analogous to another related statistical mechanical model of strong disorder which we call the random dilution model we use the latter analogy to characterize phase transitions pertaining to finite temperature slepian wolf decoding which are somewhat similar but not identical to those of finite temperature channel decoding we then provide the exact random coding exponent of the bit error rate as a function of the coding rate and the decoding temperature and discuss its properties finally a few modifications and extensions of our results are outlined and discussed

trapezoidal approximations of fuzzy numbers the problem of the trapezoidal approximation of fuzzy numbers is discussed a set of criteria for approximation operators is formulated these constraints can be used for direct operator derivation a new nearest trapezoidal approximation operator preserving expected interval is suggested

hadamard transforms of three term sequences certain three term sequences of period 2 sup n l are conjectured to have the two level autocorrelation property in this note a formula involving hadamard transforms of three term sequences is presented its validity has been verified by computer on the range of 5 spl les n spl les 23

on the awgn mac with imperfect feedback new achievable rate regions are derived for the two user additive white gaussian multiple access channel with noisy feedback the regions exhibit the following two properties irrespective of the finite gaussian feedback noise variances the regions include rate points that lie outside the no feedback capacity region and when the feedback noise variances tend to zero the regions converge to the perfect feedback capacity region the new achievable regions also apply to the partial feedback setting where one of the transmitters has a noisy feedback link and the other transmitter has no feedback at all again irrespective of the finite noise variance on the feedback link the regions include rate points that lie outside the no feedback capacity region moreover in the case of perfect partial feedback i e where the only feedback link is noise free for certain channel parameters the new regions include rate points that lie outside the cover leung region this answers in the negative the question posed by van der meulen as to whether the cover leung region equals the capacity region of the gaussian multiple access channel with perfect partial feedback finally we propose new achievable regions also for a setting where the receiver is cognizant of the realizations of the noise sequences on the feedback links

sharp bounds for mutual covering a fundamental tool in network information theory is the covering lemma which lower bounds the probability that there exists a pair of random variables among a given number of independently generated candidates falling within a given set we use a weighted sum trick and talagrand s concentration inequality to prove new mutual covering bounds we identify two interesting applications 1 when the probability of the set under the given joint distribution is bounded away from 0 and 1 the covering probability converges to 1 doubly exponentially fast in the blocklength which implies that the covering lemma does not induce penalties on the error exponents in the applications to coding theorems and 2 using hall s marriage lemma we show that the maximum difference between the probability of the set under the joint distribution and the covering probability equals half the minimum total variation distance between the joint distribution and any distribution that can be simulated by selecting a pair from the candidates thus we use the mutual covering bound to derive the exact error exponent in the joint distribution simulation problem in both applications the determination of the exact exponential or double exponential behavior relies crucially on the sharp concentration inequality used in the proof of the mutual covering lemma

ostrowski s type inequalities for some classes of continuous functions of selfadjoint operators in hilbert spaces new ostrowski s type inequalities for some classes of continuous functions of selfadjoint operators in hilbert spaces under suitable assumptions for the involved operators are given

exact random coding exponents and universal decoders for the asymmetric broadcast channel this paper contains two main contributions concerning the asymmetric broadcast channel the first is an analysis of the exact random coding error exponents for both users and the second is the derivation of universal decoders for both users these universal decoders are certain variants of the maximum mutual information universal decoder and they achieve the corresponding random coding exponents of optimal decoding in addition we introduce some lower bounds which involve optimizations over very few parameters unlike the original exact exponents which involve minimizations over auxiliary probability distributions numerical results for the binary symmetric broadcast channel show improvements over previously derived error exponents for the same model

correlation of intuitionistic fuzzy sets in probability spaces in this paper we study the concepts of correlation and correlation coefficient of intuitionistic fuzzy sets in probability spaces in the case of finite spaces these results give the results of gerstenkorn and manko 1991 and in the case of infinite spaces also give the correct forms of yu s 1993 results

the generalized stochastic likelihood decoder random coding and expurgated bounds the likelihood decoder is a stochastic decoder that selects the decoded message at random using the posterior distribution of the true underlying message given the channel output in this paper we study a generalized version of this decoder where the posterior is proportional to a general function that depends only on the joint empirical distribution of the output vector and the code word this framework allows both mismatched versions and universal versions of the likelihood decoder as well as the corresponding ordinary deterministic decoders among many others we provide a direct analysis method that yields the exact random coding exponent as opposed to separate upper bounds and lower bounds that turn out to be compatible which were derived earlier by scarlett et al we also extend the result from pure channel coding to combined source and channel coding random binning followed by random channel coding with side information available to the decoder finally returning to pure channel coding we derive also an expurgated exponent for the stochastic likelihood decoder which turns out to be at least as tight and in some cases strictly so as the classical expurgated exponent of the maximum likelihood decoder even though the stochastic likelihood decoder is suboptimal

fuzzy measures for a correlation coefficient of fuzzy numbers under tw the weakest t norm based fuzzy arithmetic operations recently the sup min convolution based on zadeh s extension principle has been used by liu and kao fuzzy measures for correlation coefficient of fuzzy numbers fuzzy sets and systems 128 2002 267 275 to calculate a fuzzy correlation coefficient they used a mathematical programming approach to derive fuzzy measures based on the classical definition of the correlation coefficient it is well known that t w the weakest t norm based addition and multiplication preserve the shape of l r fuzzy numbers in this paper we consider the computational aspect of the t w based extension principle when the principle is applied to a correlation coefficient of l r fuzzy numbers we give the exact solution of a fuzzy correlation coefficient without programming or the aid of computer resources

seminoisy deterministic multiple access channels coding theorems for list codes and codes with feedback whereas the average error capacity region r sub a for the multiple access channel mac w x spl times y spl rarr z has been known for a long time very little is known about the capacity region r sub m for the maximal error concept as predicted by ahlswede in 1971 in spite of great efforts during the past three decades even for some special examples of deterministic mac for which the maximal error concept coincides with the concept of unique decodability the progress has been slow it is known that the permission of list codes can be of great help even if list sizes are of negligible rates cf the arbitrarily varying channel avc and especially shannon s 1948 zero error capacity problem for the one way channels therefore it is theoretically appealing to look at their regions r sub m l for the mac for a nice class of deterministic mac which we call seminoisy we completely characterized r sub m l for these channels the y input is determined uniquely by the output dueck s 1978 example with r sub a spl ne r sub m and vanroose s 1988 noiseless binary switching mac with r sub a r sub m fall into this class finally for this class the capacity region r sub m f which concerns complete feedback equals r sub m l

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

an achievable rate region for the multiple access channel with feedback an achievable rate region r 1 leq i x 1 y x 2 u r 2 leq i x 2 y x 1 u r 1 r 2 leq i x 1 x 2 y where p u x l x 2 y p u p x l u p x 2 u p y x l x 2 is established for the multiple access channel with feedback time sharing of these achievable rates yields the rate region of this paper this region generally exceeds the achievable rate region without feedback and exceeds the rate point found by gaarder and wolf for the binary erasure multiple access channel with feedback the presence of feedback allows the independent transmitters to understand each other s intended transmissions before the receiver has sufficient information to achieve the desired decoding this allows the transmitters to cooperate in the transmission of information that resolves the residual uncertainty of the receiver at the same time independent information from the transmitters is superimposed on the cooperative correction information the proof involves list codes and block markov encoding

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

achievable error exponents for the private fingerprinting game fingerprinting systems in the presence of collusive attacks are analyzed as a game between a fingerprinter and a decoder on the one hand and a coalition of two or more attackers on the other hand the fingerprinter distributes to different users different fingerprinted copies of a host data covertext drawn from a memoryless stationary source embedded with different fingerprints the coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected their action is modeled by a multiple access channel mac we analyze the performance of two classes of decoders associated with different kinds of error events the decoder of the first class aims at detecting the entire coalition whereas the second is satisfied with the detection of at least one member of the coalition both decoders have access to the original covertext data and observe the forgery in order to identify member s of the coalition motivated by a worst case approach we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder while they are uninformed of the attacking scheme achievable single letter expressions for the two kinds of error exponents are obtained single letter lower bounds are also derived for the subclass of constant composition codes these lower and the upper bounds coincide for the error exponent of the first class further for the error of the first kind a decoder that is optimal is introduced and the worst case attack channel is characterized

achievable rates for multiple descriptions with feed forward the two channel multiple descriptions problem for an independent and identically distributed i i d source with feed forward to one or both side decoders is considered a single letter achievable rate region is derived it enlarges the best known rate region for multiple descriptions without feed forward the proof of the result uses a block markov superposition source coding strategy in point to point source coding feed forward does not decrease the rate distortion function of an i i d source in contrast an example is provided to show that the derived region can be strictly larger than the optimal multiple description rate distortion region without feed forward

new bounds for moments of continuous random variables in this paper some gruss and ostrowski gruss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in l p space some results of kumar are generalized p kumar inequalities involving moments of a continuous random variable defined over a finite interval comput math appl 48 2004 257 273 p kumar the ostrowski type moment integral inequalities and moment bounds for continuous random variables comput math appl 49 2005 1929 1940

the ostrowski type moment integral inequalities and moment bounds for continuous random variables we establish ostrowski type integral inequalities involving moments of a continuous random variable defined on a finite interval we also derive bounds for moments from these inequalities further we discuss applications of these bounds to the euler s beta mappings and illustrate their behaviour

m matrices and bounds for reliable transmission of information in communication systems and economic markets abstract a multivariate normal density n 0 whose covariance matrix is positive with an m matrix inverse is shown to give an upper bound to the region in which communication systems and economic markets can reliably transmit information the upper bound is known to be tight when the density is bivariate

on capacities of the two user union channel with complete feedback the exact values of the optimal symmetric rate point in the cover leung capacity region of the two user union channel with complete feedback were determined by willems when the size of the input alphabet is 2 and by vinck et al when the size is at least 6 we complete this line of research when the size of the input alphabet is 3 4 or 5 the proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality for the zero error capacity region using superposition coding we provide a practical near optimal communication scheme which improves all the previous explicit constructions

block markov superposition transmission construction of big convolutional codes from short codes a construction of big convolutional codes from short codes called block markov superposition transmission bmst is proposed the bmst is very similar to superposition block markov encoding sbme which has been widely used to prove multiuser coding theorems the bmst codes can also be viewed as a class of spatially coupled codes where the generator matrices of the involved short codes referred to as basic codes are coupled the encoding process of bmst can be as fast as that of the basic code while the decoding process can be implemented as an iterative sliding window decoding algorithm with a tunable delay more importantly the performance of bmst can be simply lower bounded in terms of the transmission memory given that the performance of the short code is available numerical results show that 1 the lower bounds can be matched with a moderate decoding delay in the low bit error rate ber region implying that the iterative sliding window decoding algorithm is near optimal 2 bmst with repetition codes and single parity check codes can approach the shannon limit within 0 5 db at the ber of 10 5 for a wide range of code rates and 3 bmst can also be applied to nonlinear codes

capacity results for the discrete memoryless network a discrete memoryless network dmn is a memoryless multiterminal channel with discrete inputs and outputs a sequence of inner bounds to the dmn capacity region is derived by using code trees capacity expressions are given for three classes of dmns 1 a single letter expression for a class with a common output 2 a two letter expression for a binary symmetric broadcast channel bc with partial feedback and 3 a finite letter expression for push to talk dmns the first result is a consequence of a new capacity outer bound for common output dmns the third result demonstrates that the common practice of using a time sharing random variable does not include all time sharing possibilities namely time sharing of channels several techniques for improving the bounds are developed 1 causally conditioned entropy and directed information simplify the inner bounds 2 code trellises serve as simple code trees 3 superposition coding and binning with code trees improves rates numerical computations show that the last technique enlarges the best known rate regions for a multiple access channel mac and a bc both with feedback in addition to the rate bounds a sequence of inner bounds to the dmn reliability function is derived a numerical example for a two way channel illustrates the behavior of the error exponents

partial correlation of fuzzy sets in data analysis and data classification finding the relationships between the attributes of a database is important our objective here is to propose a method of partial correlation analysis on fuzzy sets to investigate the partial relationship between fuzzy attributes a simple correlation coefficient provides us with a very good sense of linear relationships between fuzzy attribute pairs but very often attributes other than the two under consideration are also responsible for the observed association the effect of these fuzzy attributes may influence the relationship between the observed two fuzzy attributes it will be more complicated than a simple correlation can explain therefore the analysis of partial correlation is developed here to show the relationship between fuzzy attributes when the effects of other fuzzy attributes are partialed out definitions of partial correlation coefficients among fuzzy attributes are derived and they are defined on the membership grades of the fuzzy attributes an experiment has been conducted in order to obtain a fuzzy data set and then analysis of partial correlation is discussed on this fuzzy data set

correlation and information energy of interval valued fuzzy numbers in this paper we introduce the correlation coefficient of interval valued fuzzy numbers and study some of their properties furthermore we put forward the concept of information energy and how to compare interval valued fuzzy numbers by applying them

dependence balance bounds for single output two way channels if in a transmission the inputs of a single output two way channel exhibit some interdependence this dependence must have been created during earlier transmissions the idea that no more dependence can be consumed than is produced is used to obtain new upper bounds to the capacity region of the discrete memoryless single output two way channel with these upper bounds it is shown that c e shannon 1961 inner bound region is the capacity region for channels in a certain class and the zhang berger schalkwijk upper bound 1986 for blackwell s multiplying channel is improved upon

inequalities involving moments of a continuous random variable defined over a finite interval some results based on the korkine s identity and integral inequalities of holder and gruss are obtained for the moments of a continuous random variable whose probability distribution is a convex function on the interval of real numbers applications of these results are considered in deriving the inequalities involving higher moments and special means and also in evaluating moments of a beta random variable

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

on optimal causal coding of partially observed markov sources in single and multiterminal settings the optimal causal zero delay coding of a partially observed markov process is studied where the cost to be minimized is a bounded nonnegative additive measurable single letter function of the source and the receiver output a structural result is obtained extending witsenhausen s and walrand varaiya s structural results on optimal causal coders to more general state spaces and to a partially observed setting the decentralized multiterminal setup is also considered for the case where the source is an i i d process it is shown that an optimal solution to the decentralized causal coding of correlated observations problem is memoryless for markov sources a counterexample to a natural separation conjecture is presented

exact exponent for soft covering this paper establishes the exact exponents for the soft covering phenomenon of a memoryless channel under the total variation metric when random i i d and constant composition channel codes are used the exponents established herein are strict improvements in both directions on bounds found in the literature this complements the recent literature establishing the exact exponents under the relative entropy metric however the proof techniques have significant differences and thus neither result trivially implies the other the found exponents imply new and improved bounds for various problems that use soft covering as their achievability argument including new lower bounds for the resolvability exponent and the secrecy exponent in the wiretap channel

approximating the riemann stieltjes integral in terms of generalised trapezoidal rules abstract error bounds in approximating the riemann stieltjes integral in terms of some new generalised trapezoidal rules are given applications for approximating the riemann integral of a two function product are provided as well

large deviations behavior of the logarithmic error probability of random codes this work studies the deviations of the error exponent of the constant composition code ensemble around its expectation known as the error exponent of the typical random code trc in particular it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the trc exponent is exponentially small upper and lower bounds for this exponent are given which coincide in some cases in addition the probability of randomly drawing a codebook whose error exponent is larger than the trc exponent is shown to be double exponentially small upper and lower bounds to the double exponential exponent are given the results suggest that codebooks whose error exponent is larger than the error exponent of the trc are extremely rare the key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables

linear span of extended sequences and cascaded gmw sequences in this correspondence the linear span of extended sequences of period 2 sup em 1 which are constructed from the ideally correlated sequences of period of 2 sup m 1 is derived it is also shown that the linear span of cascaded gordon mills welch gmw sequences can be derived in the same context as examples the linear span of extended legendre sequences and cascaded gmw sequences with triple trace are computed

outer bounds for multiple access channels with feedback using dependence balance we use the idea of dependence balance to obtain a new outer bound for the capacity region of the discrete memoryless multiple access channel with noiseless feedback mac fb we consider a binary additive noisy mac fb whose feedback capacity is not known the binary additive noisy mac considered in this paper can be viewed as the discrete counterpart of the gaussian mac fb ozarow established that the capacity region of the two user gaussian mac fb is given by the cut set bound our result shows that for the discrete version of the channel considered by ozarow this is not the case direct evaluation of our outer bound is intractable due to an involved auxiliary random variable whose large cardinality prohibits an exhaustive search we overcome this difficulty by using a composite function and its properties to explicitly evaluate our outer bound our outer bound is strictly less than the cut set bound at all points on the capacity region where feedback increases capacity in addition we explicitly evaluate the cover leung achievable rate region for the binary additive noisy mac fb in consideration furthermore using the tools developed for the evaluation of our outer bound we also explicitly characterize the boundary of the feedback capacity region of the binary erasure mac for which the cover leung achievable rate region is known to be tight this last result confirms that the feedback strategies developed by kramer for the binary erasure mac are capacity achieving

an improved achievable region for the discrete memoryless two user multiple access channel with noiseless feedback an achievable region for the two user discrete memoryless multiple access channel dmmac with noiseless feedback is proposed the proposed region includes the cover leung region with the inclusion being for some channels strict this inner bound is demonstrated for the ideal two user poisson multiple access channel with noiseless feedback in which case it is shown to improve on the cover leung rate sum

new directions in the theory of identification via channels studies two problems in the theory of identification via channels the first problem concerns the identification via channels with noisy feedback whereas for shannon s transmission problem the capacity of a discrete memoryless channel does not change with feedback it is known that the identification capacity is affected by feedback the authors study its dependence on the feedback channel they prove both a direct and a converse coding theorem although a gap exists between the upper and lower bounds provided by these two theorems the known result for channels without feedback and the known result for channels with complete feedback are both special cases of these two new theorems because in these cases the bounds coincide the second problem is the identification via wiretap channels a secrecy identification capacity is defined for the wiretap channel a dichotomy theorem is proved which says that the second order secrecy identification capacity is the same as shannon s capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero and zero otherwise equivalently one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted or identified correctly with arbitrarily small error probability this is in strong contrast to the case of transmission

cardinality concepts for type two fuzzy sets in this paper we define generalized concepts of cardinality of a fuzzy valued function and obtained some properties of these new concepts also we investigate examples for the calculation of two generalized cardinality of fuzzy valued functions and compared with concepts of cardinality of a fuzzy set and a fuzzy valued function

sum rate capacity for symmetric gaussian multiple access channels with feedback the feedback sum rate capacity is established for the symmetric j user gaussian multiple access channel gmac the main contribution is a converse bound that combines the dependence balance argument of hekstra and willems 1989 with a variant of the factorization of a convex envelope of geng and nair 2014 the converse bound matches the achievable sum rate of the fourier modulated estimate correction strategy of kramer 2002

fuzzy measures for correlation coefficient of fuzzy numbers correlation coefficient of random variables has wide applications in statistical analysis this paper extends the applications to fuzzy environment with a methodology for calculating the correlation coefficient of fuzzy numbers developed different from previous studies the correlation coefficient calculated in this paper is a fuzzy number rather than a crisp value the idea is based on zadeh s extension principle a pair of nonlinear programs is formulated to find the cut of the fuzzy correlation coefficient from different values of the membership function of the fuzzy correlation coefficient is constructed to illustrate how to interpret the fuzzy correlation coefficient in real world applications the correlation between the technology level and management achievement from a sample of 15 machinery firms in taiwan is exemplified all indications show that the correlation between technology and management in taiwan machinery firms is rather low

exact random coding error exponents of optimal bin index decoding we consider ensembles of channel codes that are partitioned into bins and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs two main conclusions arise from this analysis i for independent random selection of codewords within a given type class the random coding exponent of optimal bin index decoding is given by the ordinary random coding exponent function computed at the rate of the entire code independently of the exponential rate of the size of the bin ii for this ensemble of codes sub optimal bin index decoding that is based on ordinary maximum likelihood ml decoding is as good as the optimal bin index decoding in terms of the random coding error exponent achieved finally for the sake of completeness we also outline how our analysis of exact random coding exponents extends to the hierarchical ensemble that correspond to superposition coding and optimal decoding where for each bin first a cloud center is drawn at random and then the codewords of this bin are drawn conditionally independently given the cloud center for this ensemble conclusions i and ii mentioned above no longer hold necessarily in general

a note on the correlation of fuzzy numbers abstract this short note gives counterexamples showing that yu s 1993 propositions on correlation of fuzzy numbers and gerstenkorn and manko s 1991 note on correlation of intuitionistic fuzzy sets are not valid

the entropy change of fuzzy numbers with arithmetic operations for the same type of two fuzzy sets with different supports this paper investigates the entropy relationship between both of them for the fuzzy numbers with triangular membership function the entropy change between the resultant fuzzy numbers through some arithmetic operations and the original fuzzy numbers is also studied

entropy variation on the fuzzy numbers with arithmetic operations entropy is always the measure of the fuzziness degree for a fuzzy set this paper studies the entropy variation on the fuzzy numbers or fuzzy sets under the following several cases i two fuzzy sets on the same type but different support size ii the addition of finite number of fuzzy numbers on the same type iii the subtraction of finite number of fuzzy numbers on the same type iv the multiplication of a constant and a fuzzy number it is shown that through the above arithmetic operations the resultant fuzzy number is the same type as the original fuzzy numbers and the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number

capacity region of the finite state multiple access channel with and without feedback the capacity region of the finite state multiple access channel fs mac with feedback that may be an arbitrary time invariant function of the channel output samples is considered we characterize both an inner and an outer bound for this region using massey s directed information these bounds are shown to coincide and hence yield the capacity region of indecomposable fs macs without feedback and of stationary and indecomposable fs macs with feedback where the state process is not affected by the inputs though multiletter in general our results yield explicit conclusions when applied to specific scenarios of interest for example our results allow us to do the following 1 identify a large class of fs macs that includes the additive mod2 noise mac where the noise may have memory for which feedback does not enlarge the capacity region 2 deduce that for a general fs mac with states that are not affected by the input if the capacity region without feedback is zero then so is the capacity region with feedback 3 deduce that the capacity region of a mac that can be decomposed into a multiplexer concatenated by a point to point channel with without or with partial feedback the capacity region is given by sigmam rm les c where c is the capacity of the point to point channel and m indexes the encoders moreover we show that for this family of channels source channel coding separation holds

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

feedback codes with uniformly bounded codeword lengths and zero error capacities a certain class of variable length codes with feedback whose codeword lengths are uniformly upper bounded is considered for this class of variable length codes it is shown that the zero error capacity region for the single user and multiuser channels with feedback can be extended up to the ordinary average error capacity under some conditions if variable length codes semiblock codes are used in place of fixed length codes this condition is different from that of m v burnashev 1976 for variable length codes with feedback but without any uniform bound on the codeword lengths it is also shown that the capacity region for variable length feedback codes coincides with that for fixed length feedback codes

correlation of fuzzy numbers abstract in this paper we introduce the concepts of correlation and correlation coefficient of fuzzy numbers which could be used to measure the interrelation of fuzzy numbers we also give a brief discussion about the so called information energy of fuzzy numbers

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

on ostrowski type inequalities for stieltjes integrals with absolutely continuous integrands and integrators of bounded variation some ostrowski type inequalities are given for the stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation the case when f is convex is explored applications for the mid point rule and a generalised trapezoid type rule are also presented

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

a companion of ostrowski s inequality for the riemann stieltjes integral a b f t du t where f is of bounded variation and u is of r h holder type and applications some companions of ostrowski s integral inequality for the riemann stieltjes integral a bf t du t where f is assumed to be of bounded variation on a b and u is of r h holder type on a b are proved applications to the approximation problem of the riemann stieltjes integral in terms of riemann stieltjes sums are also pointed out

achievability proof of some multiuser channel coding theorems using backward decoding new and simpler achievability proofs that are based on the backward decoding technique are presented for the well known coding theorems for the multiple access channel mac with perfect feedback and the degraded relay channel a class of macs with different generalized feedback signals is also considered and achievable rate regions that are larger than those previously presented in the literature are established

exact correct decoding exponent of the wiretap channel decoder the performance of the achievability scheme for wyner s wiretap channel model is examined from the perspective of the probability of correct decoding pc at the wiretap channel decoder in particular for finite alphabet memoryless channels the exact random coding exponent of pc is derived as a function of the total coding rate r1 and the rate of each subcode r2 two different representations are given for this function and its basic properties are provided we also characterize the region of pairs of rates r1 r2 of full security in the sense of the random coding exponent of pc in other words the region where the exponent of this achievability scheme is the same as that of blind guessing at the eavesdropper side finally an analogous derivation of the correct decoding exponent is outlined for the case of the gaussian channel

fast iterative coding techniques for feedback channels a class of capacity achieving low complexity high reliability variable rate coding schemes is developed for communication over discrete memoryless channels with noiseless feedback algorithms for encoding and decoding that require computations growing linearly with the number of channel inputs used are developed the error exponent associated with the scheme is shown to be optimal and implies that capacity is achievable simulations are performed and support the analytically predicted high performance and low complexity

n channel symmetric multiple descriptions part i n k source channel erasure codes in this two part paper we present a new achievable rate region for the general n channel symmetric multiple descriptions problem in part i inspired by the concept of maximum distance separable mds erasure channel codes we consider a special case of this rate region where the source is encoded into n descriptions each with rate r these descriptions are transmitted over n bandwidth constrained and errorless channels during transmission a subset of these channels can break down thus erasing the corresponding descriptions the decoder is interested in recovering the source with the reception of at least k descriptions thus the encoder is allowed to sample only one realization of this breakdown process during the entire transmission for gaussian sources we have the following interesting result when any k descriptions arrive the achievable distortion exactly matches the optimal distortion rate performance corresponding to a source rate of kr bits with the reception of any m k descriptions the source reconstruction quality is strictly better the improvement being nearly linear in the number of descriptions received

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

a new achievable rate region for the multiple access channel with noiseless feedback a new single letter achievable rate region is proposed for the two user discrete memoryless multiple access channel mac with noiseless feedback the proposed region includes the cover leung rate region and it is shown that the inclusion is strict the proof uses a block markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback the rates of transmission are too high for each encoder to decode the other s message directly using the feedback so they transmit correlated information in the next block to learn the message of one another they then cooperate in the following block to resolve the residual uncertainty of the decoder the coding scheme may be viewed as a natural generalization of the cover leung scheme with a delay of one extra block and a pair of additional auxiliary random variables we compute the proposed rate region for two different macs and compare the results with other known rate regions for the mac with feedback finally we show how the coding scheme can be extended to obtain larger rate regions with more auxiliary random variables

approximate capacity region for the symmetric gaussian interference channel with noisy feedback recent results have shown that feedback can significantly increase the capacity of interference networks this paper considers the impact of noise on such gains due to feedback in particular this paper considers the two user linear deterministic interference channel with noisy feedback as a stepping stone to characterize the approximate capacity region for the two user gaussian interference channel with noisy feedback first the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained it is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l it is found that excluding the regime 1 2 leq alpha leq 2 where alpha is the normalized interference level in which even full feedback does not increase symmetric capacity this threshold l is equal to the per user symmetric capacity without feedback one of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2r 1 r 2 and r 1 2r 2 these results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric gaussian interference channel with noisy feedback the outer bounds are shown to be at most 4 7 b s hz away from the achievable rate region as a corollary the generalized degrees of freedom region which approximates the capacity region of the symmetric gaussian interference channel at high snr is found