analysis and design of minimax optimal interpolators we consider a class of interpolation algorithms including the least squares optimal yen 1956 interpolator and we derive a closed form expression for the interpolation error for interpolators of this type the error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points the error expression can be used to prove that the yen interpolator is optimal the implementation of the yen algorithm suffers from numerical ill conditioning forcing the use of a regularized approximate solution we suggest a new approximate solution consisting of a sinc kernel interpolator with specially chosen weighting coefficients the newly designed sinc kernel interpolator is compared with the usual sinc interpolator using jacobian area weighting through numerical simulations we show that the sinc interpolator with jacobian weighting works well only when the sampling is nearly uniform the newly designed sinc kernel interpolator is shown to perform better than the sinc interpolator with jacobian weighting

convergence of vector quantizers with applications to optimal quantization suppose that a sequence of probability distribution functions f n converges weakly to a distribution function f does the sequence of optimal quantizers for the f n s converge to an optimal quantizer for f if so do the respective distortions converge to the optimal distortion for f sufficient conditions are given to guarantee the convergence for both scalar and vector quantizers with a general class of distortion measures these results are used to prove the existence of minimum rth power distortion vector quantizers and the convergence of a proposed algorithm for constructing optimal quantizers

a zero delay sequential scheme for lossy coding of individual sequences we consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion the encoder and the decoder are connected via a noiseless channel of capacity r and both are assumed to have zero delay no probabilistic assumptions are made on how the sequence to be encoded is generated for any bounded sequence of length n the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalar quantizer of rate r which is matched to this particular sequence we demonstrate the existence of a zero delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate n sup 1 5 log n as the length of the encoded sequence n increases without bound

anatomy of the monster ii abstract we summarise much of what is currently known about the subgroup structure of the fischer griess monster introduction the publication of the atlas of finite groups 1 henceforth referred to as the atlas marked the end of a chapter in the history of group theory in more ways than one the classification of finite simple groups had been completed and using new computational techniques the last of the sporadic groups had been constructed and enough progress had been made in classifying their maximal subgroups to make the rest seem like a tidying up job since the publication of the atlas these computational methods have been pushed further the classification of the maximal subgroups for fi 22 th fi 23 j 4 and fi 24 was completed by kleidman linton parker and wilson in 7 8 9 10 12 13 14 this means that appendix 2 of the atlas of brauer characters 11 when collated with the atlas itself completes the listing for all sporadic groups except the baby monster and monster for the baby monster four new maximal subgroups s 6 l 3 4 2 2 s 6 s 6 4 l 2 31 and l 2 49 2 3 were given in appendix 2 of 11 and wilson has since found four more m 11 l 3 3 l 2 17 2 and l 2 ll 2 for references see 23 24 25 with work on the 2 locals by meierfrankenfeld and shpektorov 15 an end to the baby monster problem is in sight with a lot of work also having been done on maximal subgroups of generic groups this leaves only the monster unfortunately the degree of its smallest representation over any field 196882 is too big for present day computational techniques to make any headway

the complex lorentzian leech lattice and the bimonster ii let d be the incidence graph of the projective plane over f3 the artin group of the graph d maps onto the bimonster and a complex hyperbolic reflection group acting on 13 dimensional complex hyperbolic space y the generators of the artin group are mapped to elements of order 2 resp 3 in the bimonster resp let y y be the complement of the union of the fixed points of reflections in daniel allcock has conjectured that the orbifold fundamental group of y surjects onto bimonster in this article we study the reflection group we show that th e artin group of d maps to the orbifold fundamental group of y thus answering a question in allcock s article a monstrous proposal and taking one step towards the proof of allcock s conjecture the finite group aut d acts on y we make a detailed study of the complex hyperbolic line fixed by the subgroup l3 3 aut d we define meromorphic automorphic forms on y invariant under with poles along mirrors we show that the restriction of these forms to the complex hyperbolic line fixed by l3 3 gives meromorphic modular forms of level 13

efficient reconstruction of band limited sequences from nonuniformly decimated versions by use of polyphase filter banks an efficient polyphase structure for the reconstruction of a band limited sequence from a nonuniformly decimated version is developed theoretically the reconstruction involves the implementation of a bank of multilevel filters and it is shown that how all these reconstruction filters can be obtained at the cost of one mth band low pass filter and a constant matrix multiplier the resulting structure is therefore more general than previous schemes in addition the method offers a direct means of controlling the overall reconstruction distortion t z by appropriate design of a low pass prototype filter p z extension of these results to multiband band limited signals and to the case of nonconsecutive nonuniform subsampling are also summarized along with generalizations to the multidimensional case design examples are included to demonstrate the theory and the complexity of the new method is seen to be much lower than earlier ones

jointly optimal lqg quantization and control policies for multi dimensional systems for controlled bbr n valued linear systems driven by gaussian noise under quadratic cost criteria we investigate the existence and the structure of optimal quantization and control policies for fully observed and partially observed systems we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists provided that the quantizers allowed are ones which have convex codecells furthermore optimal control policies are linear in the conditional estimate of the state and a form of separation of estimation and control holds

stochastic nestedness and the belief sharing information pattern solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the time horizon thus leading to non tractability of classical dynamic programming a common joint information state supplied to each of the agents leads to a tractable recursion as is evident in the one step delayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure however communication requirements for such conditions require exchange of very large data noiselessly hence these assumptions are generally impractical in this paper we present a weaker notion of nestedness which we term as stochastic nestedness which is characterized by a sequence of markov chain conditions it is shown that if the information structure is stochastically nested then an optimization problem is tractable and in particular for lqg problems the team optimal solution is linear despite the lack of deterministic nestedness or partial nestedness one other contribution of this paper is that by regarding the multiple decision makers as a single decision maker and using witsenhausen s equivalent model for discrete stochastic control it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions a pattern we refer to as k stage belief sharing pattern we discuss the minimum amount of information exchange required to achieve such an information pattern for k 1 the information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies in view of nestedness we present a discussion on the monotone values of information channels

on the gaarder slepian tracking system conjecture source coding the authors examine under what conditions and with what notion of optimality the coder of an optimal system can be operated with the information which is also accessible to the decoder after a discussion of the difficulties involved a theorem is proved for markov sources which states that the extra memory of the coder can be substituted with independent randomization the result is not tied to any specific notion of optimality the main result is shown to hold for markov sources of order k under weak assumptions on the structure and with respect to any per letter fidelity criterion

locally toroidal polytopes of rank 6 and sporadic groups abstract we augment the list of finite universal locally toroidal regular polytopes of type 3 3 4 3 3 due to p mcmullen and e schulte adding as well as removing entries this disproves a related long standing conjecture our new universal polytope is related to a well known y shaped presentation for the sporadic simple group fi 22 and admits s 4 o 8 2 s 3 as the automorphism group we also discuss further extensions of its quotients in the context of y shaped presentations as well we note that two known examples of finite universal polytopes of type 3 3 4 3 3 are related to y shaped presentations of orthogonal groups over f 2 mixing construction is used in a number of places to describe covers and 2 covers

dynamic quantizer design for hidden markov state estimation via multiple sensors with fusion center feedback this paper considers the state estimation of hidden markov models by sensor networks the objective is to minimize the long term average of the mean square estimation error for the underlying finite state markov chain by employing feedback from the fusion center a dynamic quantization scheme for the sensor nodes is proposed and analyzed by a stochastic control approach dynamic rate allocation is also considered when the sensor nodes generate mode dependent measurements

h infty optimal fractional delay filters fractional delay filters are digital filters to delay discrete time signals by a fraction of the sampling period since the delay is fractional the intersample behavior of the original analog signal becomes crucial in contrast to the conventional designs based on the shannon sampling theorem with the band limiting hypothesis the present paper proposes a new approach based on the modern sampled data h optimization that aims at restoring the intersample behavior beyond the nyquist frequency by using the lifting transform or continuous time blocking the design problem is equivalently reduced to a discrete time h optimization which can be effectively solved by numerical computation softwares moreover a closed form solution is obtained under an assumption on the original analog signals design examples are given to illustrate the advantage of the proposed method

verification of the ordinary character table of the baby monster abstract we prove the correctness of the character table of the sporadic simple baby monster group that is shown in the atlas of finite groups

the stability of conditional markov processes and markov chains in random environments we consider a discrete time hidden markov model where the signal is a stationary markov chain when conditioned on the observations the signal is a markov chain in a random environment under the conditional measure it is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate this permits a delicate exchange of the intersection and supremum of fields which is key for the stability of the nonlinear filter and partially resolves a long standing gap in the proof of a result of kunita j multivariate anal 1 1971 365 393 a similar result is obtained also in the continuous time setting the proofs are based on an ergodic theorem for markov chains in random environments in a general state space

on the structure of real time encoding and decoding functions in a multiterminal communication system a real time communication system with two encoders communicating with a single receiver over separate noisy channels is considered the two encoders make distinct partial observations of a markov source each encoder must encode its observations into a sequence of discrete symbols the symbols are transmitted over noisy channels to a finite memory receiver that attempts to reconstruct some function of the state of the markov source encoding and decoding must be done in real time that is the distortion measure does not tolerate delays under the assumption that the encoders observations are conditionally independent markov chains given an unobserved time invariant random variable results on the structure of optimal real time encoding and decoding functions are obtained it is shown that there exist finite dimensional sufficient statistics for the encoders the problem with noiseless channels and perfect memory at the receiver is then considered a new methodology to find the structure of optimal real time encoders is employed a sufficient statistic with a time invariant domain is found for this problem this methodology exploits the presence of common information between the encoders and the receiver when communication is over noiseless channels

encoding of correlated observations an important class of engineering problems involves sensing an environment and making estimates based on the phenomena sensed in the traditional model of this problem the sensors observations are available to the estimator without alteration there is growing interest in em distributed sensing systems in which several observations are communicated to the estimator over channels of limited capacity the observations must be separately encoded so that the target can be estimated with minimum distortion two questions are addressed for a special case of this problem wherein there are two sensors which observe noisy data and communicate with a single estimator 1 if the encoder is unlimited in complexity what communication rates and distortions can be achieved 2 if the encoder must be a quantizer a mapping of a single observation sample into a digital output how can it be designed for good performance the first question is treated by the techniques of information theory it is proved that a given combination of rates and distortion is achievable if there exist degraded versions of the observations that satisfy certain formulas the second question is treated by two approaches in the first the outputs of the quantizers undergo a second stage of encoding which exploits their correlation to reduce the output rate algorithms which design the second stage are presented and tested the second approach is based on the em distributional distance a measure of dissimilarity between two probability distributions an algorithm to modify a quantizer for increased distributional distance is derived and tested

the design of joint source and channel trellis waveform coders the generalized lloyd algorithm is applied to the design of joint source and channel trellis waveform coders to encode discrete time continuous amplitude stationary and ergodic sources operating over discrete memoryless noisy channels experimental results are provided for independent and autoregressive gaussian sources binary symmetric channels and absolute error and squared error distortion measures performance of the joint codes is compared with the tandem combination of a trellis source code and a trellis channel code on the independent gaussian source using the squared error distortion measure operating over an additive white gaussian noise channel it is observed that the jointly optimized codes achieve performance close to or better than that of separately optimized tandem codes of the same constraint length performance improvement via a predictive joint source and channel trellis code is demonstrated for the autoregressive gaussian source using the squared error distortion measure

functionally weighted lagrange interpolation of band limited signals from nonuniform samples a modification of the conventional lagrange interpolator is proposed in this paper that allows one to approximate a band limited signal from its own nonuniform samples with high accuracy the modification consists in applying the lagrange method to the signal but pre multiplied by a fixed function and then solving for the desired signal value its efficiency lies in the fact that the fixed function is independent of the sampling instants it is shown in this paper that the function can be selected so that the interpolation error decreases exponentially with the number of samples for the case in which the sampling instants have a maximum deviation from a uniform grid this paper includes a low complexity recursive implementation of the method its accuracy is validated in the numerical examples by comparison with several interpolators in the literature and by deriving upper and lower bounds for its maximum error

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

classical locally finite tits chamber systems of rank 3 a chamber system v 9 j zi is over some index set z is a set of chambers together with partitions in z of v if ze z and c e v then bj is the join of all partitions fijzi e z and d c is the element of fij containing c d c is again a chamber system over j with fij restricted to z we say q is connected if d c furthermore 111 is the rank of v the most important examples of chamber systems are those obtained from groups if g is a group b a subgroup of g and xi ie z are subgroups of g containing b then 5 g b xi icl has as chambers the cosets bg g e g two such cosets bg bh being i adjacent if and only if xi g xih then g acts chamber transitively on with kernel b n bg and is connected if and only if g x 1 i e z furthermore each chamber system with transitive automorphism group g can be obtained in this way by setting b g and xi gd cr a rank 2 chamber system u hi fi is called a classical generalized ma gon mq 3 if is isomorphic to g b pi p where g is an essentially simple rank 2 group of lie type in the sense of cl b is a bore1 subgroup and p pj are the two maximal parabolic subgroups of g containing b here md is given by the relation vu wj wiw g 1 defined by the weyl group of g a rank 2 chamber system is a generalized digon if is isomorphic to v g pin p pi p where pi p are different proper subgroups of g satisfying g pipj pjpi a connected chamber system over z is called a classical tits chamber system if for each ce and i j c z di j c is either a generalized digon or a classical generalized m gon for some mi e n is focally finite if all d c are finite for motivation to consider such classical locally finite tits chamber systems see 15 and 16 if is a classical tits chamber system then the diagram d z is defined in 9 0021 8693 89 3 00

optimal design of sequential real time communication systems optimal design of sequential real time communication of a markov source over a noisy channel is investigated in such a system the delay between the source output and its reconstruction at the receiver should equal a fixed prespecified amount an optimal communication strategy must minimize the total expected symbol by symbol distortion between the source output and its reconstruction design techniques or performance bounds for such real time communication systems are unknown in this paper a systematic methodology based on the concepts of information structures and information states to search for an optimal real time communication strategy is presented this methodology trades off complexity in communication length linear in contrast to doubly exponential with complexity in alphabet sizes doubly exponential in contrast to exponential as the communication length is usually order of magnitudes bigger than the alphabet sizes the proposed methodology simplifies the search for an optimal communication strategy in spite of this simplification the resultant optimality equations cannot be solved efficiently using existing algorithmic techniques the main idea is to formulate a zero delay communication problem as a dynamic team with nonclassical information structure then an appropriate choice of information states converts the dynamic team problem into a centralized stochastic control problem in function space thereafter markov decision theory is used to derive nested optimality equations for choosing an optimal design for infinite horizon problems these optimality equations give rise to a fixed point functional equation communication systems with fixed finite delay constraint a higher order markov source and channels with memory are treated in the same manner after an appropriate expansion of the state space thus this paper presents a comprehensive methodology to study different variations of real time communication

optimal causal coding decoding problems the symbols produced by a finite markov source are causally encoded so as to be transmitted through a noisy memoryless channel the encoder is assumed to have channel feedback information and the decoder to be causal the feedback information is shown to be useful in general separation results are derived and used to prove that encoding is useless for a class of symmetric channels

fast reconstruction methods for bandlimited functions from periodic nonuniform sampling a well known generalization of shannon s sampling theorem states that a bandlimited function can be reconstructed from its periodic nonuniformly spaced samples if the effective sampling rate is at least the nyquist rate analogous to shannon s sampling theorem this generalization requires that an infinite number of samples be available which however is never the case in practice most existing reconstruction methods for periodic nonuniform sampling yield very low order often not even first order accuracy when only a finite number of samples is given in this paper we propose a fast numerically robust root exponential accurate reconstruction method the efficiency and accuracy of the algorithm is obtained by fully exploiting the sampling structure and utilizing localized fourier analysis we discuss applications in analog to digital conversion where nonuniform periodic sampling arises in various situations finally we demonstrate the performance of our algorithm by numerical examples

multidimensional filter bank signal reconstruction from multichannel acquisition we study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup suppose that we have an channel convolution system referred to as analysis filters in dimensions instead of taking all the data and applying multichannel deconvolution we first reduce the collected data set by an integer uniform sampling matrix and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal first we determine the existence of perfect reconstruction pr systems for a given set of finite impulse response fir analysis filters second we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a fir pr synthesis polyphase matrix for a given set of fir analysis filters finally once a particular fir pr synthesis polyphase matrix is found we can characterize all fir pr synthesis matrices and then find an optimal one according to design criteria including robust reconstruction in the presence of noise

tracking the best quantizer an algorithm is presented for online prediction that allows to track the best expert efficiently even when the number of experts is exponentially large provided that the set of experts has a certain additive structure as an example we work out the case where each expert is represented by a path in a directed graph and the loss of each expert is the sum of the weights over the edges in the path these results are then used to construct universal limited delay schemes for lossy coding of individual sequences in particular we consider the problem of tracking the best scalar quantizer that is adaptively matched to the source sequence with piecewise different behavior a randomized algorithm is presented which can perform on any source sequence asymptotically as well as the best scalar quantization algorithm that is matched to the sequence and is allowed to change the employed quantizer for a given number of times the complexity of the algorithm is quadratic in the sequence length but at the price of some deterioration in performance the complexity can be made linear analogous results are obtained for sequential multiresolution and multiple description scalar quantization of individual sequences

on the capacity of memoryless finite state multiple access channels with asymmetric state information at the encoders a single letter characterization is provided for the capacity region of finite state multiple access channels when the channel state process is an independent and identically distributed sequence the transmitters have access to partial quantized state information and complete channel state information is available at the receiver the partial channel state information is assumed to be asymmetric at the encoders as a main contribution a tight converse coding theorem is presented the difficulties associated with the case when the channel state has memory are discussed and connections to decentralized stochastic control theory are presented

analog matching of colored sources to colored channels analog uncoded transmission provides a simple and robust scheme for communicating a gaussian source over a gaussian channel under the mean squared error mse distortion measure unfortunately its performance is usually inferior to the all digital separation based source channel coding solution which requires exact knowledge of the channel at the encoder the loss comes from the fact that except for very special cases e g white source and channel of matching bandwidth bw it is impossible to achieve perfect matching of source to channel and channel to source by linear means we show that by combining prediction and modulo lattice operations it is possible to match any colored gaussian source to any colored gaussian noise channel of possibly different bw hence achieve shannon s optimum attainable performance r d c furthermore when the source and channel bws are equal but otherwise their spectra are arbitrary this scheme is asymptotically robust in the sense that for high signal to noise ratio snr a single encoder independent of the noise variance achieves the optimum performance the derivation is based upon a recent modulo lattice modulation scheme for transmitting a wyner ziv source over a dirty paper channel

nonideal sampling and interpolation from noisy observations in shift invariant spaces digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous time signal from a sequence of corrupted discrete time samples in this paper a general formulation of this problem is developed that treats the interpolation problem from ideal noisy samples and the deconvolution problem in which the signal is filtered prior to sampling in a unified way the signal reconstruction is performed in a shift invariant subspace spanned by the integer shifts of a generating function where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter several alternative approaches to designing the correction filter are suggested which differ in their assumptions on the signal and noise the classical deconvolution solutions least squares tikhonov and wiener are adapted to our particular situation and new methods that are optimal in a minimax sense are also proposed the solutions often have a similar structure and can be computed simply and efficiently by digital filtering some concrete examples of reconstruction filters are presented as well as simple guidelines for selecting the free parameters e g regularization of the various algorithms

mean squared error sampling and reconstruction in the presence of noise one of the main goals of sampling theory is to represent a continuous time function by a discrete set of samples here we treat the class of sampling problems in which the underlying function can be specified by a finite set of samples our problem is to reconstruct the signal from nonideal noisy samples which are modeled as the inner products of the signal with a set of sampling vectors contaminated by noise to mitigate the effect of the noise and the mismatch between the sampling and reconstruction vectors the samples are linearly processed prior to reconstruction considering a statistical reconstruction framework we characterize the strategies that are mean squared error mse admissible meaning that they are not dominated in terms of mse by any other linear reconstruction we also present explicit designs of admissible reconstructions that dominate a given inadmissible method adapting several classical estimation approaches to our particular sampling problem we suggest concrete admissible reconstruction methods and compare their performance the results are then specialized to the case in which the samples are processed by a digital correction filter

minimum mean squared error reconstruction for generalized undersampling of cyclostationary processes the generalized sampling problem is considered using a filter bank model with a stochastic process framework a signal reconstruction solution minimizing the time averaged mean squared error is found using a filter bank optimization technique for cyclostationary signals the use of a stochastic model approach to find a minimized error solution rather than a perfect reconstruction solution allows consideration of sampling problems that deterministic approaches cannot solve for instance a particular sampling density is not required allowing reconstruction optimization in cases of undersampling an extension is also presented for optimal reconstruction in the presence of additive noise and interference the result is a generalized sampling model which can be used for an extensive variety of scenarios combining aspects of undersampling multiple input multiple output mimo sampling and periodic nonuniform sampling

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

solutions to a class of linear quadratic gaussian lqg stochastic team problems with nonclassical information abstract we consider a stochastic dynamic team problem with two controllers and nonclassical information which can be viewed as the transmission of a garbled version of a gaussian message over a number of noisy channels under a fidelity criterion we show that the optimum solution under a quadratic loss functional consists of linearly transforming the garbled message to a certain optimum power level p and then optimally decoding it by using a linear transformation at the receiving end the power level p is determined by the solution of a fifth order algebraic equation the paper also discusses an extension of this result to the case when the channel noise is correlated with the input random variable and shows that for the single channel case the optimum solution is again linear

reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters this paper considers the problem of reconstructing a class of nonuniformly sampled bandlimited signals of which a special case occurs in e g time interleaved analog to digital converter adc systems due to time skew errors to this end we propose a synthesis system composed or digital fractional delay filters the overall system i e nonuniform sampling and the proposed synthesis system can be viewed as a generalization of time interleaved adc systems to which the former reduces as a special case compared with existing reconstruction techniques our method has major advantages from an implementation point of view to be precise 1 we can perform the reconstruction as well as desired in a certain sense by properly designing the digital fractional delay filters and 2 if properly implemented the fractional delay filters need not be redesigned in case the time skews are changed the price to pay for these attractive features is that we need to use a slight oversampling it should be stressed however that the oversampling factor is less than two as compared with the nyquist rate the paper includes error and quantization noise analysis the former is useful in the analysis of the quantization noise and when designing practical fractional delay filters approximating the ideal filters

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

the universal nonabelian representation of the petersen type geometry related toj4 abstract let g be a geometry with three points on each line the universal representation groupr g of g is generated by a set of involutions one for each point subject to the relations that for every line the product of the three generators corresponding to the points on the line is the identity letj4be the fourth sporadic simple group of janko and let g j4 be the petersen type geometry ofj4whose points and lines are subgroups of order 2 and 22inj4with normalizers containing sylow 2 subgroups the incidence relation is given by inclusion we show thatr g j4 is exactlyj4

filterbank reconstruction of bandlimited signals from nonuniform and generalized samples this paper introduces a filterbank interpretation of various sampling strategies which leads to efficient interpolation and reconstruction methods an identity which is referred to as the interpolation identity is developed and is used to obtain particularly efficient discrete time systems for interpolation of generalized samples as well as a class of nonuniform samples to uniform nyquist samples either for further processing in that form or for conversion to continuous time the interpolation identity also leads to new sampling strategies including an extension of papoulis 1977 generalized sampling expansion

a presentation for j4 let g g j 4 be the rank 4 p geometry with janko s fourth group j 4 as a flag transitive automorphism group let a be the amalgam of maximal parabolics corresponding to the action of j 4 on g we prove that g is simply connected i e that it has no proper coverings this result is equivalent to the fact that j 4 coincides with the universal closure of the amalgam a so any presentation for a is a presentation for j 4 this implies in particular that a nice set of generators and relations given by g stroth and r weiss is a presentation for j 4 in addition we obtain a uniqueness proof for j 4

on optimal perfect reconstruction feedback quantizers this paper presents novel results on perfect reconstruction feedback quantizers prfqs i e noise shaping predictive and sigma delta a d converters whose signal transfer function is unity our analysis of this class of converters is based upon an additive white noise model of quantization errors our key result is a formula that relates the minimum achievable mse of such converters to the signal to noise ratio snr of the scalar quantizer embedded in the feedback loop this result allows us to obtain analytical expressions that characterize the corresponding optimal filters we also show that for a fixed snr of the scalar quantizer the end to end mse of an optimal prfq which uses the optimal filters which for this case turn out to be iir decreases exponentially with increasing oversampling ratio key departures from earlier work include the fact that fed back quantization noise is explicitly taken into account and that the order of the converter filters is not a priori restricted

natural representations of the p geometries of co2 type abstract we consider flag transitive p geometries that are geometries belonging to the diagrams formula where the rightmost edge means the geometry of the edges and the vertices of the petersen graph with the natural incidence relation the main result of the paper together with some earlier results provides the classification of the flag transitive p geometries possessing natural representations together with a description of all such representations

optimal zero delay coding of markov sources stationary and finite memory codes the optimal zero delay coding of a finite state markov source is considered the existence and structure of optimal codes are studied using a stochastic control formulation prior results in the literature established the optimality of deterministic markov walrand varaiya type coding policies for the finite time horizon problem and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem our main result here shows that for any irreducible and aperiodic markov source with a finite alphabet deterministic and stationary markov coding policies are optimal for the infinite horizon problem in addition the finite block length time horizon performance of an optimal stationary and markov coding policy is shown to approach the infinite time horizon optimum at a rate o 1 t the results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback

presenting the baby monster abstract we prove that y 433 is isomorphic to 2 2 f 2 where f 2 is fischer s baby monster group this answers the last open problem concerning the description of y groups the result implies in particular that y 553 and y 555 are fabulous systems of generators for the monster and bimonster respectively in a sense introduced by j conway we also give a new independent proof that y 555 is the bimonster

quantization and the method of k means asymptotic results from the statistical theory of k means clustering are applied to problems of vector quantization the behavior of quantizers constructed from long training sequences of data is analyzed by relating it to the consistency problem for k means

on causal source codes with side information we study the effect of the introduction of side information into the causal source coding setting of neuhoff and gilbert we find that the spirit of their result namely the sufficiency of time sharing scalar quantizers followed by appropriate lossless coding for attaining optimum performance within the family of causal source codes extends to many scenarios involving availability of side information at both encoder and decoder or only on one side for example in the case where side information is available at both encoder and decoder we find that time sharing side information dependent scalar quantizers at most two for each side information symbol attains optimum performance this remains true even when the reproduction sequence is allowed noncausal dependence on the side information and even for the case where the source and the side information rather than consisting of independent and identically distributed i i d pairs form respectively the output of a memoryless channel and its stationary ergodic input

memoryless multiple access channel with asymmetric noisy state information at the encoders the problem of reliable communication over the memoryless state dependent multiple access channel mac is considered where the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information csi for the case where the encoders observe causal asymmetric noisy csi and the decoder observes complete csi inner and outer bounds to the capacity region which are tight for the sum rate capacity are provided next single letter characterizations for the channel capacity regions under each of the following system settings are established 1 the csi at the encoders are asymmetric deterministic functions of the csi at the decoder and the encoders have noncausal noisy csi 2 the encoders observe asymmetric noisy csi with asymmetric delays and the decoder observes complete csi 3 a degraded message set scenario with asymmetric noisy csi at the encoders and complete and or noisy csi at the decoder the main component in these results is a generalization of a recently introduced converse coding approach for the mac with asymmetric quantized csi at the encoders and herein considerably extended and adapted for the noisy csi setup

non abelian representations of some sporadic geometries for a point line incidence system s p l with three points per line we define the universal representation group of s as formula we prove that if g is the 2 local parabolic geometry of the sporadic simple groupf1 the monster orf2 the baby monster thenr g f1or 2 f2 respectively

y groups via transitive extension abstract motivated by an earlier observation by j h fischer around 1980 b conway conjectured that the coxeter diagram y555 on fig 1 together with a single additional so called spider relation ab1c1ab2c2ab3c3 10 1 form a presentation for the wreath product of the monster group m and a group of order 2 this conjecture was proved by s p norton and the author in 1990 the original proof was rather involved relying on simple connectedness results for certain diagram geometries on numerous data obtained by coset enumeration on a computer and on some delicate calculations with subgroups coming from the 26 node theorem in the present work we follow an inductive approach to the identification of y groups by considering larger y groups as transitive extensions of smaller ones along these lines we obtain an alternative identification proof for the y groups which is almost computer free we refer to only one result of double coset enumeration our approach provides a uniform understanding of the y groups particularly of features such as centres and redundant generators

source coding with feed forward rate distortion theorems and error exponents for a general source in this work we consider a source coding model with feed forward we analyze a system with a noiseless feed forward link where the decoder has knowledge of all previous source samples while reconstructing the present sample the rate distortion function for an arbitrary source with feed forward is derived in terms of directed information a variant of mutual information we further investigate the nature of the rate distortion function with feed forward for two common types of sources discrete memory less sources and gaussian sources we then characterize the error exponent for a general source with feed forward the results are then extended to feed forward with an arbitrary delay larger than the block length

optimal linear joint source channel coding with delay constraint the problem of joint source channel coding is considered for a stationary remote noisy gaussian source and a gaussian channel the encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint it is shown that under the mean square error distortion metric an optimal encoder decoder pair from the linear and time invariant lti class can be found by minimization of a convex functional and a spectral factorization the functional to be minimized is the sum of the well known cost in a corresponding wiener filter problem and a new term which is induced by the channel noise and whose coefficient is the inverse of the channel s signal to noise ratio this result is shown to also hold in the case of vector valued signals assuming parallel additive white gaussian noise channels it is also shown that optimal lti encoders and decoders generally require infinite memory which implies that approximations are necessary a numerical example is provided which compares the performance to the lower bound provided by rate distortion theory less

26 implies the bimonster the bimonster or wreathed square 2 of the monster group is presented by the coxeter relations of the 26 node incidence graph of the projective plane of order 3 along with the additional relations that all free 12 gons of this diagram generate symmetric groups s we prove this 12 using purely geometric arguments as well as the celebrated ivanov norton theorem 6 7 9 this elementary presentation provides a natural connection from the projective plane of order 3 to the bimonster previously this connection was known in the other direction 2 3 we also consider other groups that can be obtained in a similar fashion a useful reference on coxeter and reflection groups is 5 we use the atlas 1 notation for finite groups

on optimal zero delay coding of vector markov sources optimal zero delay coding quantization of a vector valued markov source driven by a noise process is consid ered using a stochastic control problem formulation the exis tence and structure of optimal quantization policies are studied for a finite horizon problem with bounded per stage distortion measure the existence of an optimal zero delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells the bounded distortion assumption is relaxed to cover cases that include the linear quadratic gaussian problem for the infinite horizon problem and a stationary markov source the optimality of deterministic markov coding policies is shown the existence of optimal stationary markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed

extended f4 buildings and the baby monster let be the baby monster graph which is the graph on the set of 3 4 transpositions in the baby monster group b in which two such transpositions are adjacent if their product is a central involution in b then is locally the commuting graph of central root involutions in 2 e 6 2 the graph contains a family of cliques of size 120 with respect to the incidence relation defined via inclusion these cliques and the non empty intersections of two or more of them form a geometry b with diagram for t 4 and the action of b on b is flag transitive we show that b contains subgeometries 2 e 6 2 and fi 22 with diagrams c f 4 2 and c f 4 1 the stabilizers in b of these subgeometries induce on them flag transitive actions of 2 e 6 2 2 and fi 22 2 respectively the geometries b 2 e 6 2 and fi 22 possess the following properties a any two elements of type 1 are incident to at most one common element of type 2 and b three elements of type 1 are pairwise incident to common elements of type 2 if and only if they are incident to a common element of type 5 the paper addresses the classification problem of c f 4 t geometries satisfying a and b we construct three further examples for t 2 with flag transitive automorphism groups isomorphic to 3 2e2 2 e6 2 2 and 226 f4 2 and one for t 1 with flag transitive automorphism group 3 fi 22 2 we also study the graph of an arbitrary non necessary flag transitive c f 4 t geometry satisfying a and b and obtain a complete list of possibilities for the isomorphism type of subgraph induced by the common neighbours of a pair of vertices at distance 2 finally we prove that b is the only c f 4 4 geometry satisfying a and b

minimum rate sampling and reconstruction of signals with arbitrary frequency support we examine the question of reconstruction of signals from periodic nonuniform samples this involves discarding samples from a uniformly sampled signal in some periodic fashion we give a characterization of the signals that can be reconstructed at exactly the minimum rate once a nonuniform sampling pattern has been fixed we give an implicit characterization of the reconstruction system and a design method by which the ideal reconstruction filters may be approximated we demonstrate that for certain spectral supports the minimum rate can be approached or achieved using reconstruction schemes of much lower complexity than those arrived at by using spectral slicing as in earlier work previous work on multiband signals have typically been those for which restrictive assumptions on the sizes and positions of the bands have been made or where the minimum rate was approached asymptotically we show that the class of multiband signals which can be reconstructed exactly is shown to be far larger than previously considered when approaching the minimum rate this freedom allows us in certain cases to have a far less complex reconstruction system

optimization and convergence of observation channels in stochastic control this paper studies the optimization of observation channels stochastic kernels in partially observed stochastic control problems in particular existence and continuity properties are investigated mostly but not exclusively concentrating on the single stage case continuity properties of the optimal cost in channels are explored under total variation setwise convergence and weak convergence sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored

on the structure of optimal real time encoders and decoders in noisy communication the output of a discrete time markov source must be encoded into a sequence of discrete variables the encoded sequence is transmitted through a noisy channel to a receiver that must attempt to reproduce reliably the source sequence encoding and decoding must be done in real time and the distortion measure does not tolerate delays the structure of real time encoding and decoding strategies that jointly minimize an average distortion measure over a finite horizon is determined the results are extended to the real time broadcast problem and a real time variation of the wyner ziv problem

constructions of fischer s baby monster over fields of characteristic not 2 abstract in this paper we describe the computer construction of the representations of fischer s baby monster simple group in 4371 dimensions over fields of 3 and 5 elements as applications we construct representations for the thompson group which will assist in determining much of the 3 modular and 5 modular character tables

optimal entropy constrained scalar quantization of a uniform source optimal scalar quantization subject to an entropy constraint is studied for a wide class of difference distortion measures including rth power distortions with r 0 it is proved that if the source is uniformly distributed over an interval then for any entropy constraint r in nats an optimal quantizer has n e sup r interval cells such that n 1 cells have equal length d and one cell has length c spl les d the cell lengths are uniquely determined by the requirement that the entropy constraint is satisfied with equality based on this result a parametric representation of the minimum achievable distortion d sub h r as a function of the entropy constraint r is obtained for a uniform source the d sub h r curve turns out to be nonconvex in general moreover for the squared error distortion it is shown that d sub h r is a piecewise concave function and that a scalar quantizer achieving the lower convex hull of d sub h r exists only at rates r log n where n is a positive integer

decentralized optimal control of markov chains with a common past information set decentralized dynamic closed loop optimal control strategies are sought for a class of finite state markov decision processes characterized by the sharing of a common past after k steps of delay the control is considered over a finite time horizon and it is shown that a nonclassical dynamic programming procedure can be applied based on the existence of a sufficient statistic of constant dimension finally the infinite horizon case is briefly discussed in view of an extention of existing results on the minimization of average expected cost for the centralized and decentralized control of markov chains

the character table of 2 1 22 co2 abstract the second largest sporadic simple group the baby monster has a maximal subgroup 2 1 22 co 2 which is a non split extension of an extraspecial group of order 223 by the second sporadic simple conway group co 2 the construction of the character table of this group is described