joint source channel coding with side information using hybrid digital analog codes we study the joint source channel coding problem of transmitting a gaussian source over a gaussian channel in two cases i the presence of interference known only to the transmitter and ii in the presence of side information about the source known only to the receiver we introduce hybrid digital analog forms of the costa and wyner ziv coding schemes we present the random coding counterpart of schemes based on lattices proposed by kochman and zamir then we discuss applications of the hybrid digital analog schemes in the case of channel signal to noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression

generalizing capacity new definitions and capacity theorems for composite channels we consider three capacity definitions for composite channels with channel side information at the receiver a composite channel consists of a collection of different channels with a distribution characterizing the probability that each channel is in operation the shannon capacity of a channel is the highest rate asymptotically achievable with arbitrarily small error probability under this definition the transmission strategy used to achieve the capacity must achieve arbitrarily small error probability for all channels in the collection comprising the composite channel the resulting capacity is dominated by the worst channel in its collection no matter how unlikely that channel is we therefore broaden the definition of capacity to allow for some outage the capacity versus outage is the highest rate asymptotically achievable with a given probability of decoder recognized outage the expected capacity is the highest average rate asymptotically achievable with a single encoder and multiple decoders where channel side information determines the channel in use the expected capacity is a generalization of capacity versus outage since codes designed for capacity versus outage decode at one of two rates rate zero when the channel is in outage and the target rate otherwise while codes designed for expected capacity can decode at many rates expected capacity equals shannon capacity for channels governed by a stationary ergodic random process but is typically greater for general channels the capacity versus outage and expected capacity definitions relax the constraint that all transmitted information must be decoded at the receiver we derive channel coding theorems for these capacity definitions through information density and provide numerical examples to highlight their connections and differences we also discuss the implications of these alternative capacity definitions for end to end distortion source channel coding and separation

approximate characterizations for the gaussian source broadcast distortion region we consider the joint source channel coding problem of sending a gaussian source on a k user gaussian broadcast channel with bandwidth mismatch a new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable which was previously used to derive sum rate lower bound for the symmetric gaussian multiple description problem by combining this outer bound with the achievability result based on source channel separation we provide approximate characterizations of the achievable distortion region within constant multiplicative factors furthermore we show that the results can be extended to general broadcast channels and the performance of the source channel separation based approach is also within the same constant multiplicative factors of the optimum

optimal quantizer design for noisy channels an approach to combined source channel coding we present an analysis of the zero memory quantization of memoryless sources when the quantizer output is to be encoded and transmitted across a noisy channel necessary conditions for the joint optimization of the quantizer and the encoder decoder pair are presented and an iterative algorithm for obtaining a locally optimum system is developed the performance of this locally optimal system obtained for the class of generalized gaussian distributions and the binary symmetric channel is compared against the optimum performance theoretically attainable using rate distortion theoretic arguments as well as against the performance of lloyd max quantizers encoded using the natural binary code and the folded binary code it is shown that this optimal design could result in substantial performance improvements the performance improvements are more noticeable at high bit rates and for broad tailed densities

duality theorems for joint source channel coding we consider joint source channel coding for a memoryless gaussian source and an additive white gaussian noise awgn channel for a given code defined by an encoder decoder pair spl alpha spl beta its dual code is obtained by interchanging the encoder and decoder spl beta spl alpha it is shown that if a code spl alpha spl beta is optimal at rate p channel uses per source sample and if it satisfies a certain uniform continuity condition then its dual code spl beta spl alpha is optimal for rate 1 spl rho channel uses per source sample further it is demonstrated that there is a code which is optimal but its dual code is not optimal finally using random coding we show that there is an optimal code which has an optimal dual the duality concept is also presented for the cases of i binary memoryless equiprobable source and binary symmetric channel bsc and ii colored gaussian source and additive colored gaussian noise acgn channel

linecast line based distributed coding and transmission for broadcasting satellite images in this paper we propose a novel coding and transmission scheme called linecast for broadcasting satellite images to a large number of receivers the proposed linecast matches perfectly with the line scanning cameras that are widely adopted in orbit satellites to capture high resolution images on the sender side each captured line is immediately compressed by a transform domain scalar modulo quantization without syndrome coding the transmission power is directly allocated to quantized coefficients by scaling the coefficients according to their distributions finally the scaled coefficients are transmitted over a dense constellation this line based distributed scheme features low delay low memory cost and low complexity on the receiver side our proposed line based prediction is used to generate side information from previously decoded lines which fully utilizes the correlation among lines the quantized coefficients are decoded by the linear least square estimator from the received data the image line is then reconstructed by the scalar modulo dequantization using the generated side information since there is neither syndrome coding nor channel coding the proposed linecast can make a large number of receivers reach the qualities matching their channel conditions our theoretical analysis shows that the proposed linecast can achieve shannon s optimum performance by using a high dimensional modulo lattice quantization experiments on satellite images demonstrate that it achieves up to 1 9 db gain over the state of the art 2d broadcasting scheme and a gain of more than 5 db over jpeg 2000 with forward error correction

a note on the optimality of variant i permutation modulation codes in this correspondence the optimality of variant i permutation codes initially proposed by slepian see proc ieee vol 53 no 3 p 228 236 mar 1965 is shown in a simple way

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

shannon kotel nikov mappings in joint source channel coding this paper deals with lossy joint source channel coding for transmitting memoryless sources over awgn channels the scheme is based on the geometrical interpretation of communication by kotel nikov and shannon where amplitudecontinuous time discrete source samples are mapped directly onto the channel using curves or planes the source and channel spaces can have different dimensions and thereby achieving either compression or error control depending on whether the source bandwidth is smaller or larger than the channel bandwidth we present a general theory for 1 n and m 1 dimension changing mappings and provide two examples for a gaussian source and channel where we optimize both a 2 1 bandwidth reducing and a 1 2 bandwidth expanding mapping both examples show high spectral efficiency and provide both graceful degradation and improvement for imperfect channel state information at the transmitter

sending a laplacian source using hybrid digital analog codes in this paper we study transmission of a memoryless laplacian source over three types of channels additive white laplacian noise awln additive white gaussian noise awgn and slow flat fading rayleigh channels under both bandwidth compression and bandwidth expansion for this purpose we analyze two well known hybrid digital analog hda joint source channel coding schemes for bandwidth compression and one for bandwidth expansion then we obtain achievable absolute error distortion regions of the hda schemes for the matched signal to noise ratio snr case as well as the mismatched snr scenario using numerical examples it is shown that these schemes can achieve a distortion very close to the provided lower bound for the awln channel and to the optimum performance theoretically attainable bound for awgn and rayleigh fading channels on mean absolute error distortion under matched snr conditions in addition a non linear analog coding scheme is analyzed and its performance is compared to the hda schemes for bandwidth compression under both matched and mismatched snr scenarios the results show that the hda schemes outperform the non linear analog coding over the whole csnr region

tcm ssma communication systems with cascaded sequences and pam qam signal sets an expression in matrix form for the multiple access interference mai in an asynchronous direct sequence spread spectrum multiple access ds ssma communication system with cascaded sequences cvs arbitrary chip waveforms and trellis coded modulation tcm with a pulse amplitude modulation pam or quadrature amplitude modulation qam signal set is obtained tcm provides significant coding gain while the cvs decrease the correlation between the mai of adjacent data intervals the expression is used to calculate arbitrarily accurate probability density functions pdfs of the mai in the tcm system and to derive an accurate approximation of the mai variance it also helps illustrate some properties of the mai by separating contributing parameters into different matrices we derive an approximation of the upper union bound on the bit error probability and investigate its applicability the results show that cv schemes can greatly reduce the pairwise error probabilities peps until the length of the cv becomes greater than that of the error weight sequence ews under consideration

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

distortion minimization in gaussian layered broadcast coding with successive refinement a transmitter without channel state information wishes to send a delay limited gaussian source over a slowly fading channel the source is coded in superimposed layers with each layer successively refining the description in the previous one the receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion the expected distortion is minimized by optimally allocating the transmit power among the source layers for two source layers the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution all remaining power if any is allocated to the lower layer for convex distortion cost functions with convex constraints the minimization is formulated as a convex optimization problem in the limit of a continuum of infinite layers the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution as the number of channel uses per source symbol tends to zero the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity

comparison of topological and uniform structures for fuzzy numbers and the fixed point problem abstract the goal of this paper is to compare certain topological and uniform structures on sets of fuzzy numbers since fuzzy sets can be viewed as a kind of subsets they can be endowed with uniform structures in ways similar to those used for classic subsets the hausdorff construction is one such approach the structures we study are the myope structure the uniform convergence of the cuts in the sense of hausdorff and a structure induced by a metric defined by goetschel and voxman we show how these structures are related to fixed point problems for some classes of fuzzy numbers

a linear encoding approach to index assignment in lossy source channel coding we present a general scheme for the lossy transmission of a source with arbitrary statistics through a noisy channel under the mean square error fidelity criterion our approach is based on transform coding scalar quantization of the transform coefficients and linear encoding of the quantization indices entropy coding and channel coding are merged into a single linear encoding function such that the catastrophic behavior of conventional entropy coding is avoided and the full power of modern coding techniques and iterative belief propagation decoding can be exploited we show that this approach is asymptotically optimal in the limit of large block length for arbitrary source statistics and binary input output symmetric channel in the practical regime of finite block length and low decoding complexity we show through the explicit construction of codes for the lossy transmission of digital images over a binary symmetric channel that our approach yields significant improvements with respect to previously proposed channel optimized quantization schemes and also with respect to the conventional concatenation of state of the art image coding with state of the art channel coding although our constructive example focuses on a special case the approach is general and can be applied to other classes of sources of practical interest

trellis coded quantization designed for noisy channels trellis coded quantization tcq of memoryless sources is developed for transmission over a binary symmetric channel the optimized tcq coder can achieve essentially the same performance as ayanoglu and gray s 1987 unconstrained trellis coding optimized for the binary symmetric channel but with a much lower implementation complexity for transmission rates above 1 b sample in most cases the optimized tcq coder also provides larger signal to noise ratio than farvardin and vaishampayan s 1991 channel optimized vector quantization algorithms are developed for the joint design of trellis coded quantization modulation tcq tcm the jointly designed tcq tcm system outperforms the straightforward cascade of separately designed tcq and tcm systems the improvement is most significant at low channel signal to noise ratio for a first order gauss markov source the predictive tcq tcm performance can exceed that of optimum pulse amplitude modulation

joint source channel codes for mimo block fading channels we consider transmission of a continuous amplitude source over an l block rayleigh fading mt x mr multiple input multiple output mimo channel when the channel state information is only available at the receiver since the channel is not ergodic shannon s source channel separation theorem becomes obsolete and the optimal performance requires a joint source channel approach our goal is to minimize the expected end to end distortion particularly in the high signal to noise ratio snr regime the figure of merit is the distortion exponent defined as the exponential decay rate of the expected distortion with increasing snr we provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths for the lower bounds we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital analog transmission in each case by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio we prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom that is l 1 and min mt mr 1 when we have more degrees of freedom our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio we demonstrate that our results which were derived for a complex gaussian source can be extended to more general source distributions as well

on the performance and complexity of channel optimized vector quantizers the performance and complexity of channel optimized vector quantizers are studied for the gauss markov source observations on the geometric structure of these quantizers are made which have an important implication on the encoding complexity for the squared error distortion measure it is shown that an operation equivalent to a euclidean distance measurement with respect to an appropriately defined set of points used to identify the encoding regions can be used to perform the encoding this implies that the encoding complexity is proportional to the number of encoding regions it is then demonstrated that for very noisy channels and a heavily correlated source when the codebook size is large the number of encoding regions is considerably smaller than the codebook size implying a reduction in encoding complexity

hybrid digital analog hda joint source channel codes for broadcasting and robust communications we consider the problem of transmitting a band limited gaussian source on an additive band limited gaussian noise channel the well known threshold effect dictates that the more powerful a code is the more sensitive it is to the exact knowledge of the channel noise a code is said to be robust if it is asymptotically optimal for a wide range of channel noise thus robust codes have a graceful degradation characteristic and are free of the threshold effect it is demonstrated that robust codes exist whenever the source and channel bandwidths are equal in the unequal bandwidth case a collection of nearly robust joint source channel codes is constructed using a hybrid digital analog hda coding technique for designing nearly robust codes a matched tandem code whose channel encoder s output is partially fully matched to its input is proposed and the existence of an asymptotically optimal matched tandem code is shown the nearly robust codes achieve the shannon limit theoretically optimum distortion and have a less severe threshold effect finally for the case of two different noise conditions the distortion regions of these codes are determined

topological properties of fuzzy numbers fuzzy numbers are defined and a metric is assigned to this class of fuzzy sets topological properties of the resulting metric space are studied the notion of q crisp fuzzy numbers is introduced and in particular it is shown that this class of fuzzy numbers is homeomorphic to the hilbert cube

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

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

successive refinement of information the successive refinement of information consists of first approximating data using a few bits of information then iteratively improving the approximation as more and more information is supplied the goal is to achieve an optimal description at each stage in general an ongoing description which is rate distortion optimal whenever it is interrupted is sought it is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a markov chain in particular all finite alphabet signals with hamming distortion satisfy these requirements it is also shown that the same is true for gaussian signals with squared error distortion and for laplacian signals with absolute error distortion a simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented

analogue signalling by phase shifting this paper presents a novel method for overlaying an analogue value on top of a digital signal by adding a phase rotation and a signature sequence to a block of digitally modulated data symbols this analogue value can be conveyed to a receiver without significant degradation to the underlying digital data a near ml estimator is derived which is non data driven and hence independent of the digital data sequence it is shown that this method of signalling a value is superior to quantising it and adding it to the digital data stream we analyse the performance of the analogue and digital methods and also compare them using simulations

multiple description analog joint source channel coding to exploit the diversity in parallel channels the complexity and delay introduced by efficient digital coding strategies may be a barrier in some real time communications in this sense these last years joint source channel coding schemes based on analog mappings have gained prominence precisely for their simplicity and their implicit low delay in this work analog mappings originally designed for point to point communications are adapted to the case of parallel channels by following the multiple description strategy traditionally used in source coding in principle the coding scheme is designed to transmit over parallel awgn on off channels which are characterized by the possibility of having failures we also show that our scheme performs satisfactorily over slow rayleigh fading parallel channels

analog multiple description joint source channel coding based on lattice scaling joint source channel coding schemes based on analog mappings for point to point channels have recently gained attention for their simplicity and low delay in this paper these schemes are extended either to scenarios with or without side information at the decoders to transmit multiple descriptions of a gaussian source over independent parallel channels they are based on a lattice scaling approach together with bandwidth reduction analog mappings adapted for this multiple description scenario the rationale behind lattice scaling is to improve performance through bandwidth expansion another important contribution of this paper is the proof of the separation theorem for the communication scenario of multiple description with side information at the decoders this proof allows us to compare the performance of the proposed schemes with the theoretical limits when considering awgn channels finally when the channels are parallel slow fading rayleigh the proposed schemes are optimal in terms of distortion exponent

joint trellis coded quantization modulation a joint source channel coding system constructed using trellis coded quantization tcq and trellis coded modulation tcm is described identical trellises are used in the tcq and tcm systems and a straightforward mapping of tcq codewords to tcm symbols is presented which guarantees that euclidean squared distance in the channel is commensurate with quantization mean square error mse hence likely tcm error events of small euclidean distance cause only a small increase in overall source coding mse

joint unitary triangularization for mimo networks this paper considers communication networks where individual links can be described as those based on multiple input multiple output channels unlike orthogonal modulation methods such as the singular value decomposition we allow interference between subchannels which can be removed by the receivers via successive cancellation the degrees of freedom earned by this relaxation are used for obtaining a basis and corresponding decomposition which are simultaneously good for more than one link specifically we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast channel receivers we then apply this decomposition to two scenarios first in digital multicasting we present a practical capacity achieving scheme which uses only scalar codes and linear processing then we consider the joint source channel problem of transmitting a gaussian source over a two user multiple input multiple output channel where we show the existence of nontrivial cases where the optimal distortion pair which for high signal to noise ratios snrs equals the optimal point to point distortions of the individual users may be achieved by employing a hybrid digital analog scheme over the induced equivalent channel these scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network thus we coin the approach network modulation

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

a source channel separation theorem with application to the source broadcast problem a converse method is developed for the source broadcast problem specifically it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source channel separation theorem can be leveraged via a reduction argument to establish a necessary condition for the original problem which unifies several existing results in the literature somewhat surprisingly this method albeit based on the source channel separation theorem can be used to prove the optimality of non separation based schemes and determine the performance limits in certain scenarios where the separation architecture is suboptimal

on robustness of hybrid digital analog source channel coding with bandwidth mismatch for transmission of memoryless gaussian sources over channels with additive white gaussian noise the tradeoff between the distortion when the channel quality is good versus bad is investigated under the constraint that the distortion is optimal when the channel has the targeted median quality the problem was proposed by tian and shamai who subsequently proved remarkable achievability results for bandwidth expansion ratios kappa which are integers or unit fractions i e kappa 2 3 4 ldots or kappa 1 2 1 3 1 4 ldots their result is extended here to all kappa geq 2 and kappa leq 1 2 by generalizing the hybrid digital analog hda scheme of wilson et al to the case of bandwidth mismatch finally novel schemes are proposed for 1 2 leq kappa and 1 achieving nontrivial tradeoffs outperforming all known schemes these latter schemes rely on another extension of the hda scheme by wilson et al namely the relaxation of the independence of source and channel input sequences

single sample robust joint source channel coding achieving asymptotically optimum scaling of sdr versus snr in this paper we consider the problem of zero delay encoding a single source sample robust joint source channel coding over an additive white gaussian noise channel we propose a new scheme that unlike previously known coding schemes achieves the optimal scaling of the source signal to distortion ratio sdr versus channel signal to noise ratio snr also we propose a family of robust codes which together maintain a bounded gap with the optimum sdr curve in terms of decibel to show the importance of this result we derive some theoretical bounds on the asymptotic performance of a widely used class of delay limited hybrid digital analog hda coding schemes based on superposition of analog and digital components we show that unlike the delay unlimited case for this class of delay limited hda codes the asymptotic performance loss is unbounded in terms of decibels although the main focus of this paper is on uniform sources it is also shown that the results are also valid for a more general class of well behaved distributions

joint source channel coding with correlated interference we study the joint source channel coding problem of transmitting a discrete time analog source over an additive white gaussian noise awgn channel with interference known at transmitter we consider the case when the source and the interference are correlated we first derive an outer bound on the achievable distortion and then we propose two joint source channel coding schemes the first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a wyner ziv encoder and a dirty paper encoder in the second scheme the digital part is replaced by the hybrid digital and analog scheme proposed by wilson et al when the channel signal to noise ratio snr is perfectly known at the transmitter both proposed schemes are shown to provide identical performance which is substantially better than that of existing schemes in the presence of an snr mismatch both proposed schemes are shown to be capable of graceful enhancement and graceful degradation interestingly unlike the case when the source and interference are independent neither of the two schemes outperforms the other universally as an application of the proposed schemes we provide both inner and outer bounds on the distortion region for the generalized cognitive radio channel

design and performance of vq based hybrid digital analog joint source channel codes a joint source channel hybrid digital analog hda vector quantization vq system is presented the main advantage of the new vq based hda system is that it achieves excellent rate distortion capacity performance at the design signal to noise ratio snr while maintaining a graceful improvement characteristic at higher snrs it is demonstrated that within the hda framework the parameters of the system can be optimized using an iterative procedure similar to that of channel optimized vector quantizer design comparisons are made with three purely digital systems and one purely analog system it is found that at high snrs the vq based hda system is superior to the other investigated systems at low snrs the performance of the new scheme can be improved using the optimization procedure and using soft decoding in the digital part of the system these results demonstrate that the introduced scheme provides an attractive method for terrestrial broadcasting applications

on source transmission over mimo channels with limited feedback the problem of source channel coding over a multiple antenna mimo channel with quantized channel state information at the transmitter csit is considered upper bounds on the distortion exponents achieved with partial csit under a long term power constraint are developed it is shown that the distortion exponent with perfect csit grows unbounded as the ratio between the channel and source bandwidth increases while the exponent achieved with any feedback link of fixed finite resolution is bounded above by a polynomial of the product between the number of transmit and number of receive antennas the resolution of the feedback link should grow with the bandwidth ratio to make the distortion exponent scale as fast as that in the perfect csit case we show that in order to achieve the optimal scaling the csit feedback resolution must grow logarithmically with the bandwidth ratio for mimo channels and faster than linear for the single input single output channel the achievable distortion exponent of some hybrid schemes with heavily quantized feedback is also derived the results demonstrate that dramatic performance improvement over the case of no csit can be achieved by combining simple schemes with a very coarse csit feedback

linear analog coding of correlated multivariate gaussian sources the effect of prior knowledge when linear analog codes are used as joint source channel codes for sources modeled as multivariate gaussian processes is analyzed we use information theoretic tools to evaluate the achievable performance gain obtained by exploiting prior knowledge in order to assess the validity of linear codes in practical scenarios where exact source statistics are not known we study the effect of having partial knowledge of the statistics we model the mismatch of the statistics as an additive perturbation matrix between the real covariance matrix and the postulated covariance matrix in the recovery process in this setting we obtain closed form expressions for a deterministic perturbation matrix and using random matrix theory tools we characterize the performance loss for i i d random matrices

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

on the distortion snr exponent of hybrid digital analog space time coding we consider the transmission of a real independent and identically distributed i i d analog source over a quasi static m input n output multiple input multiple output mimo block fading channel the relevant performance criterion is end to end average quadratic distortion d versus channel signal to noise ratio snr for given spectral efficiency eta defined as the ratio of the source bandwidth over the channel bandwidth in the limit of high snr we define the distortion snr exponent a eta as the largest a such that d esdot snr a over all possible source channel coding schemes of spectral efficiency eta we find a simple upper bound on a eta an achievable lower bound asep eta achievable by separated tandem source channel coding and a tighter lower bound ahybrid eta achievable by new hybrid digital analog space time coding schemes as a corollary we have that a eta is completely determined for the scalar case m n 1 and for the bandwidth compression case eta ges 2 min m n expiicit and simple construction of hybrid space time codes achieving ahybrid eta are also given

a unified approach to tree structured and multistage vector quantization for noisy channels the large encoding complexity and sensitivity to channel errors of vector quantization vq are discussed the performance of two low complexity vqs the tree structured vq tsvq and the multistage vq msvq when used over noisy channels are analyzed an algorithm is developed for the design of channel matched tsvq cm tsvq and channel matched msvq cm msvq under the squared error criterion extensive numerical results are given for the correlation coefficient 0 9 comparisons with the ordinary tsvq and msvq designed for the noiseless channel show substantial improvements when the channel is very noisy the cm msvq which can be regarded as a block structured combined source channel coding scheme is compared with a block structured tandem source channel coding scheme with the same block length as the cm msvq for the gauss markov source the cm msvq outperforms the tandem scheme in all cases that the authors have considered it is demonstrated that the cm msvq is fairly robust to channel mismatch

source interference recovery over broadcast channels asymptotic bounds and analog codes we consider the problem of joint recovery of a bivariate gaussian source and of interference over the two user gaussian degraded broadcast channel in the presence of common interference the interference that is available non causally at the encoder is assumed to be gaussian and correlated to the sources the tradeoff between the distortion of the sources and the interference estimation error is studied information theoretic outer and inner bounds based on ideas from rate distortion theory and hybrid coding are derived respectively more precisely the outer bound is found by assuming additional knowledge at each user the inner bound however is obtained by analyzing the distortion of a layered hybrid scheme based on proper power splitting costa and wyner ziv coding low delay and complexity coding schemes based on analog mapping are next proposed more specifically parametric mappings based on linear and sawtooth curves are studied and optimized by minimizing an upper bound on the system s distortion nonparametric mappings based on joint optimization between the encoder and the decoder using an iterative algorithm are designed numerical results show that for the special cases that are previously considered by abou saleh et al with no fading the derived outer bound is tighter and the proposed hybrid scheme has a lower complex structure with no loss in performance in addition the proposed low delay nonlinear schemes outperform the linear scheme and perform relatively close to the inner bound under certain system settings

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

distortion bounds for broadcasting with bandwidth expansion we consider the problem of broadcasting a single gaussian source to two listeners over a gaussian broadcast channel with rho channel uses per source sample where rho 1 a distortion pair d1 d2 is said to be achievable if one can simultaneously achieve a mean squared error mse d1 at receiver 1 and d2 at receiver 2 the main result of this correspondence is an outer bound for the set of all achievable distortion pairs that is we find necessary conditions under which d1 d2 is achievable we then apply this result to the problem of point to point transmission over a gaussian channel with unknown signal to noise ratio snr and rho 1 we show that if a system must be optimal at a certain snrmin then asymptotically the system distortion cannot decay faster than o 1 snr as for achievability we show that a previously reported scheme due to mittal and phamdo 2002 is optimal at high snr we introduce two new schemes for broadcasting with bandwidth expansion combining digital and analog transmissions we finally show how a system with a partial feedback returning from the bad receiver to the transmitter and to the good receiver achieves a distortion pair that lies on the outer bound derived here

joint source channel coding of a gaussian mixture source over the gaussian broadcast channel suppose that we want to send a description of a single source to two listeners through a gaussian broadcast channel where the channel is used once per source sample the problem of joint source channel coding is to design a communication system to minimize the distortion d sub 1 at receiver 1 and at the same time minimize the distortion d sub 2 at receiver 2 if the source is gaussian the optimal solution is well known and it is achieved by an uncoded analog scheme we consider a gaussian mixture source we derive inner and outer bounds for the distortion region of all d sub 1 d sub 2 pairs that are simultaneously achievable the outer bound is based on the entropy power inequality while the inner bound is attained by a digital over analog encoding scheme which we present we also show that if the modes of the gaussian mixture are highly separated our bounds are tight and hence our scheme attains the entire distortion region this optimal region exceeds the region attained by separating source and channel coding although it does not contain the ideal point d sub 1 d sub 2 r sup 1 c sub 1 r sup 1 c sub 2