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

modulated lattice vector quantization how to make quantization index modulation an efficient variable rate source coder the design of a variable rate joint watermarking and compression jwc scheme is examined in this paper the proposed approach called modulated lattice vector quantization mlvq is based on dither modulation quantization index modulation dm qim which allows for embedding information while maintaining good coding performance in the first part we propose a specific indexing method to make mlvq with a multidimensional codebook feasible furthermore a quantization parameter estimation was designed to ensure the invertibility of the embedding the limitations of the compression performance of jwc schemes are studied in the second part we show the existence of a coding rate lower bound which depends mainly on the codebook characteristics and dramatically decreases coding performance to circumvent this drawback two improved mlvq schemes are proposed in the first one called arbitrary mlvq the embedding is performed on part of the signal to ensure a low embedding coding ratio in the second one called deadzone mlvq the coding efficiency is further improved by maintaining the sparsity of the quantized host signal it consists in excluding the sparse signal components from the embedding process then thresholding them these schemes both applying wavelet coding demonstrate their efficiency as variable rate coders

transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

duality between channel capacity and rate distortion with two sided state information we show that the duality between channel capacity and data compression is retained when state information is available to the sender to the receiver to both or to neither we present a unified theory for eight special cases of channel capacity and rate distortion with state information which also extends existing results to arbitrary pairs of independent and identically distributed i i d correlated state information s sub 1 s sub 2 available at the sender and at the receiver respectively in particular the resulting general formula for channel capacity c max sub p u x s sub 1 i u s sub 2 y i u s sub 1 assumes the same form as the generalized wyner ziv 1976 rate distortion function r d min sub p u x s sub 1 p x spl i cap u s sub 2 i u s sub 1 x 1 u s sub 2

toward a practical scheme for binary broadcast channels with varying channel quality using dirty paper coding we consider practical schemes for binary dirty paper channels and broadcast channels bcs with two receivers and varying channel quality with the bc application in mind this paper proposes a new design for binary dirty paper coding dpc by exploiting the concept of coset binning the complexity of the system is greatly reduced when compared to the existing works some design challenges of the coset binning approach are identified and addressed the proposed binary dpc system achieves similar performance to the state of the art superposition coding based system while demonstrating significant advantages in terms of complexity and flexibility of system design for binary bcs achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non uniform bit distribution the non uniform bit distribution is chosen according to the channel conditions therefore to achieve the capacity for binary bcs with varying channel quality it is necessary to use quantization codes of different rates which significantly increases the implementation complexity in this paper we also propose a broadcast scheme that generalizes the concept of binary dpc which we term soft dpc by combining soft dpc with time sharing we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead our scheme uses only one fixed pair of codes for users 1 and 2 and a single quantization code which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance

wyner ziv coding over broadcast channels hybrid digital analog schemes a new hybrid digital analog scheme is proposed for lossy transmission of a gaussian source over a bandwidth matched gaussian broadcast channel with source side information available at each receiver the proposed scheme combines two schemes that were previously shown to achieve optimal point to point distortion power tradeoff simultaneously at all receivers under two distinct conditions stated in terms of channel and side information quality parameters for the two receiver case the combined scheme is shown to achieve the same kind of optimality for the entire region in the parameter space sandwiched between those two conditions crucial to this result is a new degree of freedom discovered in designing point to point hybrid digital analog schemes with side information when superimposed with analog transmission the proposed scheme outperforms all previously known schemes even outside the optimality region in the parameter space

on gaussian mimo bc mac duality with multiple transmit covariance constraints owing to the special structure of the gaussian multiple input multiple output mimo broadcast channel bc the associated capacity region computation and beamforming optimization problems are typically non convex and thus cannot be solved directly one feasible approach is to consider the respective dual multiple access channel mac problems which are easier to deal with due to their convexity properties the conventional bc mac duality has been established via bc mac signal transformation and is applicable only for the case in which the mimo bc is subject to a single transmit sum power constraint an alternative approach is based on minimax duality which can be applied to the case of the sum power constraint or per antenna power constraint in this paper the conventional bc mac duality is extended to the general linear transmit covariance constraint ltcc case which includes sum power and per antenna power constraints as special cases the obtained general bc mac duality is applied to solve the capacity region computation for the mimo bc and beamforming optimization for the multiple input single output miso bc respectively with multiple ltccs the relationship between this new general bc mac duality and the minimax duality is also discussed and it is shown that the general bc mac duality leads to simpler problem formulations moreover the general bc mac duality is extended to deal with the case of nonlinear transmit covariance constraints in the mimo bc

a proof of marton s coding theorem for the discrete memoryless broadcast channel corresp a simple proof using random partitions and typicality is given for marton s coding theorem for broadcast channels

relative contributions of specific frequency bands to the loudness of broadband sounds listeners with normal hearing nh and sensorineural hearing loss snhl were asked to compare pairs of noise stimuli and choose the louder noise in each pair each noise was made up of 15 two erbn equivalent rectangular bandwidth wide frequency bands that varied independently over a 12 db range from one presentation to the next mean levels of the bands followed the long term average speech spectrum ltass or were set to 43 51 or 59 db sound pressure level spl the relative contribution of each band to the total loudness of the noise was determined by computing the correlation between the difference in levels for a given band on every trial and the listener s decision on that trial weights for snhl listeners were governed by audibility and the spectrum of the noise stimuli with bands near the spectral peak of the ltass noise receiving greatest weight nh listeners assigned greater weight to the lowest and highest bands an effect that increased with overall level but did not assign greater weight to bands near the ltass peak additional loudness matching and paired comparison studies using stimuli missing one of the 15 bands showed a significant contribution by the highest band but properties other than loudness may have contributed to the decisions

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

joint wyner ziv dirty paper coding by modulo lattice modulation the combination of source coding with decoder side information the wyner ziv problem and channel coding with encoder side information the gel fand pinsker problem can be optimally solved using the separation principle in this work we show an alternative scheme for the quadratic gaussian case which merges source and channel coding this scheme achieves the optimal performance by applying a modulo lattice modulation to the analog source thus it saves the complexity of quantization and channel decoding and remains with the task of ldquoshapingrdquo only furthermore for high signal to noise ratio snr the scheme approaches the optimal performance using an snr independent encoder thus it proves for this special case the feasibility of universal joint source channel coding

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

perceptual weights in auditory level discrimination perceptual weights in level discrimination also called intensity discrimination were determined for 3 7 15 and 24 component tone complexes with flat spectral envelopes using a correlational paradigm each frequency component was randomly and independently perturbed in level on each presentation for the target interval frequency component levels were additionally increased by the level increment to be detected l 20 log10 p p p where p is pressure weights were calculated from the across trial correlation between the level perturbations for each frequency component and the interval chosen by the listener two conditions were investigated 1 l was equal across frequency components and 2 l increased progressively across frequency components for both conditions data for four listeners usually showed the greatest weight for the highest frequency component the two to four highest frequency components generally were most important for level discrimination the effect of increasing l

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

broadcast and mac aware coding strategies for multiple user information embedding multiple user information embedding is concerned with embedding several messages into the same host signal this paper presents several implementable dirty paper coding dpc based schemes for multiple user information embedding through emphasizing their tight relationship with conventional multiple user information theory we first show that depending on the targeted application and on whether the different messages are asked to have different robustness and transparency requirements or not multiple user information embedding parallels one of the well known multiuser channels with state information available at the transmitter the focus is on the gaussian broadcast channel gbc and the gaussian multiple access channel gmac for each of these channels two practically feasible transmission schemes are compared the first approach consists in a straightforward rather intuitive superimposition of dpc schemes the second consists in a joint design of these dpc schemes this joint approach heavily relies on a recent work by kim in which the authors extend the single user costa s dpc to the multiple user case the results in this paper extend the practical implementations quantization index modulation qim distortion compensated qim dc qim and scalar costa scheme scs that have been originally conceived for one user to the multiple user case after presenting the key features of the joint design within the context of structured scalar codebooks we broaden our view to discuss the framework of more general lattice based vector codebooks and show that the gap to full performance can be bridged up using finite dimensional lattice codebooks performance evaluations including bit error rates bers and achievable rate region curves are provided for both methods illustrating the improvements brought by a joint design

spectral weights for overall level discrimination in listeners with sensorineural hearing loss a conditional on a single stimulus coss analysis procedure b g berg j acoust soc am 86 1743 1746 1989 was used to measure the weight or relative reliance that normal hearing and hearing impaired listeners give to different frequencies in the discrimination of the overall level of a multitone complex on each trial two multitone tone complexes comprised of six octave frequencies from 250 to 8000 hz were presented to subjects the levels of the frequencies for each complex were randomly varied the listeners task was to identify the complex with the higher overall intensity level normal hearing listeners used a variety of listening strategies to perform the task showing no general preference to weight one component over another hearing impaired listeners however showed a general tendency to give greatest weight to the spectral information in the region of their hearing loss thirteen of the 14 hearing impaired listeners all of whom had a high frequency sensorineural hearing loss weighted one or more of the high frequency components in the complex the greatest

practical dirty paper coding with sum codes in this paper we present a practical method to construct dirty paper coding dpc schemes using sum codes unlike the commonly used approach to dpc where the coding scheme involves concatenation of a channel code and a quantization code the proposed method embodies a unified approach that emulates the binning method used in the proof of the dpc result auxiliary bits are used to create the desired number of code vectors in each bin sum codes are obtained when information sequences augmented with auxiliary bits are encoded using linear block codes sum code based dpc schemes can be implemented using any linear block code and entail a relatively small increase in decoder complexity when compared to standard communication schemes they can also lead to significant reduction in transmit power in comparison to standard schemes

capacity region of cooperative multiple access channel with states we consider a two user state dependent multiaccess channel in which the states of the channel are known noncausally to one of the encoders and only strictly causally to the other encoder both encoders transmit a common message and in addition the encoder that knows the states noncausally transmits an individual message we find explicit characterizations of the capacity region of this communication model in both discrete memoryless and memoryless gaussian cases in particular the capacity region analysis demonstrates the utility of the knowledge of the states only strictly causally at the encoder that sends only the common message in general more specifically in the discrete memoryless setting we show that such a knowledge is beneficial and increases the capacity region in general in the gaussian setting we show that such a knowledge does not help and the capacity is same as if the states were completely unknown at the encoder that sends only the common message furthermore we also study the special case in which the two encoders transmit only the common message and show that the knowledge of the states only strictly causally at the encoder that sends only the common message is not beneficial in this case in both discrete memoryless and memoryless gaussian settings the analysis also reveals optimal ways of exploiting the knowledge of the state only strictly causally at the encoder that sends only the common message when such a knowledge is beneficial the encoders collaborate to convey to the decoder a lossy version of the state in addition to transmitting the information messages through a generalized gel fand pinsker binning particularly important in this problem are the questions of 1 optimal ways of performing the state compression and 2 whether or not the compression indices should be decoded uniquely by developing two optimal coding schemes that perform this state compression differently we show that when used as parts of appropriately tuned encoding and decoding processes both compression a la noisy network coding by lim or the quantize map and forward by avestimeher i e with no binning and compression using wyner ziv binning are optimal the scheme that uses wyner ziv binning shares elements with cover and el gamal original compress and forward but differs from it mainly in that backward decoding is employed instead of forward decoding and the compression indices are not decoded uniquely finally by exploring the properties of our outer bound we show that although not required in general the compression indices can in fact be decoded uniquely essentially without altering the capacity region but at the expense of larger alphabets sizes for the auxiliary random variables

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

approximate capacity of the dirty multiple access channel with partial state information at the encoders in this paper we consider the k user gaussian multiple access channel with multiple independent additive white gaussian interferences each interference is known to exactly one transmitter non causally the capacity region is characterized to within a bounded gap regardless of channel parameters these results are based on a layered modulo lattice scheme which realizes distributed interference cancellation

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

static output feedback controllers stability and convexity the main objective of this paper is to solve the following stabilizing output feedback control problem given matrices a b sub 2 c sub 2 with appropriate dimensions find if one exists a static output feedback gain l such that the closed loop matrix a b sub 2 lc sub 2 is asymptotically stable it is known that the existence of l is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs hence this paper provides a new sufficient but not necessary condition for the solvability of the above stabilizing output feedback control problem as a natural extension we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index some examples borrowed from the literature are solved to illustrate the theoretical results

high snr analysis for mimo broadcast channels dirty paper coding versus linear precoding in this correspondence we compare the achievable throughput for the optimal strategy of dirty paper coding dpc to that achieved with suboptimal and lower complexity linear precoding techniques zero forcing and block diagonalization both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain but an absolute difference in terms of throughput does exist the sum rate difference between the two strategies is analytically computed at asymptotically high snr furthermore the difference is not affected by asymmetric channel behavior when each user has a different average snr weighted sum rate maximization is also considered in the process it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate

augmented lagrangian approach to design of structured optimal state feedback gains we consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers these constraints are in the form of sparsity requirements for the feedback matrix implying that each controller has access to information from only a limited number of subsystems the minimizer of this constrained optimal control problem is sought using the augmented lagrangian method notably this approach does not require a stabilizing structured gain to initialize the optimization algorithm motivated by the structure of the necessary conditions for optimality of the augmented lagrangian we develop an alternating descent method to determine the structured optimal gain we also utilize the sensitivity interpretation of the lagrange multiplier to identify favorable communication architectures for structured optimal design examples are provided to illustrate the effectiveness of the developed method

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

achievable rates of multi antenna downlink channels with peak power constraints this paper considers a gaussian multiple input single output miso broadcast channel with a per antenna peak power constraint or simply peak power constraint it is more realistic to consider the peak power constraint on each transmit antenna because in many practical implementations each antenna is equipped with its own power amplifier assuming the perfect knowledge of the channel state information csi at the transmitter we propose an achievable scheme using dirty tape coding dtc the ideal dirty paper coding dpc which is a capacity achieving scheme for the gaussian multiple input multiple output mimo broadcast channel cannot be used for our model because its optimal input distribution is gaussian and thus the peak power constraint is violated on the other hand the channel input of dtc is uniformly distributed in a fixed range which helps to control the peak power of the transmit signal easily we also present an algorithm that finds capacity achieving beamforming vectors and power allocation factors under a per antenna average power constraint and use the optimized parameters in the proposed scheme simulation results show that the proposed scheme provides gains of 2 7db over a non dtc scheme based on minimum mean square error mmse beamforming at high signal to noise ratio snr when there are three receivers and the transmitter has three antennas

spectral weights for sample discrimination as a function of overall level doherty and lutfi 1996 spectral weights for overall level discrimination in listeners with sensorineural hearing loss j acoust soc am 99 1053 1058 examined the weights assigned to individual components of a six tone complex during a sample discrimination task and reported that hearing impaired subjects gave the most weight to components in the region of their high frequency hearing loss in contrast weighting patterns varied for normal hearing subjects in the current study the same six tone complex comprised of the octave frequencies from 0 25 to 8 khz was presented to three subjects with normal hearing in high pass noise in low pass noise and in quiet at two overall levels consistent with doherty and lutfi subjects assigned more weight to the 4 khz component in the high pass noise condition but roughly equal weight to all components in the lower level quiet condition weights in the low pass noise and higher level quiet conditions however were similar to those in the high pass no

quantization based methods additive attacks performance analysis the main goal of this study consists in the development of the worst case additive attack wcaa for ary quantization based data hiding methods using as design criteria the error probability and the maximum achievable rate of reliable communications our analysis focuses on the practical scheme known as distortion compensated dither modulation dc dm from the mathematical point of view the problem of the worst case attack wca design using probability of error as a cost function is formulated as the maximization of the average probability of error subject to the introduced distortion for a given decoding rule when mutual information is selected as a cost function a solution of the minimization problem should provide such an attacking noise probability density function pdf that will maximally decrease the rate of reliable communications for an arbitrary decoder structure the obtained results demonstrate that within the class of additive attacks the developed attack leads to a stronger performance decrease for the considered class of embedding techniques than the additive white gaussian or uniform noise attacks

an alternate numerical solution to the linear quadratic problem this note proposes a new method based on convex programming for solving the linear quadratic problem lqp directly on the parameter space generated by the feedback control gain all stabilizing controllers are mapped into a convex set the problem is then formulated as a minimization of a linear function over this convex set its optimal solution furnishes under certain conditions the same feedback control gain obtained from the classical riccati equation generalizations to decentralized control and output feedback control design are included the theory is illustrated by some numerical examples

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

hybrid mu miso scheduling with limited feedback using hierarchical codebooks the multiuser mimo mu mimo systems tend to have inter user interference in practical systems with limited feedback practical mu mimo systems with limited feedback can be divided into two classes in general one is zero forcing beamforming zfbf and the other is per user unitary rate control pu2rc which is an extended version of random beamforming rbf to improve performance zfbf needs more feedback bits and pu2rc needs a larger number of users we propose a new hybrid mu miso system which has the advantages of the two mu mimo schemes simultaneously and analyze the sum rate performance and the quantization error of the hybrid scheme the analysis shows how the number of feedback bits the number of users and the signal power affect the sum rate the throughput scaling laws are also derived in the high and the medium snr regimes simulation results show that the proposed hybrid mu miso system performs better than either of the two mu mimo systems with the same number of feedback bits another advantage is that it has lower complexity for codeword search since it has a hierarchical codebook structure

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

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

on a markov lemma and typical sequences for polish alphabets in this paper we consider a new definition of typicality based on the weak topology that is applicable to polish alphabets which includes mathbb r n this notion is a generalization of strong typicality in the sense that it degenerates to strong typicality in the finite alphabet case and can also be applied to mixed and continuous distributions furthermore it is strong enough to prove a markov lemma and thus can be used to directly prove a more general class of results than entropy or weak typicality we provide two example applications of this technique first using the markov lemma we directly prove a coding result for gel fand pinsker channels with an average input constraint for a large class of alphabets and channels without first proving a finite alphabet result and then resorting to delicate quantization arguments this class of alphabets includes for example real and complex inputs subject to a peak amplitude restriction while this large class does not directly allow for gaussian distributions with average power constraints it is shown to be straightforward to recover this case by considering a sequence of truncated gaussian distributions as a second example we consider a problem of coordinated actions i e empirical distributions for a two node network where we derive necessary and sufficient conditions for a given desired coordination

on the capacity of the carbon copy onto dirty paper channel the carbon copy onto dirty paper ccdp channel is the compound writing on dirty paper channel in which the channel output is obtained as the sum of the channel input white gaussian noise and a gaussian state sequence randomly selected among a set possible realizations the transmitter has non causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output we study the capacity of the ccdp channel for two scenarios 1 the state sequences are independent and identically distributed and 2 the state sequences are scaled versions of the same sequence in the first scenario we show that a combination of superposition coding time sharing and gel fand pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations in the second scenario we derive capacity to within 4 bits per channel use for the case of two possible state sequences this result is extended to the ccdp channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as strong fading regime we conclude by providing some remarks on the capacity of the ccdp channel in which the state sequences have any jointly gaussian distribution

on error exponents of modulo lattice additive noise channels modulo lattice additive noise mlan channels appear in the analysis of structured binning codes for costa s dirty paper channel and of nested lattice codes for the additive white gaussian noise awgn channel in this paper we derive a new lower bound on the error exponents of the mlan channel with a proper choice of the shaping lattice and the scaling parameter the new lower bound coincides with the random coding lower bound on the error exponents of the awgn channel at the same signal to noise ratio snr in the sphere packing and straight line regions this result implies that at least for rates close to channel capacity 1 writing on dirty paper is as reliable as writing on clean paper and 2 lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes with maximum likelihood decoding for the awgn channel

multiple description quantization via gram schmidt orthogonalization the multiple description md problem has received considerable attention as a model of information transmission over unreliable channels a general framework for designing efficient md quantization schemes is proposed in this paper we provide a systematic treatment of the el gamal cover egc achievable md rate distortion region and show it can be decomposed into a simplified egc segc region and a superimposed refinement operation furthermore any point in the segc region can be achieved via a successive quantization scheme along with quantization splitting for the quadratic gaussian case the proposed scheme has an intrinsic connection with the gram schmidt orthogonalization which implies that the whole gaussian md rate distortion region is achievable with a sequential dithered lattice based quantization scheme as the dimension of the optimal lattice quantizers becomes large moreover this scheme is shown to be universal for all independent and identically distributed i i d smooth sources with performance no worse than that for an i i d gaussian source with the same variance and asymptotically optimal at high resolution a class of md scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically the performance is analyzed in the high resolution regime which exhibits a noticeable improvement over the existing md scalar quantization schemes

lmi relaxations for reduced order robust cal h _ infty control of continuous time uncertain linear systems this technical note is concerned with the problem of reduced order robust h dynamic output feedback control design for uncertain continuous time linear systems the uncertain time invariant parameters belong to a polytopic domain and affect all the system matrices the search for a reduced order controller is converted in a problem of static output feedback control design for an augmented system to solve the problem a two stage linear matrix inequality lmi procedure is proposed at the first step a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined this parameter dependent state feedback controller is used at the second stage which synthesizes the robust parameter independent output feedback h dynamic controller a homogeneous polynomially parameter dependent lyapunov function of arbitrary degree is used to assess closed loop stability with a prescribed h attenuation level as illustrated by numerical examples the proposed method provides better results than other lmi based conditions from the literature

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

use of perceptual weights to test a model of loudness summation leibold et al j acoust soc am 121 2822 2831 2007 examined the perceptual weight subjects assigned to individual components of a multitone complex while performing a loudness matching task weights agreed with the moore et al loudness model j audio eng soc 45 224 237 1997 except when components were widely spaced in frequency in an effort to account for the data the just noticeable difference jnd for intensity discrimination was measured for each component and compared to the weight for that component the model predicts greater improvement in intensity discrimination with increasing bandwidth than was observed in the data jnds were not correlated with weights in the widest frequency spacing condition

vector perturbation based on symbol scaling for limited feedback miso downlinks we propose a low complexity vector precoding vp scheme for the downlink of multi user multiple input single output mu miso systems with limited feedback conventional vp requires the use of modulo operation and knowledge of the scaling factor used at the transmitter in order to remove the perturbation quantity at the receiver the latter may be problematic in certain limited feedback scenarios where only quantized versions of the scaling factor can be made available at the receiver to circumvent this shortcoming we propose a modified vp technique where the search of perturbing vectors is limited to the area in the symbol constellation which is constrictive to the information symbols i e the area where the distances from the decision thresholds are increased with respect to a distance threshold by doing this the perturbation quantities can only enhance detection and need not be removed at the receiver successful detection can therefore be done without the use of the modulo operation and the scaling factor which makes the proposed vp scheme applicable to limited feedback scenarios analytical and simulation results show that the performance of the proposed scheme is free of the error floor typically encountered with conventional vp in the presence of limited feedback

brief the infinite time near optimal decentralized regulator problem for singularly perturbed systems a convex optimization approach this paper presents lq decentralized pole location for singularly perturbed systems the poles are located in a sector included in the left half complex plane the singular perturbation method is used to define reduced and well behaved problems it is shown that the lq control problem with pole location in a sector can be solved using the lmi tool the associated parametrical optimization problem involves a linear cost objective under lmi constraints the decentralized control problem is then solved in the reduced slow system by just introducing structure constraints on the matrix variables constraints that do not destroy the linearity and then the convexity of the problem

on the loss of single letter characterization the dirty multiple access channel for general memoryless systems the existing information theoretic solutions have a ldquosingle letterrdquo form this reflects the fact that optimum performance can be approached by a random code or a random binning scheme generated using independent and identically distributed copies of some scalar distribution is that the form of the solution of any information theoretic problem in fact some counter examples are known the most famous one is the ldquotwo help onerdquo problem korner and marton showed that if we want to decode the modulo two sum of two correlated binary sources from their independent encodings then linear coding is better than random coding in this paper we provide another counter example the ldquodoubly dirtyrdquo multiple access channel mac like the korner marton problem this is a multiterminal scenario where side information is distributed among several terminals each transmitter knows part of the channel interference while the receiver only observes the channel output we give an explicit solution for the capacity region of the binary doubly dirty mac demonstrate how this region can be approached using a linear coding scheme and prove that the ldquobest known single letter regionrdquo is strictly contained in it we also state a conjecture regarding the capacity loss of single letter characterization in the gaussian case

exact sum rate analysis of mimo broadcast channels with random unitary beamforming random unitary beamforming rub is an attractive transmission scheme for mimo broadcast channels because of its ability to achieve high sum rate capacity with limited feedback in this letter we derive the exact analytical expressions for the ergodic sum rate of mimo broadcast channels with rub the analysis is facilitated by the development of the complete statistical characterization of ordered beam sinrs for a user which can find their application in many related problems

perceptual weights for loudness judgments of six tone complexes subjects with normal hearing nh and with sensorineural hearing loss snhl judged the overall loudness of six tone complexes comprised of octave frequencies from 0 25 to 8 khz the level of each tone was selected from a normal distribution with a standard deviation of 5 db and subjects judged which of two complexes was louder overall level varied across conditions in the loudness task there was no difference in mean level across the two stimuli in the sample discrimination task the two complexes differed by an average of 5 db for both tasks perceptual weights were derived by correlating the differences in level between matched frequency tones in the complexes and the loudness decision on each trial weights obtained in the two tasks showed similar shifts from low to high frequency components with increasing overall level simulation of these experiments using a model of loudness perception moore and glasberg 2004 hear res 188 70 88 yielded predicted weights for these stimuli that were highly correlated with predicted specific loudness but not with the observed weights

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

relative estimates of combination weights decision criteria and internal noise based on correlation coefficients a means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent normally distributed random variables xi s the first theorem presents the correlation between the binary response variables signal versus no signal and the component xi the second theorem presents a parallel result for the case that additive internal noise is present thus in psychophysical experiments the relative combination weights may be obtained by correlating the observers responses and the input random variables third three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

categorical loudness scaling and equal loudness contours in listeners with normal hearing and hearing loss this study describes procedures for constructing equal loudness contours elcs in units of phons from categorical loudness scaling cls data and characterizes the impact of hearing loss on these estimates of loudness additionally this study developed a metric level dependent loudness loss which uses cls data to specify the deviation from normal loudness perception at various loudness levels and as function of frequency for an individual listener with hearing loss cls measurements were made in 87 participants with hearing loss and 61 participants with normal hearing an assessment of the reliability of cls measurements was conducted on a subset of the data cls measurements were reliable there was a systematic increase in the slope of the low level segment of the cls functions with increase in the degree of hearing loss elcs derived from cls measurements were similar to standardized elcs international organization for standardization iso 226 2003 the presence of hearing loss decreased the vertical spacing of the elcs reflecting loudness recruitment and reduced cochlear compression representing cls data in phons may lead to wider acceptance of cls measurements like the audiogram that specifies hearing loss at threshold level dependent loudness loss describes deficit for suprathreshold sounds such information may have implications for the fitting of hearing aids

successive refinement for the wyner ziv problem and layered code design we examine successive refinement for the wyner ziv problem described in a recent paper by steinberg and merhav where the authors showed that if the side information for all stages is identical then the jointly gaussian source with squared error distortion measure is successively refinable we first extend this result to the case where the difference between the source and the side information is gaussian and independent of the side information as a byproduct we give an alternative proof that the wyner ziv problem for these sources has no rate loss a result that was recently shown by pradhan et al through invoking the duality between the gaussian wyner ziv problem and the costa problem we then perform layered wyner ziv code design for this general type of source based on nested scalar quantization bit plane coding and low density parity check ldpc code based slepian wolf coding source coding with side information we show that density evolution can be used to analyze the slepian wolf code performance provided that certain symmetry conditions which have been dubbed dual symmetry are satisfied by the hypothetical channel between the source and the side information we also show that the dual symmetry condition is indeed satisfied by the hypothetical channel in our slepian wolf coding setup this justifies the use of density evolution in our ldpc code based slepian wolf code design for wyner ziv coding for the jointly gaussian source our layered coder performs 1 29 to 3 45 db from the wyner ziv bound for rates ranging from 0 47 to 4 68 bits per sample when the side information is laplacian and the source equals the side information plus an independent gaussian noise term our layered coder performs 1 33 to 3 90 db from the wyner ziv bound for rates ranging from 0 48 to 4 64 bits per sample

low order controller design for siso systems using coprime factors and lmi this paper develops a low order controller design method for linear continuous time invariant single input single output systems requiring only the solution of a convex optimization problem the technique integrates several well known results in control theory an important step is the use of coprime factors so that based on strictly positive real functions feedback stabilization using low order controllers becomes a zero placement problem which is convex from this result we develop algorithms to solve two optimal control problems

weighted sum rate optimization for downlink multiuser mimo coordinated base station systems centralized and distributed algorithms this paper considers the joint linear transceiver design problem for the downlink multiuser multiple input multiple output mimo systems with coordinated base stations bss we consider maximization of the weighted sum rate with per bs antenna power constraint problem we propose novel centralized and computationally efficient distributed iterative algorithms that achieve local optimum to the latter problem these algorithms are described as follows first by introducing additional optimization variables we reformulate the original problem into a new problem second for the given precoder matrices of all users the optimal receivers are computed using minimum mean square error mmse method and the optimal introduced variables are obtained in closed form expressions third by keeping the introduced variables and receivers constant the precoder matrices of all users are optimized by using second order cone programming socp and matrix fractional minimization approaches for the centralized and distributed algorithms respectively finally the second and third steps are repeated until these algorithms converge we have shown that the proposed algorithms are guaranteed to converge we also show that the proposed algorithms require less computational cost than that of the existing linear algorithm all simulation results demonstrate that our distributed algorithm achieves the same performance as that of the centralized algorithm moreover the proposed algorithms outperform the existing linear algorithm in particular when each of the users has single antenna we have observed that the proposed algorithms achieve the global optimum

information embedding and the triple role of control we consider the problem of information embedding where the encoder modifies a white gaussian host signal in a power constrained manner to encode a message and the decoder recovers both the embedded message and the modified host signal this partially extends the recent work of sumszyk and steinberg to the continuous alphabet gaussian setting through a control theoretic lens we observe that the problem is a minimalist example of what is called the triple role of control actions we show that a dirty paper coding strategy achieves the optimal rate for perfect recovery of the modified host and the message for any message rate for imperfect recovery of the modified host by deriving bounds on the minimum mean square error mmse in recovering the modified host signal we show that dirty paper coding based strategies are guaranteed to attain within a uniform constant factor of 16 of the optimal weighted sum of power required in host signal modification and the mmse in the modified host signal reconstruction for all weights and all message rates when specialized to the zero rate case our results provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in decentralized control the witsenhausen counterexample numerically this tighter bound helps us characterize the asymptotically optimal costs for the vector witsenhausen problem to within a factor of 1 3 for all problem parameters improving on the earlier best known bound of 2

rank constrained separable semidefinite programming with applications to optimal beamforming consider a downlink communication system where multiantenna base stations transmit independent data streams to decentralized single antenna users over a common frequency band the goal of the base stations is to jointly adjust the beamforming vectors to minimize the transmission powers while ensuring the signal to interference noise ratio requirement of each user within the system at the same time it may be necessary to keep the interference generated on other coexisting systems under a certain tolerable level in addition one may want to include general individual shaping constraints on the beamforming vectors this beamforming problem is a separable homogeneous quadratically constrained quadratic program and it is difficult to solve in general in this paper we give conditions under which strong duality holds and propose efficient algorithms for the optimal beamforming problem first we study rank constrained solutions of general separable semidefinite programs sdps and propose rank reduction procedures to achieve a lower rank solution then we show that the sdp relaxation of three classes of optimal beamforming problem always has a rank one solution which can be obtained by invoking the rank reduction procedures

informational processing of complex sound i intensity discrimination this paper reports on some initial experiments using the sample discrimination paradigm to investigate normal hearing listeners ability to process information in complex nonspeech sounds an important feature of the sample discrimination experiment is that the value of the d i f f e r e n c e to be discriminated randomly varies from trial to trial it is this variation that yields potential information in the present study listeners heard a pair of multitone complexes or sequences on each trial the individual levels of the tones were drawn from two normal distributions differing only in mean the listener s task was to identify the sound having the higher mean tone level for an ideal observer in these experiments performance in d grows as the square root n where n is the number of tones obtained d grew more nearly as the cube root of n regardless of whether the tones were played sequentially or simultaneously or whether they were increased in number from high frequencies to low or from low frequencies to high a preliminary model is proposed in which discrimination performance depends predominantly on the information content of the sounds and is largely independent of the physical dimensions along which the sounds vary information content is defined in terms of the variance of the underlying stimulus distributions and a stimulus equivocation factor that is derived from the data based on this model transmitted information is estimated to be between 1 0 and 2 6 bits

causal state communication the problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available strictly causally at the encoder it is shown that block markov encoding in which the encoder communicates a description of the state sequence in the previous block by incorporating side information about the state sequence at the decoder yields the minimum state estimation error when the same channel is used to send additional independent information at the expense of a higher channel state estimation error the optimal tradeoff between the rate of the independent information and the state estimation error is characterized via the capacity distortion function it is shown that any optimal tradeoff pair can be achieved via rate splitting these coding theorems are then extended optimally to the case of causal channel state information at the encoder using the shannon strategy

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

on loudness at threshold absolute thresholds for and loudness matches between pure tones and four and ten tone complexes were used to assess the form of the function relating loudness to sensation level sl at low and moderate levels the components of the tone complexes had equal sls and were separated by one two four or six critical bands six listeners with normal hearing were tested the thresholds for the multitone complexes indicate that they generally can be detected even when the level of a single component is a few db below the threshold the average detection advantage is consistent with predictions for multiple observations in independent frequency selective auditory channels but differences among listeners are apparent the loudness matches also vary somewhat among listeners five of the six listeners matched tone complexes composed of subthreshold components to a pure tone a few db above threshold this indicates that the loudness of tones at or even below threshold is greater than zero for these five listeners a simple model of loudness summation was used to obtain loudness functions from the individual listeners loudness matches the slopes of the loudness functions log loudness plotted as a function of log intensity generally exceed unity at low levels and are near 0 2 at 40 db sl this shallow slope at moderate levels agrees with loudness functions derived from data on temporal integration of loudness the average loudness function derived from the present data also is in good agreement with a variety of previous data obtained by magnitude estimation magnitude production ratio production and measurements of binaural loudness summation

contributions of individual components to the overall loudness of a multitone complex the contributions of individual components to the overall loudness of a multitone complex were examined in a two interval loudness judgment task stimuli were five tone complexes centered on 1000hz with six different logarithmic frequency spacings corresponding to bandwidths from 46 to 2119hz stimuli were presented for 300ms 10ms rise fall the overall level of the standard complex was fixed at 60db spl 53db component levels of the individual components of the comparison complex were selected at random from a rectangular distribution with a range of 20db perceptual weights were computed by calculating the point biserial correlation between the difference in the level of each component across the two intervals and the subject s response when all components fell within the same critical band weights varied little across components in contrast the range of weights increased with increasing frequency separation with more weight given to the lowest and highest frequency components a relation be

entropy amplification property and the loss for writing on dirty paper costa s celebrated ldquowriting on dirty paperrdquo wdp shows that the power constrained channel y x s z with gaussian z has the same capacity as the standard awgn channel y x z provided that the ldquointerferencerdquo s no matter how strong it is is known at the transmitter while this ability for perfect interference cancelation is very appealing it relies heavily on the gaussianity of the unknown noise z we construct an example of ldquobadrdquo noise for writing on dirty paper namely ldquodifference set noiserdquo if the interference s is strong then difference set noise limits the wdp capacity to at most 2 bits at the same time like in the awgn case the zero interference capacity grows without bound with the input constraint thus almost 100 of the available capacity is lost in wdp in the presence of difference set noise this high capacity loss is due to the ldquoentropy amplification propertyrdquo eap of noise with an aperiodic probability distribution using the eap and the duality between wdp and wyner ziv source coding we also give an example of dramatic rate loss in quantizing encrypted source