improved bounds for the transition temperature of directed polymers in a finite dimensional random medium we consider the problem of directed polymers in a random medium of a finitedimensional lattice in the high temperature phase of this system it is known that the annealed and quenched free energies coincide upper bounds on the transition temperature to a low temperature phase had previously been obtained by calculating the first two moments z and z2 of the partition function we improve these bounds by estimating noninteger moments z for 1 2

a general formula for compound channel capacity a general formula for the capacity of arbitrary compound channels with the receiver channel state information is obtained using the information density approach no assumptions of ergodicity stationarity or information stability are made and the channel state set is arbitrary a direct constructive proof is given to prove achievability we generalize feinstein lemma to the compound channel setting and to prove converse we generalize verdu han lemma to the same compound setting a notion of a uniform compound channel is introduced and the general formula is shown to reduce to the familiar sup inf expression for such channels as a by product the arbitrary varying channel capacity is established under maximum error probability and deterministic coding conditions are established under which the worst case and compound channel capacities are equal so that the full channel state information at the transmitter brings in no advantage the compound inf information rate plays a prominent role in the general formula its properties are studied and a link between the information unstable and information stable regimes of a compound channel is established the results are extended to include varepsilon capacity of compound channels sufficient and necessary conditions for the strong converse to hold are given

on the capacity of a class of mismatched gaussian channels corresp the capacity is considered for gaussian channels where the channel noise covariance is not the same as the constraint covariance an upper bound is obtained sharper results are obtained under additional assumptions

optimum linear causal coding schemes for gaussian stochastic processes in the presence of correlated jamming the complete solution is obtained to the following problem a gaussian stochastic process theta sub t t in 0 t sub f satisfying a certain stochastic differential equation is to be transmitted through a stochastic channel to a receiver under minimum mean squared error distortion measure the channel is to be used for exactly t sub f seconds and in addition to white gaussian noise with a given energy level the channel is corrupted by another source whose output may be correlated with the input to the channel and which satisfied a given power constraint there is an input power constraint to the channel and noiseless feedback is allowed between the receiver decoder and the transmitter encoder the authors determine the linear causal encoder and decoder structures that function optimally under the worst admissible noise inputs to the channel the least favorable probability distribution for this unknown noise is found to be gaussian and is correlated with the transmitted signal also included is a comparative study of these results with earlier ones that addressed a similar problem without a causality restriction imposed on the transmitter

capacity of the gaussian arbitrarily varying channel the gaussian arbitrarily varying channel with input constraint gamma and state constraint lambda admits input sequences x x sub 1 x sub n of real numbers with sigma x sub i sup 2

lyapunov exponents of large sparse random matrices and the problem of directed polymers with complex random weights we present results on two different problems the lyapunov exponent of large sparse random matrices and the problem of polymers on a cayley tree with random complex weights we give an analytic expression for the largest lyapunov exponent of products of random sparse matrices with random elements located at random positions in the matrix this expression is obtained through an analogy with the problem of random directed polymers on a cayley tree i e in the mean field limit which itself can be solved using its relationship with random energy models rem and grem for the random polymer problem with complex weights we find that in addition to the high and the low temperature phases which were already known in the case of positive weights the mean field theory predicts a new phase phase iii which is dominated by interference effects

capacity of the class of mimo channels with incomplete cdi properties of mutual information for a class of channels this paper is concerned with multiple input multiple output mimo wireless channel capacity when the probability distribution of the channel matrix p h is not completely known to the transmitter and the receiver the partial knowledge of a true probability distribution of the channel matrix p h is modelled by a relative entropy d middot middot such that d p pnom les d d ges 0 where d is the distance from the so called nominal channel matrix distribution pnom h the capacity of this compound channel is equal to the maximin of the mutual information where the minimum is with respect to the channel matrix distribution and the maximum is with respect to the covariance matrix of a transmitted signal the existence of a minimizing probability distribution is proved and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution pnom h and parameter d a number of properties of the mutual information minimized over the set of channel distributions are derived specifically upper and lower bounds are derived for the minimized mutual information while its convexity with respect to d is shown in the case of the rayleigh fading an explicit formula for the capacity and the optimal transmit covariance matrix are derived

correlated jamming on mimo gaussian fading channels we consider a zero sum mutual information game on multiple input multiple output mimo gaussian rayleigh fading channels the players are an encoder decoder pair as the maximizer and a jammer as the minimizer of the mutual information between the input and the output of the channel there are total power constraints on both the jammer and the encoder also the jammer has access to the encoder output we find the unique saddle point of this game and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer

approaching capacity of a continuous channel by discrete input distributions in this paper memoryless channels with general alphabets and input constraint are considered sufficient conditions are given that channel capacity can be approached by discrete input distributions or by uniform input distributions with finite support as an example the additive white gaussian noise channel is considered

the worst additive noise under a covariance constraint the maximum entropy noise under a lag p autocorrelation constraint is known by burg s theorem to be the pth order gauss markov process satisfying these constraints the question is what is the worst additive noise for a communication channel given these constraints is it the maximum entropy noise the problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints r sub 0 r sub p for high signal powers the worst additive noise is gauss markov of order p as expected but for low powers the worst additive noise is gaussian with a covariance matrix in a convex set which depends on the signal power

a framework for evaluating the data hiding capacity of image sources an information theoretic model for image watermarking and data hiding is presented in this paper previous theoretical results are used to characterize the fundamental capacity limits of image watermarking and data hiding systems capacity is determined by the statistical model used for the host image by the distortion constraints on the data hider and the attacker and by the information available to the data hider to the attacker and to the decoder we consider autoregressive block dct and wavelet statistical models for images and compute data hiding capacity for compressed and uncompressed host image sources closed form expressions are obtained under sparse model approximations models for geometric attacks and distortion measures that are invariant to such attacks are considered

capacity and decoding rules for classes of arbitrarily varying channels the capacity of an arbitrarily varying channel avc is considered for deterministic codes with the average probability of error criterion and typically subject to at state constraint first sufficient conditions are provided that enable relatively simple decoding rules such as typicality maximum mutual information and minimum distance to attain capacity then the possibly noisy or channels and group adder channels are studied in detail for the former the capacity is explicitly determined and shown to be attainable by minimum distance decoding next for a large class of addictive avcs in addition to providing an intuitively suggestive simplification of the general avc capacity formula it is proven that capacity can be attained by a universal decoding rule finally the effect of random state selections on capacity is studied the merits and limitations of a previous mutual information game approach are also discussed

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

capacity of the mismatched gaussian channel information capacity is determined for the additive gaussian channel when the constraint is given in terms of a covariance different from that of the channel noise these results combined with previous results on capacity when the constraint covariance is the same as the noise covariance provide a complete and general solution for the information capacity of the gaussian channel without feedback the results are valid for both continuous time and discrete time channels and require only two assumptions the noise is due to a stochastic process with sample paths having finite energy over the observation period w p 1 and the constraint is given in terms of a hilbert space norm such a constraint is implicit in any constraint giving finite capacity

numerical complex zeros of the random energy model abstract the distribution of zeros of the partition function of the random energy model rem is numerically estimated in order to do this we devise a discrete version of the model drem for which the partition function is a polynomial and whose roots can therefore be numerically obtained a continuous limit transforms drem into rem so the zeros of the latter can be obtained from those of the former

the capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

a comparison of maximum length and legendre sequences for the derivation of brain stem auditory evoked responses at rapid rates of stimulation experiments were performed in which brain stem auditory evoked responses baers were elicited by two types of pseudorandom pulse trains maximum length sequences mls and legendre sequences lgs in experiment 1 each pulse sequence was presented at 50 db nhl with minimum pulse intervals varying from 1 to 10 ms wave v latency increased and wave v amplitude decreased with decreasing minimum pulse intervals with no significant effect of the type of sequence mls vs lgs and no significant interaction between sequence and minimum pulse interval in terms of wave v amplitude or latency in a second experiment the minimum pulse interval was held constant at 4 ms while mls and lgs levels were varied from 20 to 60 db nhl with increasing click intensity there is a decrease in wave v latency and an increase in wave v amplitude there was no significant effect of type of sequence lgs vs mls or interaction between type of sequence and stimulus intensity for wave v amplitude or latency despite the obvious

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

a complete characterization of minimax and maximin encoder decoder policies for communication channels with incomplete statistical description the problem is considered of transmitting a sequence of independent and identically distributed gaussian random variables over a channel whose statistical description is incomplete the channel is modeled as one that is conditionally gaussian with the unknown part being controlled by a so called jammer who may have access to the input to the encoder and operates under a given power constraint by adopting a game theoretic approach a complete set of solutions is obtained encoder and decoder mappings and least favorable distributions for the channel noise for this statistical decision problem under two different sets of conditions depending on whether the encoder mapping is deterministic or stochastic in the latter case existence of a mixed saddle point solution can be verified when a side channel of a specific nature is available between the transmitter and the receiver in the former case however only minimax and maximin solutions can be derived

optimal robust signaling with pseudonoise modulated orthogonal signals it is well known that orthogonal signal sets approach the channel capacity and reliability function of the infinite bandwidth additive white gaussian noise channel it is shown that pseudonoise modulated orthogonal signals play a similar role for the infinite bandwidth gaussian arbitrarily varying channel

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

coding capacity for a class of additive channels coding capacity is considered for a class of additive dimension limited channels the channels may be with or without memory stationary or nonstationary the constraint is partially given in terms of an increasing family of finite dimensional subspaces a general expression for the capacity is obtained which depends on the family of subspaces and the relation between the noise covariance and the covariance giving the energy frequency constraint on the transmitted signal this result holds for all classical discrete time gaussian channels and for continuous time gaussian channels with fixed time of transmission so long as a peak energy constraint is used on the codewords the expression also provides upper bounds for a class of non gaussian channels several results are obtained that aid in calculation of capacity for specific applications for this class of channels it is shown that coding capacity is equal to information capacity error bounds are given for gaussian channels

bottlenose dolphin tursiops truncatus auditory brainstem responses recorded using conventional and randomized stimulation and averaging auditory brainstem response abr measurements using conventional averaging i e constant interstimulus interval isi are limited to stimulus rates low enough to prevent overlapping of the abrs to successive stimuli to overcome this limitation stimuli may be presented at high rates using pseudorandom sequences e g maximum length sequences or quasi periodic sequences however these methods restrict the available stimulus sequences and require deconvolution to recover the abr from the overlapping responses randomized stimulation and averaging rsa is an alternate method where evoked responses at high rates are obtained by averaging responses to stimuli with isis drawn from a random distribution the rsa method enables precise control over stimulus jitter is flexible with respect to stimulus sequence parameters and does not require deconvolution to extract the abr waveform in this study abrs were measured in three normal hearing dolphins using conventional averaging and rsa results show the rsa method to be effective in dolphins if the isi jitter 1 5 ms and that the influence of stimulus artifacts in the averaged abr can be substantially reduced by alternating stimulus polarity on successive presentations rather than employing digital blanking or iterative processes

auditory brainstem and middle latency responses recorded at fast rates with randomized stimulation randomized stimulation and averaging rsa allows auditory evoked potentials aeps to be recorded at high stimulation rates this method does not perform deconvolution and must therefore deal with interference derived from overlapping transient evoked responses this paper analyzes the effects of this interference on auditory brainstem responses abrs and middle latency responses mlrs recorded at rates of up to 300 and 125 hz respectively with randomized stimulation sequences of a jitter both greater and shorter than the dominant period of the abr mlr components additionally this paper presents an advanced approach for rsa iterative randomized stimulation and averaging i rsa which includes the removal of the interference associated with overlapping responses through an iterative process in the time domain experimental results show that a rsa can be efficiently used in the recording of aeps when the jitter of the stimulation sequence is greater than the dominant period of the aep components and b i rsa maintains all the advantages of rsa and is not constrained by the restriction of a minimum jitter the significance of the results of this study is discussed

an information theoretic and game theoretic study of timing channels this paper focuses on jammed timing channels pure delay jammers with a maximum delay constraint an average delay constraint or a maximum buffer size constraint are explored for continuous time or discrete time packet waveforms fluid waveform approximations of each of these classes of waveforms are employed to aid in analysis channel capacity is defined and an information theoretic game based on mutual information rate is studied min max optimal jammers and max min optimal input processes are sought bounds on the min max and max min mutual information rates are described and numerical examples are given for maximum delay constrained mdc jammers with continuous time packet waveforms saddle point input and jammer strategies are identified the capacity of the maximum delay constrained jamming channel with continuous time packet waveforms is shown to equal the mutual information rate of the saddle point for mdc jammers with discrete time packet waveforms saddle point strategies are shown to exist jammers which have quantized batch departures at regular intervals are shown to perform well input processes with batches at regular intervals perform well for mdc or maximum buffer size constrained jammers

the renyi capacity and center renyi s information measures the renyi information mean capacity radius and center are analyzed relying on the elementary properties of the renyi divergence and the power means the van erven harremoes conjecture is proved for any positive order and for any set of probability measures on a given measurable space and a generalization of it is established for the constrained variant of the problem the finiteness of the order alpha renyi capacity is shown to imply the continuity of the renyi capacity on 0 alpha and the uniform equicontinuity of the renyi information both as a family of functions of the order indexed by the priors and as a family of functions of the prior indexed by the orders

information capacity of channels with partially unknown noise i finite dimensional channels information capacity is considered for a finite dimensional communication channel in which the noise is the sum of a known gaussian noise and an independent component with unknown statistical properties the problem is modeled as a zero sum two person game between the coder and a jammer with mutual information as the payoff function the jammer does not control the ambient gaussian noise the constraints employed are appropriate for extension to infinite dimensional channels and for consideration of coding capacity the original problem is reformulated to prove existence of both a saddle value and a saddle point the saddle value and a saddle point are determined along with the jammer s minimax strategy

exponential error bounds for random codes on gaussian arbitrarily varying channels the main objective is to develop exponential bounds to the best error probability achievable with random coding on the gaussian arbitrarily varying channel gavc in the one case where a strong capacity exists i e with peak time averaged power constraints on both the transmitter and interference the gavc models a channel corrupted by thermal noise and by an unknown interfering signal of bounded power the upper and lower bounds to the best error probability achievable on this channel with random coding are presented the asymptotic exponents of these bounds agree in a range of rates near capacity the exponents are universally larger than the corresponding exponents for the discrete time gaussian channel with the same capacity it is further shown that the decoder can be taken to be the minimum euclidean distance rule at all rates less than capacity

the zeroes of the partition function of the random energy model abstract the random energy model is one of the simplest disordered models containing some of the physics of spin glasses the zeroes of the partition function in the complex temperature plane are determined for this model they either lie on simple lines or are dense in some regions of the complex plane

signal to noise ratio and frequency analysis of continuous loop averaging deconvolution clad of overlapping evoked potentials in this study a frequency domain formulation of continuous loop averaging deconvolution clad of overlapping evoked potentials is developed and applied for the extraction of transient responses from recordings obtained at high stimulation rates this formulation allows for a faster execution of clad by using fast fourier transform algorithms the frequency characteristics of the deconvolution filter depends exclusively on the stimulus sequence and determines whether the noncoherent noise is amplified or attenuated in different frequencies a formula for calculating the signal to noise ratio snr achieved by the deconvolution process is developed the newly developed theory and the methodology is applied to the extraction of the auditory brainstem and middle latency responses using various sequences the effects of the sequence used and the number of sweeps averaged in ongoing acquisition on snr are examined by using single sweep recordings the results verify the deconvolution theory and the methodology and show its limitations depending on the frequency characteristics of the sequence the deconvolution process can amplify or attenuate the eeg noise proper selection of the stimulus sequence can increase the snr enhancement obtained with conventional averaging

the capacity of a vector gaussian arbitrarily varying channel the random coding capacity of a vector gaussian arbitrarily varying channel vgavc is determined along with a simple general method for computing this capacity the vgavc is a discrete time memoryless vector channel with an input power constraint and additive gaussian noise that is further corrupted by an additive jamming signal the statistics of this jamming signal are unknown and can be arbitrary subject only to a power constraint

the gaussian test channel with an intelligent jammer the problem of transmitting a sequence of identically distributed independent gaussian random variables through a gaussian memoryless channel with a given input power constraint in the presence of an intelligent jammer is considered the jammer taps the channel and feeds back a signal at a given energy level for the purpose of jamming the transmitting sequence under a square difference distortion measure which is to be maximized by the jammer and to be minimized by the transmitter and the receiver this correspondence obtains the complete set of optimal saddle point policies the solution is essentially unique and it is structurally different in three different regions in the parameter space which are determined by the signal to noise ratios and relative magnitudes of the noise variances the best maximin policy of the jammer is either to choose a linear function of the measurement he receives through channel tapping or to choose in addition and additively an independent gaussian noise sequence depending on the region where the parameters lie the optimal minimax policy of the transmitter is to amplify the input sequence to the given power level by a linear transformation and that of the receiver is to use a bayes estimator

state constraints for the multiple access arbitrarily varying channel a discrete multiple access arbitrarily varying channel with two transmitters and one receiver is considered it has recently been shown that if such a channel is symmetrizable then the capacity region has an empty interior it is shown that if the channel is subject to a suitable state constraint then the capacity region can contain certain open rectangles and thereby possess a nonempty interior even if the channel is symmetrizable a new weak converse under a state constraint is also proved these results are then used to establish the capacity region of the two user adder channel under state constraint 1 2

on equivalent results in minimax theory abstract in this paper we review known minimax theorems with applications in game theory and show that these theorems can be proved using the first minimax theorem for a two person zero sum game with finite strategy sets published by von neumann in 1928 among these results are the well known minimax theorems of wald ville and kneser and their generalizations due to kakutani ky fan konig neumann and gwinner oettli actually it is shown that these results form an equivalent chain and this chain includes the strong separation result in finite dimensional spaces between two disjoint closed convex sets of which one is compact to show the implications the authors only use simple properties of compact sets and the well known weierstrass lebesgue lemma

the shannon lower bound is asymptotically tight the shannon lower bound is one of the few lower bounds on the rate distortion function that holds for a large class of sources in this paper which considers exclusively norm based difference distortion measures it is demonstrated that its gap to the rate distortion function vanishes as the allowed distortion tends to zero for all sources having finite differential entropy and whose integer part has finite entropy conversely it is demonstrated that if the integer part of the source has infinite entropy then its rate distortion function is infinite for every finite distortion level thus the shannon lower bound provides an asymptotically tight bound on the rate distortion function if and only if the integer part of the source has finite entropy

nearest neighbor decoding for additive non gaussian noise channels we study the performance of a transmission scheme employing random gaussian codebooks and nearest neighbor decoding over a power limited additive non gaussian noise channel we show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white gaussian noise channel with signal and noise power equal to those of the original channel the results are presented for single user channels as well as multiple access channels and are extended to fading channels with side information at the receiver

mean field theory of directed polymers with random complex weights we show that for the problem of directed polymers on a tree with i i d random complex weights on each bond three possible phases can exist the phase of a particular system is determined by the distribution of the random weights for each of these three phases we give the expression of the free energy per unit length in the limit of infinitely long polymers our proofs require several hypotheses on the distribution most importantly that the amplitude and the phase of each complex weight be statistically independent the main steps of our proofs use bounds on noninteger moments of the partition function and self averaging properties of the free energy we illustrate our results by some examples and discuss possible generalizations to a larger class of distributions to random energy models and to the finite dimensional case we note that our results are not in agreement with the predictions of a recent replica approach to a similar problem

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

kpp equation and supercritical branching brownian motion in the subcritical speed area application to spatial trees if r t is the position of the rightmost particle at time t in a one dimensional branching brownian motion u t x p r t x is a solution of kpp equation frac partial u partial t frac 1 2 frac partial 2 u partial x 2 f u where f u 1 u g 1 u g is the generating function of the reproduction law and the inverse of the mean lifetime if m g 1 1 and g 0 0 it is known that frac r t t xrightarrow p c 0 sqrt 2a m 1 text when t to infty for the general kpp equation we show limit theorems for u t ct c c 0 t large deviations for r t and probabilities of presence of particles for the branching process are deduced where z t denotes the random point measure of particles living at time t and a yaglom type theorem is proved the conditional distribution of the spatial tree given z t ct 0 is studied in the limit as t

optimal zero delay jamming over an additive noise channel this paper considers the problem of optimal zero delay jamming over an additive noise channel building on a sequence of recent results on conditions for linearity of optimal estimation and of optimal mappings in source channel coding the saddle point solution to the jamming problem is derived for general sources and channels without recourse to gaussianity assumptions the linearity conditions are shown to play a pivotal role in jamming in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings i e the jammer ensures whenever possible that the transmitter and the receiver cannot benefit from non linear strategies this result is shown to subsume the known result for gaussian source and channel the conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer are analyzed moreover a numerical procedure is provided to approximate the optimal jamming strategy in the remaining source channel cases where the jammer cannot impose linearity on the transmitter and the receiver next the analysis is extended to vector sources and channels this extension involves a new aspect of optimization the allocation of available transmit and jamming power over source and channel components similar to the scalar setting the saddle point solution is derived using the linearity conditions in vector spaces the optimal power allocation strategies for the jammer and the transmitter have an intuitive interpretation as the jammer allocates power according to water filling over the channel eigenvalues while the transmitter performs water pouring reverse water filling over the source eigenvalues

a framework for assessing the relative efficiency of stimulus sequences in evoked response measurements a general matrix based framework for characterizing the performance of cross correlation techniques for recovering the response to an arbitrary stimulus sequence is presented in general an infinite number of recovery sequences can be identified for any given stimulus sequence the recovery sequence that minimizes the noise in the recovered response is derived and the effect of the recovery operation on the noise is analyzed this general framework is employed to develop analytic expressions for the relative efficiencies of conventional signal averaging and binary mls based methods for the most commonly used recovery operation and the one that optimizes snr assuming the background noise is uncorrelated the results depend on the ratio of response length to mls minimum pulse interval and the amplitude loss as a function of stimulus rate examples based on measured amplitude loss functions for abr recordings are employed to evaluate the relative efficiencies of mls techniques when the noise is uncorrelated conventional signal averaging is from two to five times as efficient as mls techniques the relative advantage of averaging is shown to decrease when the noise is dominated by low frequency components

csi usage over parallel fading channels under jamming attacks a game theory study consider a parallel channel with m independent flat fading subchannels there exists a smart jammer which has possession of a copy of perfect channel state information csi measured and sent back by a receiver to its transmitter under this model a class of two person zero sum games is investigated where either achievable mutual information rate or chernoff bound is taken as the underlying pay off function with the strategy space of each player determined by respective power control and hopping functions more specifically we have tackled and answered the following three fundamental questions the first one is about whether the transmitter and jammer should hop or fully use all degrees of freedom over the entire parallel channels given the full csi available to both of them i e to hop or not to hop the second question is about the impact of sending back csi on system performance considering that the smart jammer can exploit csi to further enhance its interference effects i e to feedback or not to feedback the last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer i e when to feedback and when not to

mutual information games in multiuser channels with correlated jamming we investigate the behavior of two users and one jammer in an additive white gaussian noise awgn channel with and without fading when they participate in a noncooperative zero sum game with the channel s input output mutual information as the objective function we assume that the jammer can eavesdrop on the channel and can use the information obtained to perform correlated jamming we also differentiate between the availability of perfect and noisy information about the user signals at the jammer under various assumptions on the channel characteristics and the extent of information available at the users and the jammer we show the existence or otherwise nonexistence of a simultaneously optimal set of strategies for the users and the jammer and characterize those strategies whenever they exist

arbitrarily varying channels with general alphabets and states previous results of csiszar and narayan 1988 1989 1991 on the capacity of discrete arbitrarily varying channels with input and state constraints are extended to the case of arbitrary alphabets and state sets for channels with scalar or vector inputs and additive interference consisting of a deterministic part and noise both arbitrarily varying subject to power constraints the capacity for deterministic codes is shown to be equal to the random coding capacity if the input power exceeds the power of the deterministic interference and zero otherwise explicit capacity formulas are also given

coding theorem and converse for abstract channels with time structure and memory a coding theorem and converse are proved for a large class of abstract stationary channels with time structure including the result by kadota and wyner 1972 on continuous time real valued channels as special cases as main contribution the coding theorem is proved for a significantly weaker condition on the channel output memory called total ergodicity with respect to finite alphabet block memoryless input sources and under a crucial relaxation of the measurability requirement for the channel these improvements are achieved by introducing a suitable characterization of information rate capacity it is shown that the psi mixing output memory condition used by kadota and wyner is quite restrictive and excludes important channel models in particular for the class of gaussian channels in fact it is proved that for gaussian e g fading or additive noise channels the psi mixing condition is equivalent to finite output memory furthermore it is demonstrated that the measurability requirement of kadota and wyner is not satisfied for relevant continuous time channel models such as linear filters whereas the condition used in this paper is satisfied for these models moreover a weak converse is derived for all stationary channels with time structure intersymbol interference as well as input constraints are taken into account in a general and flexible way including amplitude and average power constraints as special case formulated in rigorous mathematical terms complete explicit and transparent proofs are presented as a side product a gap in the proof of kadota and wyner illustrated by a counterexample is closed by providing a corrected proof of a lemma on the monotonicity of some sequence of normalized mutual information quantities an operational perspective is taken and an abstract framework is established which allows to treat discrete and continuous time channels with possibly infinite input and output memory and arbitrary alphabets simultaneously in a unified way

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

a note on the diffusion of directed polymers in a random environment a simple martingale argument is presented which proves that directed polymers in random environments satisfy a central limit theorem ford 3 and if the disorder is small enough this simplifies and extends an approach by j imbrie and t spencer

on weak convergence of probability measures channel capacity and code error probabilities the relationship between weak convergence of channel probability measures channel capacity and error probability of block codes is examined for memoryless channels with general input and output alphabets it is shown that channel capacity is a lower semi continuous function and that every block code with maximal probability of error spl delta for a nominal channel for any spl epsiv 0 can be modified such that the modification has a probability of error less than spl delta spl epsiv for all channels in a sufficiently small neighborhood of the nominal channel

error bounds for the euclidean channel subject to intentional jamming we address the problem of communicating over channels subject to intentional interference the problem is described in terms of a two person zero sum game with the probability of error as the pay off function we give upper and lower bounds on the error probability for antijamming codes when used over the euclidean channel

communication over individual channels a communication problem in considered where no mathematical model is specified for the channel the achievable rates are determined as a function of the channel input and output sequences known a posteriori without assuming any a priori relation between them for discrete channels the empirical mutual information between the input and output sequences is shown to be achievable while for continuous channels the achievable rate is based on the empirical correlation between the sequences a rate adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability without prior knowledge of the channel behavior is presented

on the capacity region of the discrete additive multiple access arbitrarily varying channel the discrete additive multiple access arbitrarily varying channel avc with two senders and one receiver is considered necessary and sufficient conditions are given for its deterministic code average probability of error capacity region under a state constraint to have a nonempty interior in the case that no state constraint is present the capacity region is characterized exactly in the case of the noiseless mod 2 adder avc using state constraint function l s s and subject to a state constraint l less than or equal to 0 13616917 the capacity region is shown to be a 45 degree triangle whose legs have length 1 h l where h denotes the binary entropy function

capacity analysis for continuous alphabet channels with side information part i a general framework capacity analysis for channels with side information at the receiver has been an active area of interest this problem is well investigated for the case of finite alphabet channels however the results are not easily generalizable to the case of continuous alphabet channels due to analytical difficulties inherent with continuous alphabets in the first part of this two part paper we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver for this purpose we establish novel necessary and sufficient conditions for weak continuity and strict concavity of the mutual information these conditions are used in investigating the existence and uniqueness of the capacity achieving measures furthermore we derive necessary and sufficient conditions that characterize the capacity value and the capacity achieving measure for continuous alphabet channels with side information at the receiver

on the capacity of channels with unknown interference the process of communicating in the presence of interference that is unknown or hostile is modeled as a two person zero sum game with the communicator and the jammer as the players the objective function considered is the rate of reliable communication the communicator s strategies are encoders and distributions on a set of quantizers the jammer s strategies are distributions on the noise power subject to certain constraints various conditions are considered on the jammer s strategy set and on the communicator s knowledge for the case where the decoder is uninformed of the actual quantizer chosen it is shown that from the communicator s perspective the worst case jamming strategy is a distribution concentrated on a finite number of points thereby converting a functional optimization problem into a nonlinear programming problem moreover the worst case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify for the case where the decoder is informed of the actual quantizer chosen the existence of saddle point strategies is demonstrated the analysis is also seen to be valid for a number of situations where the jammer is adaptive

rateless codes for avc models the arbitrarily varying channel avc is a channel model whose state is selected maliciously by an adversary fixed blocklength coding assumes a worst case bound on the adversary s capabilities which leads to pessimistic results this paper defines a variable length perspective on this problem for which achievable rates are shown that depend on the realized actions of the adversary specifically rateless codes are constructed which require a limited amount of common randomness these codes are constructed for two kinds of avc models in the first the channel state cannot depend on the channel input and in the second it can as a by product the randomized coding capacity of the avc with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness the results for this model are proved using a randomized strategy based on list decoding

signal to noise ratio analysis of maximum length sequence deconvolution of overlapping evoked potentials in this study a general formula for the signal to noise ratio snr of the maximum length sequence mls deconvolution averaging is developed using the frequency domain framework of the generalized continuous loop averaging deconvolution procedure ozdamar and bohorquez j acoust soc am 119 429 438 2006 this formulation takes advantage of the well known equivalency of energies in the time and frequency domains parseval s theorem to show that in mls deconvolution snr increases with the square root of half of the number of stimuli in the sweep this increase is less than that of conventional averaging which is the square root of the number of sweeps averaged unlike arbitrary stimulus sequences that can attenuate or amplify phase unlocked noise depending on the frequency characteristics the mls deconvolution attenuates noise in all frequencies consistently furthermore mls and its zero padded variations present optimal attenuation of noise at all frequencies yet they present a highly jittered stimulus sequence in real recordings of evoked potentials the time advantage gained by noise attenuation could be lost by the signal amplitude attenuation due to neural adaptation at high stimulus rates

shannon meets von neumann a minimax theorem for channel coding in the presence of a jammer we study the setting of channel coding over a family of channels whose state is controlled by an adversarial jammer by viewing it as a zero sum game between a finite blocklength encoder decoder team and the jammer the encoder decoder team choose stochastic encoding and decoding strategies to minimize the average probability of error in transmission while the jammer chooses a distribution on the state space to maximize this probability the min max value of the game is equivalent to channel coding for a compound channel we call this the shannon solution of the problem the max min value corresponds to finding a mixed channel with the largest value of the minimum achievable probability of error when the min max and max min values are equal the problem is said to admit a saddle point or von neumann solution while a shannon solution always exists the communicating team s problem is nonconvex for finite blocklengths whereby a von neumann solution may not exist despite this we show that the min max and max min values become equal asymptotically in the large blocklength limit for all but finitely many rates we explicitly characterize this limiting value as a function of the rate and obtain tight finite blocklength bounds on the min max and max min value as a corollary we get an explicit expression for the epsilon capacity of a compound channel under stochastic codes the first such result to the best of our knowledge our results demonstrate a deeper relation between the compound channel and mixed channel than was previously known they also show that the conventional information theoretic viewpoint articulated via the shannon solution coincides asymptotically with the game theoretic one articulated via the von neumann solution key to our results is the derivation of new finite blocklength upper bounds on the min max value of the game via a novel achievability scheme and lower bounds on the max min value obtained via the linear programming relaxation based approach we introduced in 2

information theoretic proofs of entropy power inequalities while most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information up to now shannon s entropy power inequality epi is an exception existing information theoretic proofs of the epi hinge on representations of differential entropy using either fisher information or minimum mean square error mmse which are derived from de bruijn s identity in this paper we first present an unified view of these proofs showing that they share two essential ingredients 1 a data processing argument applied to a covariance preserving linear transformation 2 an integration over a path of a continuous gaussian perturbation using these ingredients we develop a new and brief proof of the epi through a mutual information inequality which replaces stam and blachman s fisher information inequality fii and an inequality for mmse by guo shamai and verdu used in earlier proofs the result has the advantage of being very simple in that it relies only on the basic properties of mutual information these ideas are then generalized to various extended versions of the epi zamir and feder s generalized epi for linear transformations of the random variables takano and johnson s epi for dependent variables liu and viswanath s covariance constrained epi and costa s concavity inequality for the entropy power

oblivious communication channels and their capacity let be c x1 xn sub 0 1 n be an n n binary error correcting code not necessarily linear let e 0 1 n be an error vector a codeword xepsic is said to be disturbed by the error e if the closest codeword to xopluse is no longer x let ae be the subset of codewords in c that are disturbed by e in this work we study the size of ae in random codes c i e codes in which each codeword is chosen uniformly and independently at random from 0 1 n using recent results of vu random structures and algorithms vol 20 no 3 pp 262 316 2002 on the concentration of non lipschitz functions we show that ae is strongly concentrated for a wide range of values of n and e we apply this result in the study of communication channels we refer to as oblivious roughly speaking a channel w y x is said to be oblivious if the error distribution imposed by the channel is independent of the transmitted codeword x a family of channels psi is said to be oblivious if every member w of the family is oblivious in this work we define oblivious and partially oblivious families of not necessarily memoryless channels and analyze their capacity when considering the capacity of a family of channels psi one must address the design of error correcting codes which allow communication under the uncertainty of which channel wepsipsi is actually used the oblivious channels we define have connections to arbitrarily varying channels with state constraints

on the statistical physics of directed polymers in a random medium and their relation to tree codes using well known results from statistical physics concerning the almost sure behavior of the free energy of directed polymers in a random medium we prove that random tree codes achieve the distortion rate function not only on the average but moreover almost surely under a certain symmetry condition

arbitrarily varying channels with constrained inputs and states random coding theorems are proved for discrete memoryless arbitrarily varying channels avcs with constraints on the transmitted codewords and channel state sequences two types of constraints are considered peak i e required for each n length sequence almost surely and average over the message set or over an ensemble for peak constraints on the codewords and on the channel state sequences the avc is shown to have a strong random coding capacity if the codewords and or the channel state sequences are constrained in the average sense the avcs do not possess strong capacities only epsilon capacities are shown to exist

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

a min max theorem for antijamming group codes slepian s idea of group codes for analog channels is adapted to the case of antijamming codes the main result is a codeword error probability characterized by a min max theorem the result is illustrated by the special cases of frequency hopping fh and direct sequence ds

directed polymers on trees a martingale approach the authors use martingale methods and simple convexity arguments to compute rigorously the limiting free energy in the problem of directed polymers on a tree the limit is a degenerate random variable and convergence holds almost surely the only assumption on the common distribution of the random potentials attached to the bonds of the tree is that its laplace transform exists everywhere in 0 infinity

signal detection games with power constraints formulates and solves maximin and minimax detection problems for signals with power constraints these problems arise whenever it is necessary to distinguish between a genuine signal and a spurious one designed by an adversary with the principal goal of deceiving the detector the spurious or deceptive signal is subject to certain constraints such as limited power which preclude it from replicating the genuine signal exactly the detection problem is formulated as a zero sum game involving two players the detector designer and the signal designer the payoff is the probability of error of the detector which the detector designer tries to minimize and the deceptive signal designer to maximize for this detection game saddle point solutions whenever possible or otherwise maximin and minimax solutions are derived under three distinct constraints on the deceptive signal power these distinct constraints involve lower bounds on i the signal amplitude ii the time averaged power and iii the expected power the cases of independent and identically distributed and correlated signals are considered

analysis of an on off jamming situation as a dynamic game the process of communication jamming can be modeled as a two person zero sum noncooperative dynamic game played between a communicator a transmitter receiver pair and a jammer we consider a one way time slotted packet radio communication link in the presence of a jammer where the data rate is fixed and 1 in each slot the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value 2 both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating the payoff function is the time average of the mean payoff per slot the game is solved for certain ranges of the players transmitter parameters structures of steady state solutions to the game are also investigated the general behavior of the players strategies and payoff increment is found to depend on a parameter related to the payoff matrix which me call the payoff parameter and the transmitters parameters when the payoff parameter is lower than a threshold the optimal steady state strategies are mixed and the payoff increment constant over time whereas when it is greater than the threshold the strategies are pure and the payoff increment exhibits oscillatory behavior

directed polymers in a random medium abstract the problem of a polymer in a random medium can be formulated as follows consider a regular lattice with on each bond ij a random energy ij the energy e w of a self avoiding walk w on this lattice is the sum of the energies of all the bonds visited by the walk then the problem is to compute the partition function z w exp e w t several recent results will be presented 1 the mean field version of this problem can be solved exactly and one observes a low temperature phase similar to the spin glass phase 2 for finite dimensional lattices one can derive bounds on the transition temperature in high enough dimension 3 for hierarchical lattices the problem can be reduced to finding stable laws when one combines random variables in a non linear way for example z z 1 z 2 z 3 z 4

weak disorder expansion for the anderson model on a tree we show how certain properties of the anderson model of a tree are related to the solutions of a nonlinear integral equation whether the wave function is extended or localized for example corresponds to whether or not the equation has a complex solution we show how the equation can be solved in a weakdisorder expansion we find that for small disorder strength there is an energyec above which the density of states and the conducting properties vanish to all orders in perturbation theory we compute pertubatively the position of the lineec which begins in the limit of zero disorder at the band edge of the pure system inside the band of the pure system the density of states and conducting properties can be computed perturbatively this expansion breaks down nearec because of small denominators we show how it can be resummed by choosing the appropriate scaling of the energy for energies greater thanec we show that nonperturbative effects contribute to the density of states but we have been unable to tell whether they also contribute to the conducting properties

some information theoretic saddlepoints in order to study communication in the presence of jamming or vice versa one can formulate a two person zero sum game with mutual information as the payoff function since mutual information is convex concave in just the right way one often finds saddlepoint strategies which are simultaneously optimal for both players in this paper we shall discuss these saddlepoints for four distinct cases additive noise average power constraints and any combination of hard soft input output quantization one of these cases soft soft has been previously studied shannon dobrushin blachman but the other three appear to be new

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

complex random energy model zeros and fluctuations the partition function of the random energy model at inverse temperature beta is a sum of random exponentials mathcal z n beta sum k 1 n exp beta sqrt n x k where x 1 x 2 ldots are independent real standard normal random variables random energies and n log n we study the large n limit of the partition function viewed as an analytic function of the complex variable beta we identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature we prove limit theorems for the random partition function at complex beta both on the logarithmic scale and on the level of limiting distributions our results cover also the case of the sums of independent identically distributed random exponentials with any given correlations between the real and imaginary parts of the random exponent

the e equilibrium in transportation networks abstract the principle of traffic equilibrium wardrop 1952 demands that the trip makers have enough knowledge of transportation networks which needs to be attained by accumulating experiences for a long time because of the complexity of traffic situation in the networks the route choice decisions for trip makers are however not always optimal objectively as a consequence it is impossible to strictly attain wardrop equilibrium in this paper a new concept of equilibrium equilibrium is proposed under the realistic assumption i e the fuzzy road information and random route choices equilibrium in the network is discussed by adopting fuzzy set theory mixed stochastic games and brouwer fixed point theorem in topological space the conclusion is that there is equilibrium in the real transportation network and this equilibrium has some deviations from the strict wardrop equilibrium the notion of equilibrium extends the traditional notion of network equilibrium it shows that traffic flow in the network converges to a region rather than to the points

matrix games with nonuniform payoff distributions abstract the theoretical analysis of the statistical properties of 2 person zero sum games with random payoff matrices is generalized to payoff matrices with elements whose average and variance depend on the column they belong to the value of the game and the distribution of the strategies are solved analytically using methods from statistical mechanics of neural networks the analytical results are confirmed by simulations

the feasibility of maximum length sequences to reduce acquisition time of the middle latency response maximum length sequences mls have been used to improve the signal to noise ratio snr of otoacoustic emissions thornton j acoust soc am 94 132 136 1993 and the auditory brainstem response thornton and slaven br j audiol 27 205 210 1993 by implication a shorter recording time would be required to give equal signal to noise ratio snr this study aimed to establish whether it is also possible to improve the snr of the auditory evoked potential termed the middle latency response mlr using maximum length sequences mls recordings of 180 s each were made using a conventional recording rate and mls rates of 42 89 and 185 clicks s three different stimulus intensities were used in the range 30 to 70 db nhl the rate of 89 clicks s was found to produce most improvement in snr for both the na pa region of the mlr and the na pb region this improvement in snr using mls implies that an mls rate of 89 clicks s would produce a fourfold reduction in recording time for equal snr over conventional recording for the pa nb region of the mlr at a stimulus intensity of 70 db nhl the latency of the nb wave was found to reduce significantly using mls an mlr could not be recorded from every subject in this study but more subjects had an identifiable response for mls than for conventional recordings use of mls to record the mlr appears to offer the potential for reduction in test time and better wave identification

on the deterministic code capacity of the multiple access arbitrarily varying channel a method that allows one to decide whether or not the capacity region of a multiple access arbitrarily varying channel avc has a nonempty interior is discussed using the method of types and an approach different from j h jahn ibid vol 27 no 3 p 212 226 1981 this problem is partially solved the notion of symmetrizability for the two user avc as an extension of the same notion for the single user avc is considered it is shown that if a multiple access avc is symmetrizable then its capacity region has an empty interior for the two user avc this means that at least one and perhaps both users cannot reliably transmit information across the channel more importantly it is shown that if the channel is suitably nonsymmetrizable then the capacity region has a nonempty interior and both users can reliably transmit information across the channel the proofs rely heavily on a complicated decoding rule conditions under which simpler multiple message decoding techniques might suffice are therefore examined in particular conditions under which the universal maximal mutual information decoding rule will be effective are given

the capacity of channels with feedback in this paper we introduce a general framework for treating channels with memory and feedback first we prove a general feedback channel coding theorem based on massey s concept of directed information second we present coding results for markov channels this requires determining appropriate sufficient statistics at the encoder and decoder we give a recursive characterization of these sufficient statistics third a dynamic programming framework for computing the capacity of markov channels is presented fourth it is shown that the average cost optimality equation acoe can be viewed as an implicit single letter characterization of the capacity fifth scenarios with simple sufficient statistics are described sixth error exponents for channels with feedback are presented

gaussian arbitrarily varying channels the em arbitrarily varying channel avc can be interpreted as a model of a channel jammed by an intelligent and unpredictable adversary we investigate the asymptotic reliability of optimal random block codes on gaussian arbitrarily varying channels gavc s a gavc is a discrete time memoryless gaussian channel with input power constraint p t and noise power n e which is further corrupted by an additive jamming signal the statistics of this signal are unknown and may be arbitrary except that they are subject to a power constraint p j we distinguish between two types of power constraints em peak and em average for peak constraints on the input power and the jamming power we show that the gavc has a random coding capacity for the remaining cases in which either the transmitter or the jammer or both are subject to average power constraints no capacities exist and only lambda capacities are found the asymptotic error probability suffered by optimal random codes in these cases is determined our results suggest that if the jammer is subject only to an average power constraint reliable communication is impossible at any positive code rate

deconvolution of evoked responses obtained at high stimulus rates continuous loop averaging deconvolution clad is a new general mathematical theory and method developed to deconvolve overlapping auditory evoked responses obtained at high stimulation rates using clad arbitrary stimulus sequences are generated and averaged responses deconvolved until now only a few special stimulus series such as maximum length sequences mls and legendre sequences lgs were capable of performing this task a clad computer algorithm is developed and implemented in an evoked potential averaging system computer simulations are used to verify the theory and methodology auditory brainstem responses abr and middle latency responses mlr are acquired from subjects with normal hearing at high stimulation rates to validate and show the feasibility of the clad technique