on the joint source channel coding error exponent for discrete memoryless systems we investigate the computation of csisza spl acute r s bounds for the joint source channel coding jscc error exponent e sub j of a communication system consisting of a discrete memoryless source and a discrete memoryless channel we provide equivalent expressions for these bounds and derive explicit formulas for the rates where the bounds are attained these equivalent representations can be readily computed for arbitrary source channel pairs via arimoto s algorithm when the channel s distribution satisfies a symmetry property the bounds admit closed form parametric expressions we then use our results to provide a systematic comparison between the jscc error exponent e sub j and the tandem coding error exponent e sub t which applies if the source and channel are separately coded it is shown that e sub t spl les e sub j spl les 2e sub t we establish conditions for which e sub j e sub t and for which e sub j 2e sub t numerical examples indicate that e sub j is close to 2e sub t for many source channel pairs this gain translates into a power saving larger than 2 db for a binary source transmitted over additive white gaussian noise awgn channels and rayleigh fading channels with finite output quantization finally we study the computation of the lossy jscc error exponent under the hamming distortion measure

symmetric trellis coded vector quantization we present here design techniques for trellis coded vector quantizers with symmetric codebooks that facilitate low complexity quantization as well as partitioning into equiprobable sets for trellis coding the quantization performance of this coder on the independently identically distributed i i d laplacian source matches the performance of trellis based scalar vector quantization tb svq but requires less computational complexity

a survey of the theory of source coding with a fidelity criterion the purpose of this paper is threefold 1 to acquaint the reader with the types of problems that have been considered in the area of source coding with a fidelity criterion 2 to survey results that have been obtained on these problems and 3 to outline future research trends in the area

coded continuous phase modulation using ring convolutional codes rate 1 2 convolutional codes over the ring of integers modulo m are combined with m ary continuous phase modulation cpm schemes whose modulation indices are of the form h 1 m an m ary cpm scheme with h 1 m can be modeled by a continuous phase encoder cpe followed by a memoryless modulator mm where the cpe is linear over the ring of integers modulo m the fact that the convolutional code and the cpe are over the same algebra allows the state of the cpe to be fed back and used by the convolutional encoder a modified euclidean distance function that substantially simplifies the search for good codes has been derived and used to find new codes numerical results show that this approach consistently improves the performance as compared to coded schemes using binary convolutional codes with the same decoding complexity

critical exponents for semilinear dissipative wave equations in rn abstract we shall present new critical exponents 1 2m n with m 1 2 to the cauchy problem utt u ut u p 1u with the initial data u 0 u 1 h 1 r n l m r n l 2 r n l m r n that is the small data global existence property can be derived to the cauchy problem above with power 1 2m n

quantization of memoryless and gauss markov sources over binary markov channels joint source channel coding for stationary memoryless and gauss markov sources and binary markov channels is considered the channel is an additive noise channel where the noise process is an mth order markov chain two joint source channel coding schemes are considered the first is a channel optimized vector quantizer optimized for both source and channel the second scheme consists of a scalar quantizer and a maximum a posteriori detector in this scheme it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise these two schemes are then compared against two schemes which use channel interleaving numerical results show that the proposed schemes outperform the interleaving schemes for very noisy channels with high noise correlation gains of 4 5 db in signal to noise ratio are possible

a structured fixed rate vector quantizer derived from a variable length scalar quantizer i memoryless sources for pt i see ibid vol 39 no 3 p 851 67 1993 the fixed rate scalar vector quantizer svq for quantizing stationary memoryless sources is extended to a specific type of vector source in which each component is a stationary memoryless scalar subsource independent of the other components algorithms for the design and implementation of the original svq are modified to apply to this case the resulting svq referred to as the extended svq esvq is then used to quantize stationary sources with memory with known autocorrelation function numerical results are presented for the quantization of first order gauss markov sources using this scheme it is shown that the esvq based scheme performs very close to entropy coded transform quantization while maintaining a fixed rate output and outperforms the fixed rate scheme that uses scalar lloyd max quantization of the transform coefficients it is also shown that this scheme performs better than implementable vector quantizers especially at high rates

tradeoff between source and channel coding on a gaussian channel consider a system that quantizes and encodes analog data for transmission across an additive noise gaussian channel to minimize distortion the channel code rate must be chosen to optimally allocate the available transmission rate between lossy source coding and block channel coding we establish tight upper and lower bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a gaussian channel thus extending some recently obtained results for the binary symmetric channel the upper hounds are obtained by averaging whereas the lower bounds are uniform over all possible index assignments analytic expressions are derived for large and small signal to noise ratios and also for large source vector dimension as in the binary symmetric channel the optimal channel code rate is often substantially smaller than the channel capacity and the distortion decays exponentially with the number of channel uses exact exponents are derived

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

critical regularity of nonlinearities in semilinear classical damped wave equations in this paper we consider the cauchy problem for the semilinear damped wave equation begin aligned u tt vardelta u u t h u quad u 0 x phi x quad u t 0 x psi x end aligned where h s s 1 frac 2 n mu s here n is the space dimension and mu is a modulus of continuity our goal is to obtain sharp conditions on mu to obtain a threshold between global in time existence of small data solutions stability of the zero solution and blow up behavior even of small data solutions

a decomposition approach to cpm it is shown that any continuous phase modulation cpm system can be decomposed into a continuous phase encoder and a memoryless modulator in such a way that the former is a linear modulo some integer p time invariant sequential circuit and the latter is also time invariant this decomposition is exploited to obtain alternative realizations of the continuous phase encoder and hence of cpm and also to obtain alternative forms of the optimum decoding algorithm when p is a prime p so that the encoder is linear over the finite field gf p it is shown that cascading it with an outside convolutional encoder is equivalent to a single convolutional encoder it is pointed out that the cascade of the modulator the waveform channel which it is assumed is characterized by additive white gaussian noise and the demodulator that operates over one symbol interval yield a discrete memoryless channel that can be studied without the distractions introduced by continuous phase encoding

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

trellis coded vector quantization trellis coded quantization is generalized to allow a vector reproduction alphabet three encoding structures are described several encoder design rules are presented and two design algorithms are developed it is shown that for a stationary ergodic vector source if the optimized trellis coded vector quantization reproduction process is jointly stationary and ergodic with the source then the quantization noise is zero mean and of a variance equal to the difference between the source variance and the variance of the reproduction sequence several examples illustrate the encoder design procedure and performance

joint source and channel coding using punctured ring convolutional coded cpm in this paper a novel trellis source encoding scheme based on punctured ring convolutional codes is presented joint source and channel coding jscc using trellis coded continuous phase modulation cpm with punctured convolutional codes over rings is investigated the channels considered are the additive white gaussian noise awgn channel and the rayleigh fading channel optimal soft decoding for the proposed jscc scheme is studied the soft decoder is based on the a posteriori probability app algorithm for trellis coded cpm with punctured ring convolutional codes it is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal to noise ratio snr furthermore adaptive jscc approaches based on the proposed source coding scheme are investigated compared with jscc schemes with fixed source coding rates the proposed adaptive approaches can achieve much better performance in the high snr region the novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes the use of a soft decoder the app algorithm for the combined systems and the adaptive approaches to the jscc problem

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

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

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

soft decision demodulation design for covq over white colored and isi gaussian channels in this work the design of a q bit scalar and vector soft decision demodulator for gaussian channels with binary phase shift keying modulation is investigated the demodulator is used in conjunction with a soft decision channel optimized vector quantization covq system the covq is constructed for an expanded q 1 discrete channel consisting of the concatenation of the modulator the gaussian channel and the demodulator it is found that as the demodulator resolution q increases the capacity of the expanded channel increases resulting in an improvement of the covq performance consequently the soft decision demodulator is designed to maximize the capacity of the expanded channel three gaussian channel models are considered as follows 1 additive white gaussian noise channels 2 additive colored gaussian noise channels and 3 gaussian channels with intersymbol interference comparisons are made with a hard decision covq systems b covq systems which utilize interleaving and c an unquantized q spl infin soft decision decoder proposed by skoglund and hedelin 1999 it is shown that substantial improvements can be achieved over covq systems which utilize hard decision demodulation and or channel interleaving the performance of the proposed covq system is comparable with the system by skoglund and hedelin though its computational complexity is substantially less

channel optimized soft trellis waveform coding we provide a new fuzzy relaxation trellis codebook search algorithm over noisy channels the new algorithm solves the problems associated with the lbg algorithm in the sense of delivering relatively lower distortion configurations using short training sequences furthermore the new approach is significantly less sensitive to the initialization process the algorithm minimizes a weighted distortion measure averaged over both the source and the channel statistics the weights are soft distortion related reliability information which are delivered by a soft trellis vector quantization algorithm stvq the concept of soft compression is introduced by haddad and yongacoglu see proc globecom rio de janeiro brazil dec 1999 in another paper using the forward backward symbol map algorithm the work introduced in this paper is an extension of the work established for the noiseless channel case by haddad and yongacoglu see proc ieee icassp istanbul turkey june 2000 in yet another paper testing is performed using first and second order gauss markov sources over several trellis structures vector dimensions and compression rates moreover the robustness of the optimal configurations is tested under channel mismatch conditions and compared with tandem coding systems

joint source and noisy channel trellis encoding corresp in a trellis encoding communication system the decoder is a time invariant nonlinear filter with finite memory sliding block code and the encoder is a trellis search algorithm matched to the decoder a coding theorem is established for a trellis encoding of a stationary and ergodic source over a discrete memoryless noisy channel which shows that such communication systems can perform arbitrarily close to the source distortion rate function evaluated at the channel capacity

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

non markovianity and negative entropy production rates entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems its positivity can be ensured for a wide class of setups but the entropy production rate can become negative sometimes this is often taken as an indicator of non markovianity we make this link precise by showing under which conditions a negative entropy production rate implies non markovianity and when it does not for a system coupled to a single heat bath this can be established within a unified language for two setups i the dynamics resulting from a coarse grained description of a markovian master equation and ii the classical hamiltonian dynamics of a system coupled to a bath the quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case the instantaneous fixed point of a non markovian dynamics plays an important role in our study our key contribution is to provide a consistent theoretical framework to study the finite time thermodynamics of a large class of dynamics with a precise link to its non markovianity

construction and evaluation of trellis coded quantizers for memoryless sources new constructions of trellis waveform coders trellis coded quantizers and trellis coded vector quantizers are proposed the performances of the new quantizers are determined for the memoryless laplacian gaussian and uniform sources they are better than for the gaussian and laplacian sources or equal to for the uniform source the best previously published results

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

sharp upper bound for lifespan of solutions to some critical semilinear parabolic dispersive and hyperbolic equations via a test function method abstract this paper is concerned with the blowup phenomena for initial boundary value problem 0 1 t 2 u x t u x t a x t u x t u x t p x t c 0 t u x t 0 x t c 0 t u x 0 e f x x c t u x 0 e g x x c where c is a cone like domain in r n n 2 defined as c int r r n r 0 with a connected open set in s n 1 with smooth boundary if n 1 then we only consider two cases c 0 and c r here a x is a non zero coefficient of t u which could be complex valued and space dependent is a fixed constant and e 0 is a small parameter the constants 0 1 switch the parabolicity and hyperbolicity of the problem 0 1 the result proposes an argument for sharp upper lifespan estimates of solutions to 0 1 by a test function method based on mitidieri and pokhozhaev 2001 the crucial idea is to introduce an ordinary differential inequality with a parameter as a variable

vector predictive coding of speech at 16 kbits s vector quantization in its simplest form may be regarded as a generalization of pcm independent quantization of each sample of a waveform to what might be called vector pcm where a block of consecutive samples a vector is simultaneously quantized as one unit in theory a performance arbitrarily close to the ultimate rate distortion limit is achievable with waveform vector quantization if the dimension of the vector k is large enough the main obstacle in effectively using vector quantization is complexity a vector quantizer of dimension k operating at a rate of r bits sample requires a number of computations on the order of k2 kr and a memory of the same order however a low dimensional vector quantizer dimensions 4 8 achieves a remarkable improvement over scalar quantization pcm consequently using the vector quantizer as a building block and imbedding it with other waveform data compression techniques may lead to the development of a new and powerful class of waveform coding systems this paper proposes and analyzes a waveform coding system adaptive vector predictive coding avpc in which a low dimensionality vector quantizer is used in an adaptive predictive coding scheme in the encoding process a locally generated prediction of the current input vector is subtracted from the current vector and the resulting error vector is coded by a vector quantizer each frame consisting of many vectors is classified into one of m statistical types this classification determines which one of m fixed predictors and of m vector quantizers will be used for encoding the current frame

fluctuation theorem for hidden entropy production elimination of seemingly unnecessary variables in markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics we show that such difference which we call the hidden entropy production obeys an integral fluctuation theorem if all variables are time reversal invariant or if the density function is symmetric with respect to the change of sign of the time reversal antisymmetric variables the theorem has wide applicability since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated the main consequence of this theorem is that the entropy production decreases by the coarse graining procedure by contrast in the case where a stochastic process is obtained by coarse graining a deterministic and reversible dynamics the entropy production may increase implying that the integral fluctuation theorem should not hold for such reductions we reveal with an explicit example that the nonequilibrated time reversal antisymmetric variables play a crucial role in distinguishing these two cases thus guaranteeing the consistency of the presented theorem

optimal soft decoding for combined trellis coded quantization modulation the maximum a posteriori map algorithm is used as a minimum mean squared error decoder for combined trellis coded quantization and modulation the optimal trellis coded quantizer is derived when the soft decoding map algorithm is used as a decoder the trellis coded quantizer and the soft decoder are optimized iteratively for minimum overall distortion from transmitter input to receiver output significant performance improvement is achieved for both memoryless gaussian and uniform source especially for very noisy channels

gradient algorithms for designing predictive vector quantizers a predictive vector quantizer pvq is a vector extension of a predictive quantizer it consists of two parts a conventional memoryless vector quantizer vq and a vector predictor two gradient algorithms for designing a pvq are developed in this paper the steepest descent sd algorithm and the stochastic gradient sg algorithm both have the property of improving the quantizer and the predictor in the sense of minimizing the distortion as measured by the average mean squared error the differences between the two design approaches are the period and the step size used in each iteration to update the codebook and predictor the sg algorithm updates once for each input training vector and uses a small step size while the sd updates only once for a long period possibly one pass over the entire training sequence and uses a relatively large step size code designs and tests are simulated for both gauss markov sources and for sampled speech waveforms and the results are compared to codes designed using techniques that attempt to optimize only the quantizer for the predictor and not vice versa

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

trellis based scalar vector quantizer for memoryless sources the paper describes a structured vector quantization approach for stationary memoryless sources that combines the scalar vector quantizer svq ideas laroia and farvardin 1993 with trellis coded quantization marcellin and fischer 1990 the resulting quantizer is called the trellis based scalar vector quantizer tb svq the svq structure allows the tb svq to realize a large boundary gain while the underlying trellis code enables it to achieve a significant portion of the total granular gain for large block lengths and powerful possibly complex trellis codes the tb svq can in principle achieve the rate distortion bound as indicated by the results obtained even for reasonable block lengths and relatively simple trellis codes the tb svq outperforms all other fixed rate quantizers at reasonable complexity

cross entropy and iterative decoding in this correspondence the relationship between iterative decoding and techniques for minimizing cross entropy is explained it is shown that minimum cross entropy mce decoding is an optimal lossless decoding algorithm but its complexity limits its practical implementation use of a maximum a posteriori map symbol estimation algorithm instead of the true mce algorithm provides practical algorithms that are identical to those proposed in the literature in particular turbo decoding is shown to be equivalent to an optimal algorithm for iteratively minimizing cross entropy under an implicit independence assumption

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

binary lattice vector quantization with linear block codes and affine index assignments we determine analytic expressions for the performance of some low complexity combined source channel coding systems the main tool used is the hadamard transform in particular we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments linear block channel coding and a binary symmetric channel the distortion formulas are specialized to nonredundant channel codes for a binary symmetric channel and then extended to affine index assignments on a binary asymmetric channel various structured index assignments are compared our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes one interesting result shown is that for a uniform source and uniform quantizer the natural binary code is never optimal for a nonsymmetric channel even though it is known to be optimal for a symmetric channel

model simplification and loss of irreversibility in this paper we reveal a general relationship between model simplification and irreversibility based on the model of continuous time markov chains with time scale separation according to the topological structure of the fast process we divide the states of the chain into the transient states and the recurrent states we show that a two time scale chain can be simplified to a reduced chain in two different ways removal of the transient states and aggregation of the recurrent states both the two operations will lead to a decrease in the entropy production rate and its adiabatic part and will keep its nonadiabatic part the same this suggests that although model simplification can retain almost all the dynamic information of the chain it will lose some thermodynamic information as a trade off

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

joint optimization of tcq tcm systems signal set expansion and set partitioning ideas from trellis coded modulation tcm have been previously applied to develop a source coding technique known as trellis coded quantization tcq it has been also known that joint optimization of source and channel encoders decoders results in substantial performance improvement in this work we investigate the performance of joint tcq tcm systems and develop various system optimization techniques we consider channel optimized tcq levels and asymmetric tcm symbol sets and propose a simulated annealing based algorithm for joint optimization of tcq levels and tcm symbols using these techniques signal to quantization noise ratio sqnr gains of 0 5 4 db over nonoptimized systems are attained off line this in turn provides all the gain of going to a one step higher order trellis

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

a sequence based approximate mmse decoder for source coding over noisy channels using discrete hidden markov models in previous work on source coding over noisy channels it was recognized that when the source has memory there is typically residual redundancy between the discrete symbols produced by the encoder which can be capitalized upon by the decoder to improve the overall quantizer performance sayood and borkenhagen 1991 and phamdo and farvardin see ieee trans inform theory vol 40 p 186 93 1994 proposed detectors at the decoder which optimize suitable criteria in order to estimate the sequence of transmitted symbols phamdo and farvardin also proposed an instantaneous approximate minimum mean squared error iammse decoder these methods provide a performance advantage over conventional systems but the maximum a posteriori map structure is suboptimal while the iammse decoder makes limited use of the redundancy alternatively combining aspects of both approaches we propose a sequence based approximate mmse sammse decoder for a markovian sequence of encoder produced symbols and a discrete memoryless channel we approximate the expected distortion at the decoder under the constraint of fixed decoder complexity for this simplified cost the optimal decoder computes expected values based on a discrete hidden markov model using the wellknown forward backward f b algorithm performance gains for this scheme are demonstrated over previous techniques in quantizing gauss markov sources over a range of noisy channel conditions moreover a constrained delay version is also suggested

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

entropy production in stochastic systems with fast and slow time scales the behavior of stochastic systems with interacting fast and slow degrees of freedom is investigated both for discrete and continuous processes effective equations that govern the process on the slow timescale are derived by asymptotic methods both for the propagator and the entropy production of the systems it is found that in general the result of the limiting procedure for entropy does not coincide with the one defined for the effective slow process and features an additional contribution the specific conditions under which such a correction does or does not arise are stated and the general explicit form of this remnant entropy production is offered finally the fluctuation theorems that are satisfied by this additional term are given

trellis coded continuous phase frequency shift keying with ring convolutional codes trellis coding techniques are applied to continuous phase frequency shift keying cpfsk a new coding scheme based on convolutional codes on the ring of integers modulo p is shown to be a natural way to apply trellis coding to cpfsk previous work has decomposed cpfsk into two parts a linear encoder with memory called the continuous phase encoder cpe and a memoryless modulator mm where the cpe often has a code structure defined over the ring of integers modulo p the combination of a modulo p convolutional channel encoder ce and the cpe is a linear modulo p encoder design examples are given for rate 1 2 coded quaternary cpfsk with modulation indexes 1 2 and 1 4 and rate 2 3 coded octal cpfsk with modulation index 1 8 combinations are optimized in the normalized minimum euclidean distance sense for a given total number of states in the overall mlse receiver numerical results show that this new coding scheme consistently obtains better performance than previous schemes

trellis coded vector quantization a vector generalization of trellis coded quantization tcq called trellis coded vector quantization tcvq and experimental results showing its performance for an i i d gaussian source are presented for a given rate tcvq yields a lower distortion that tcq at the cost of an increase in implementation complexity in addition tcvq allows fractional rates which tcq does not