design and analysis of optimal noisy channel quantization with random index assignment this paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance given a tandem source channel coding system with vector quantization block channel coding and random index assignment a closed form formula is first derived for computing the average end to end distortion eed of the system which reveals a structural factor called the scatter factor of a noisy channel quantizer based on this formula we propose a noisy channel quantization design method by minimizing the eed experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the eed when compared with quantizers designed separately without reference to channel conditions which reveals a practical and effective design for noisy channel quantization as to simplify the channel model by considering a random index assignment furthermore we have presented the high rate asymptotic analysis of the eed for the tandem system while convergence analysis of the iterative algorithm is included in the appendix

combined source channel vector quantization using deterministic annealing the authors present a new approach to combined source channel vector quantization the method derived within information theory and probability theory utilizes deterministic annealing to avoid some local minima that trap conventional descent algorithms such as the generalized lloyd algorithm the resulting vector quantizers satisfy the necessary conditions for local optimality for the noisy channel case they tested the method against several versions of the noisy channel generalized lloyd algorithm on stationary first order gauss markov sources with a binary symmetric channel the method outperformed other methods under all test conditions with the gains over noisy channel gla growing with the codebook size the quantizers designed using deterministic annealing are also shown to behave robustly under channel mismatch conditions as a comparison with a separate source channel system over a large range of test channel conditions the method outperformed a bandwidth equivalent system incorporating a hamming code also for severe channel conditions the method produces solutions with explicit error control coding

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

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

combining beamforming and space time coding using noisy quantized feedback the goal of combining beamforming and spacetime coding is to obtain full diversity order and to provide additional received power array gain compared to conventional space time codes in this work a class of code constellations is proposed called generalized partly orthogonal designs pods and both high rate and low rate feedback information is incorporated with possible feedback errors a binary symmetric channel bsc model characterizes feedback errors two cases are studied first when the bsc bit error probability is known a priori to the transmission ends and second when it is not known exactly based on a minimum pairwise error probability pep design criterion we design a channel optimized vector quantizer covq for feedback information and a precoder matrix codebook to adjust the transmission codewords the attractive property of our combining scheme is that it converges to conventional space time coding with low rate and erroneous feedback and to directional beamforming with high rate and error free feedback this scheme also shows desirable robustness against feedback channel modeling mismatch

quantized feedback information in orthogonal space time block coding this work considers how the presence of quantized channel information obtained from a feedback link may be utilized for determining a transmit weighting matrix that improves the performance of a predetermined orthogonal space time block ostb code to reduce the effects of feedback delay quantization errors and feedback channel bit errors methods based on vector quantization for noisy channels are used in the design of the feedback link the resulting transmission scheme and feedback link take the imperfect nature of the channel information into account while combining the benefits of conventional beamforming with those provided by ostb coding

on the unified dispersion problem efficient formulations and exact algorithms abstract facility dispersion problems involve placing a number of facilities as far apart from each other as possible four different criteria of facility dispersal have been proposed in the literature erkut neuman 1991 despite their formal differences these four classic dispersion objectives can be expressed in a unified model called the partial sum dispersion model lei church 2013 in this paper we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by ogryczak and tamir 2003 we also present a fast branch and bound based exact algorithm

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

a bayesian analysis of self organizing maps in this paper bayesian methods are used to analyze some of the properties of a special type of markov chain the forward transitions through the chain are followed by inverse transitions using bayes theorem backward through a copy of the same chain this will be called a folded markov chain if an appropriately defined euclidean error between the original input and its reconstruction via bayes theorem is minimized with respect to the choice of markov chain transition probabilities then the familiar theories of both vector quantizers and self organizing maps emerge this approach is also used to derive the theory of self supervision in which the higher layers of a multilayer network supervise the lower layers even though overall there is no external teacher

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

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

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

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

design of channel optimized vector quantizers in the presence of channel mismatch we study the design of channel optimized vector quantizers in the presence of channel mismatch we show that when the statistics of the channel bit error rate ber are not known a minimax solution is the one obtained by designing for the worst possible channel then we consider the case when the probability density function of channel ber is known and propose an algorithm that provides a minimum average distortion also by using an estimate of the channel ber at the decoder we develop a decoder adaptive scheme that further improves the performance in all cases we have limited ourselves to table lookup decoders which amount to very small computational complexities finally the utilization of lookup tables at the encoder and the effects of imperfect estimation of channel bers are considered

efficient source decoding over memoryless noisy channels using higher order markov models exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth efficient way to combat noisy channel degradations this redundancy can be employed to either assist the channel decoder for improved performance or design better source decoders in this work a family of solutions for the asymptotically optimum minimum mean squared error mmse reconstruction of a source over memoryless noisy channels is presented when the redundancy in the source encoder output stream is exploited in the form of a spl gamma order markov model spl gamma spl ges 1 and a delay of spl delta spl delta 0 is allowed in the decoding process it is demonstrated that the proposed solutions provide a wealth of tradeoffs between computational complexity and the memory requirements a simplified mmse decoder which is optimized to minimize the computational complexity is also presented considering the same problem setup several other maximum a posteriori probability map symbol and sequence decoders are presented as well numerical results are presented which demonstrate the efficiency of the proposed algorithms

positive solutions of superlinear boundary value problems using a fixed point theorem on operators expanding a cone in a banach space we prove the existence of positive solutions of superlinear boundary value problems at the same time we get bounds or even inclusions of positive solutions

transmission of analog signals using multicarrier modulation a combined source channel coding approach we have proposed and analyzed a combined source channel coding scheme using multicarrier modulation by changing the power and modulation of subchannels carrying different bits of the quantized signal the channel induced distortion can be minimized we derive an algorithm for the allocation of power among subchannels analog sources quantized by scalar and vector quantizers are considered for a gaussian source scalar quantized to 8 bit multicarrier transmission yields a 13 db improvement of signal to distortion ratio over a single carrier system quantizers having a smaller number of bits yield smaller improvements we consider both full search and binary tree search vector quantizers using a natural binary coding scheme for a vector quantizer using 2 b sample multicarrier transmission yields an improvement in signal to distortion ratio that lies between 0 3 and 0 8 db depending on the quantizer design

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

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

a soft decoding scheme for vector quantization over a cdma channel the optimal decoding of vector quantization vq over a code division multiple access cdma channel is too complicated for systems with a medium to large number of users this paper presents a low complexity suboptimal decoder for vq over a cdma channel the proposed decoder is built from a soft output multiuser detector a soft bit estimator and the optimal soft vq decoding of an individual user simulation results obtained over both additive white gaussian noise and flat rayleigh fading channels show that with a lower complexity and good performance the proposed decoding scheme is an attractive alternative to the more complicated optimal decoder

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

pseudo gray coding a pseudo gray code is an assignment of n bit binary indexes to 2 points in a euclidean space so that the hamming distance between two points corresponds closely to the euclidean distance pseudo gray coding provides a redundancy free error protection scheme for vector quantization vq of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise a globally optimal solution to this problem is generally intractable due to an inherently large computational complexity a locally optimal solution the binary switching algorithm is introduced based on the objective of minimizing a useful upper bound on the average system distortion the algorithm yields a significant reduction in average distortion and converges in reasonable running times the sue of pseudo gray coding is motivated by the increasing need for low bit rate vq based encoding systems that operate on noisy channels such as in mobile radio speech communications

channel optimized quantization with soft decision demodulation for space time orthogonal block coded channels we introduce three soft decision demodulation channel optimized vector quantizers covqs to transmit analog sources over space time orthogonal block stob coded flat rayleigh fading channels with binary phase shift keying bpsk modulation one main objective is to judiciously utilize the soft information of the stob coded channel in the design of the vector quantizers while keeping a low system complexity to meet this objective we introduce a simple space time decoding structure that consists of a space time soft detector followed by a linear combiner and a scalar uniform quantizer with resolution q the concatenation of the space time encoder modulator fading channel and space time receiver can be described by a binary input 2q output discrete memoryless channel dmc the scalar uniform quantizer is chosen so that the capacity of the equivalent dmc is maximized to fully exploit and capture the system s soft information by the dmc we next determine the statistics of the dmc in closed form and use them to design three covq schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and or receiver the performance of each quantization scheme is evaluated for memoryless gaussian and gauss markov sources and various stob codes and the benefits of each scheme is illustrated as a function of the antenna diversity and soft decision resolution q comparisons to traditional coding schemes which perform separate source and channel coding operations are also provided

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

quantizers with uniform decoders and channel optimized encoders scalar quantizers with uniform decoders and channel optimized encoders are studied for a uniform source on 0 1 and binary symmetric channels two families of affine index assignments are considered the complemented natural code cnc introduced here and the natural binary code nbc it is shown that the nbc never induces empty cells in the quantizer encoder whereas the cnc can nevertheless we show that the asymptotic distributions of quantizer encoder cells for the nbc and the cnc are equal and are uniform over a proper subset of the source s support region empty cells act as a form of implicit channel coding an effective channel code rate associated with a quantizer designed for a noisy channel is defined and computed for the codes studied by explicitly showing that the mean squared error mse of the cnc can be strictly smaller than that of the nbc we also demonstrate that the nbc is suboptimal for a large range of transmission rates and bit error probabilities this contrasts with the known optimality of the nbc when either both the encoder and decoder are not channel optimized or when only the decoder is channel optimized

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

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

image transmission over the polya channel via channel optimized quantization we introduce two progressive methods for image transmission over binary channels with additive bursty noise modeled by the finite memory polya contagion channel the methods which are based on channel optimized scalar quantization cosq of the wavelet transform coefficients exploit channel memory to offer superior performance over a number of more complex systems designed for the fully interleaved channel

content based multiple bitstream image transmission over noisy channels we propose a novel combined source and channel coding scheme for image transmission over noisy channels the main feature of the proposed scheme is a systematic decomposition of image sources so that unequal error protection can be applied according to not only bit error sensitivity but also visual content importance the wavelet transform is adopted to hierarchically decompose the image the association between the wavelet coefficients and what they represent spatially in the original image is fully exploited so that wavelet blocks are classified based on their corresponding image content the classification produces wavelet blocks in each class with similar content and statistics therefore enables high performance source compression using the set partitioning in hierarchical trees spiht algorithm to combat the channel noise an unequal error protection strategy with rate compatible punctured convolutional cyclic redundancy check rcpc crc codes is implemented based on the bit contribution to both peak signal to noise ratio psnr and visual quality at the receiving end a postprocessing method making use of the spiht decoding structure and the classification map is developed to restore the degradation due to the residual error after channel decoding experimental results show that the proposed scheme is indeed able to provide protection both for the bits that are more sensitive to errors and for the more important visual content under a noisy transmission environment in particular the reconstructed images illustrate consistently better visual quality than using the single bitstream based schemes