sample adaptive product quantization asymptotic analysis and examples vector quantization vq is an efficient data compression technique for low bit rate applications however the major disadvantage of vq is that its encoding complexity increases dramatically with bit rate and vector dimension even though one can use a modified vq such as the tree structured vq to reduce the encoding complexity it is practically infeasible to implement such a vq at a high bit rate or for large vector dimensions because of the huge memory requirement for its codebook and for the very large training sequence requirement to overcome this difficulty a structurally constrained vq called the sample adaptive product quantizer sapq has recently been proposed we extensively study the sapq that is based on scalar quantizers in order to exploit the simplicity of scalar quantization through an asymptotic distortion result we discuss the achievable performance and the relationship between distortion and encoding complexity we illustrate that even when sapq is based on scalar quantizers it can provide vq level performance we also provide numerical results that show a 2 3 db improvement over the lloyd max 1982 1960 quantizers for data rates above 4 b point

full abstraction for pcf an intensional model for the programming language pcf is described in which the types of pcf are interpreted by games and the terms by certain history free strategies this model is shown to capture definability in pcf more precisely every compact strategy in the model is definable in a certain simple extension of pcf we then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder we then obtain an order extensional fully abstract model of pcf by quotienting the intensional model by the intrinsic preorder this is the first syntax independent description of the fully abstract model for pcf hyland and ong have obtained very similar results by a somewhat different route independently and at the same time we then consider the effective version of our model and prove a universality theorem every element of the effective extensional model is definable in pcf equivalently every recursive strategy is definable up to observational equivalence

practical codes for collaborative estimation in collaborative estimation a network of nodes each indirectly observing an underlying source communicate with each other to form improved estimates of the underlying source this paper derives an efficient collaborative estimation algorithm achieving high performance estimates with low communication and complexity utilizing tools from multiterminal source coding theory and modern practical coding theory relevant theoretical limits based on achievability from multiterminal source coding are first presented in order to characterize efficient tradeoffs between communication and estimation performance and inspire the architecture of the collaborative estimation code next low complexity tools from modern practical coding theory are utilized to get a practical collaborative estimation algorithm approaching these performance limits the developed algorithm utilizes successively refined trellis coded quantization sr tcq to provide necessary diverse descriptions of the source and low density parity check ldpc codes to provide an efficient means of compressing these descriptions for low complexity belief propagation decoding with side information comparing the communication versus estimate quality tradeoff performance attained by the developed low complexity scheme with that obtainable with an inner bound an average distortion gap of only 1 0 and 1 6 db at average rates of 3 32 and 2 33 b s respectively is observed

quantization based on a novel sample adaptive product quantizer sapq in this paper we propose a novel feedforward adaptive quantization scheme called the sample adaptive product quantizer sapq this is a structurally constrained vector quantizer that uses unions of product codebooks sapq is based on a concept of adaptive quantization to the varying samples of the source and is very different from traditional adaptation techniques for nonstationary sources sapq quantizes each source sample using a sequence of quantizers even when using scalar quantization in sapq we can achieve performance comparable to vector quantization with the complexity still close to that of scalar quantization we also show that important lattice based vector quantizers can be constructed using scalar quantization in sapq we mathematically analyze sapq and propose a algorithm to implement it we numerically study sapq for independent and identically distributed gaussian and laplacian sources through our numerical study we find that sapq using scalar quantizers achieves typical gains of 13 db in distortion over the lloyd max quantizer we also show that sapq can he used in conjunction with vector quantizers to further improve the gains

near capacity dirty paper code design a source channel coding approach this paper examines near capacity dirty paper code designs based on source channel coding we first point out that the performance loss in signal to noise ratio snr in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss which is a function of the granular loss from source coding and the target dirty paper coding rate or snr we then examine practical designs by combining trellis coded quantization tcq with both systematic and nonsystematic irregular repeat accumulate ira codes like previous approaches we exploit the extrinsic information transfer exit chart technique for capacity approaching ira code design but unlike previous approaches we emphasize the role of strong source coding to achieve as much granular gain as possible using tcq instead of systematic doping we employ two relatively shifted tcq codebooks where the shift is optimized via tuning the exit charts to facilitate the ira code design our designs synergistically combine tcq with ira codes so that they work together as well as they do individually by bringing together tcq the best quantizer from the source coding community and exit chart based ira code designs the best from the channel coding community we are able to approach the theoretical limit of dirty paper coding for example at 0 25 bit per symbol b s our best code design with 2048 state tcq performs only 0 630 db away from the shannon capacity

reduced complexity delayed decision algorithm for context based image processing systems it is well known that the performance of context based image processing systems can be improved by allowing the processor e g an encoder or a denoiser a delay of several samples before making a processing decision often however for such systems traditional delayed decision algorithms can become computationally prohibitive due to the growth in the size of the space of possible solutions in this paper we propose a reduced complexity one pass delayed decision algorithm that systematically reduces the size of the search space while also preserving its structure in particular we apply the proposed algorithm to two examples of adaptive context based image processing systems an image coding system that employs a context based entropy coder and a spatially adaptive image denoising system for these two types of widely used systems we show that the proposed delayed decision search algorithm outperforms instantaneous decision algorithms with only a small increase in complexity we also show that the performance of the proposed algorithm is better than that of other higher complexity delayed decision algorithms

image coding using wavelet transforms and entropy constrained trellis coded quantization the discrete wavelet transform has recently emerged as a powerful technique for decomposing images into various multi resolution approximations multi resolution decomposition schemes have proven to be very effective for high quality low bit rate image coding in this work we investigate the use of entropy constrained trellis coded quantization ectcq for encoding the wavelet coefficients of both monochrome and color images ectcq is known as an effective scheme for quantizing memoryless sources with low to moderate complexity the ectcq approach to data compression has led to some of the most effective source codes found to date for memoryless sources performance comparisons are made using the classical quadrature mirror filter bank of johnston and nine tap spline filters that were built from biorthogonal wavelet bases we conclude that the encoded images obtained from the system employing nine tap spline filters are marginally superior although at the expense of additional computational burden excellent peak signal to noise ratios are obtained for encoding monochrome and color versions of the 512 spl times 512 lenna image comparisons with other results from the literature reveal that the proposed wavelet coder is quite competitive

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

rate distortion performance of dpcm schemes for autoregressive sources an analysis of the rate distortion performance of differential pulse code modulation dpcm schemes operating on discrete time auto regressive processes is presented the approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence at each stage the iterative algorithm optimizes the quantizer structure given the probability distribution of the prediction error while simultaneously updating the distribution of the resulting prediction error different orthogonal expansions specifically matched to the source are used to express the prediction error density a complete description of the algorithm including convergence and uniqueness properties is given results are presented for rate distortion performance of the optimum dpcm scheme for first order gauss markov and laplace markov sources including comparisons with the corresponding rate distortion bounds furthermore asymptotic formulas indicating the high rate performance of these schemes are developed for both first order gaussian and laplacian autoregressive sources

wyner ziv coding based on tcq and ldpc codes this paper considers trellis coded quantization tcq and low density parity check ldpc codes for the quadratic gaussian wyner ziv coding problem after tcq of the source x ldpc codes are used to implement slepian wolf coding of the quantized source q x with side information y at the decoder assuming 256 state tcq and ideal slepian wolf coding in the sense of achieving the theoretical limit h q x y we experimentally show that slepian wolf coded tcq performs 0 2 db away from the wyner ziv distortion rate function dwz r at high rate this result mirrors that of entropy constrained tcq in classic source coding of gaussian sources furthermore using 8 192 state tcq and assuming ideal slepian wolf coding our simulations show that slepian wolf coded tcq performs only 0 1 db away from dwz r at high rate these results establish the practical performance limit of slepian wolf coded tcq for quadratic gaussian wyner ziv coding practical designs give performance very close to the theoretical limit for example with 8 192 state tcq irregular ldpc codes for slepian wolf coding and optimal non linear estimation at the decoder our performance gap to dwz r is 0 20 db 0 22 db 0 30 db and 0 93 db at 3 83 bit per sample b s 1 83 b s 1 53 b s and 1 05 b s respectively when 256 state 4 d trellis coded vector quantization instead of tcq is employed the performance gap to dwz r is 0 51 db 0 51 db 0 54 db and 0 80 db at 2 04 b s 1 38 b s 1 0 b s and 0 5 b s respectively

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

enumeration encoding and decoding algorithms for pyramid cubic lattice and trellis codes a pyramid source code is a code that assigns equal length binary strings to all reproduction codevectors of equal weighted spl epsiv sub 1 norm a pyramid source encoding is partitioned into two concatenated mappings the first from source word to reproduction codeword within a codebook the second from the reproduction codevector to a binary string the first mapping allows distortion and is accomplished using lattice quantization or trellis coded quantization the second mapping is noiseless and is denoted as enumeration efficient pyramid enumeration encoding and decoding algorithms are presented for use with fixed rate or variable rate pyramid lattice and trellis codes

necessary conditions for the optimality of variable rate residual vector quantizers necessary conditions for the optimality of variable rate residual vector quantizers are derived and an iterative descent algorithm based on a lagrangian formulation is introduced for designing residual vector quantizers having minimum average distortion subject to an entropy constraint simulation results for entropy constrained residual vector quantizers are presented for memoryless gaussian laplacian and uniform sources a gauss markov source is also considered the rate distortion performance is shown to be competitive with that of entropy constrained vector quantization and entropy constrained trellis coded quantization

trellis excitation speech coding at low bit rates trellis coded vector quantization tcvq and code excited linear prediction celp coding are combined to form an efficient low bit rate speech coding system the resulting system uses a trellis search to select the synthesis filter excitation sequence and is referred to as trellis excitation coding tec simulations are performed for encoding rates of 6 4 and 8 kbps informal listening tests indicate that the 8 kbps tec system has quality roughly between that of 6 bit and 7 bit spl mu law pcm with spl mu 255 the 6 4 kbps tec system provides speech quality between 5 bit and 6 bit spl mu law pcm a subjective comparison with vector sum excited linear prediction vselp indicates that the 8 kbps tec and the vselp reconstructed speech is about equally preferable

two terminal video coding following recent works on the rate region of the quadratic gaussian two terminal source coding problem and limit approaching code designs this paper examines multiterminal source coding of two correlated i e stereo video sequences to save the sum rate over independent coding of both sequences two multiterminal video coding schemes are proposed in the first scheme the left sequence of the stereo pair is coded by h 264 avc and used at the joint decoder to facilitate wyner ziv coding of the right video sequence the first i frame of the right sequence is successively coded by h 264 avc intracoding and wyner ziv coding an efficient stereo matching algorithm based on loopy belief propagation is then adopted at the decoder to produce pixel level disparity maps between the corresponding frames of the two decoded video sequences on the fly based on the disparity maps side information for both motion vectors and motion compensated residual frames of the right sequence are generated at the decoder before wyner ziv encoding in the second scheme source splitting is employed on top of classic and wyner ziv coding for compression of both i frames to allow flexible rate allocation between the two sequences experiments with both schemes on stereo video sequences using h 264 avc ldpc codes for slepian wolf coding of the motion vectors and scalar quantization in conjunction with ldpc codes for wyner ziv coding of the residual coefficients give a slightly lower sum rate than separate h 264 avc coding of both sequences at the same video quality

progressive image coding using trellis coded quantization in this work we present coding techniques that enable progressive transmission when trellis coded quantization tcq is applied to wavelet coefficients a method for approximately inverting tcq in the absence of least significant bits is developed results are presented using different rate allocation strategies and different entropy coders the proposed wavelet tcq coder yields excellent coding efficiency while supporting progressive modes analogous to those available in jpeg

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

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

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

vector quantizers and predictive quantizers for gauss markov sources low rate vector quantizers are designed and simulated for highly correlated gauss markov sources and the resulting performance is compared with arnstein s optimized predictive quantizer and with huang and schultheiss optimized transform coder two implementations of vector quantizers are considered full search vector quantizers which are optimal but require large codebook searches and tree searched vector quantizers which are suboptimal but require far less searching the various systems are compared on the basis of performance complexity and generality of design techniques

a new trellis source code for memoryless sources the trellis based scalar vector quantizer tb svq for memoryless sources combines the scalar vector quantizer svq with trellis coded quantization tcq to achieve both boundary gain and granular gain the resulting quantizer outperforms all other reasonable complexity fixed rate quantizers unfortunately the resulting code is catastrophic a single bit error within a block can propagate indefinitely into other blocks this correspondence presents a new trellis source code that can achieve essentially the same or in some cases better performance as the tb svq for error free channels but limits the propagation of channel errors

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

noncoherent trellis coded quantization a practical limited feedback technique for massive mimo systems accurate channel state information csi is essential for attaining beamforming gains in single user su multiple input multiple output mimo and multiplexing gains in multi user mu mimo wireless communication systems state of the art limited feedback schemes which rely on pre defined codebooks for channel quantization are only appropriate for a small number of transmit antennas and low feedback overhead in order to scale informed transmitter schemes to emerging massive mimo systems with a large number of transmit antennas at the base station one common approach is to employ time division duplexing tdd and to exploit the implicit feedback obtained from channel reciprocity however most existing cellular deployments are based on frequency division duplexing fdd hence it is of great interest to explore backwards compatible massive mimo upgrades of such systems for a fixed feedback rate per antenna the number of codewords for quantizing the channel grows exponentially with the number of antennas hence generating feedback based on look up from a standard vector quantized codebook does not scale in this paper we propose noncoherent trellis coded quantization ntcq whose encoding complexity scales linearly with the number of antennas the approach exploits the duality between source encoding in a grassmannian manifold for finding a vector in the codebook which maximizes beamforming gain and noncoherent sequence detection for maximum likelihood decoding subject to uncertainty in the channel gain furthermore since noncoherent detection can be realized near optimally using a bank of coherent detectors we obtain a low complexity implementation of ntcq encoding using an off the shelf viterbi algorithm applied to standard trellis coded quantization we also develop advanced ntcq schemes which utilize various channel properties such as temporal spatial correlations monte carlo simulation results show the proposed ntcq and its extensions can achieve near optimal performance with moderate complexity and feedback overhead

turbo quantization of oversampled signals we present a new iterative quantization procedure for oversampled frames with guaranteed convergence and stability the procedure uses similar concepts to that of turbo decoding in the context of error control coding the quantization process is modeled as a quadratic integer programming problem a trellis structure is introduced to solve the problem where the quantized coefficients represent a path through the trellis diagram the quantization metric is iteratively improved through turbo iterations by exchanging quantization extrinsic information the proposed procedure is shown to provide significant improvement over prior art in quantization and integer programming

progressive coding of a gaussian source using matching pursuit in this paper the application of matching pursuit mp in progressive coding of memoryless gaussian sources is studied in addition a detailed analysis of the rate distortion performance of our proposed mp encoder is presented and the distortion of the mp encoder is derived in terms of dictionary size and number of quantization levels and the optimum parameters are calculated our analysis is based on a probabilistic model for matching pursuit residual vectors our simulation results verify the accuracy of our analysis and show that matching pursuit can produce an embedded bitstream with comparable quality to existing quantizers the mp encoder outperforms quantizers that are capable of producing embedded bitstreams

synchronizable codes for the optical oppm channel random overlapping pulse position modulation oppm sequences result in an unrecoverable error floor on both the probability of erroneous synchronization and the probability of symbol error when only chip synchronization is present it is known however that for a given sequence length m a subset of the set of all possible sequences is synchronizable in the sense that in the absence of noise the receiver can correctly symbol synchronize by observing m or more symbol intervals the authors design finite state machines and codes over a j ary alphabet which produce sequences with the property that every subsequence of length l is synchronizable some of the codes in addition to being synchronizable produce a coding gain for an optical poisson channel the authors introduce joint synchronization and detection algorithms that utilize the memory in the encoded sequences to produce joint estimates of timing and sequences their performance is analyzed through simulations and analytical results

2 step scalar deadzone quantization for bitplane image coding modern lossy image coding systems generate a quality progressive codestream that truncated at increasing rates produces an image with decreasing distortion quality progressivity is commonly provided by an embedded quantizer that employs uniform scalar deadzone quantization usdq together with a bitplane coding strategy this paper introduces a 2 step scalar deadzone quantization 2sdq scheme that achieves same coding performance as that of usdq while reducing the coding passes and the emitted symbols of the bitplane coding engine this serves to reduce the computational costs of the codec and or to code high dynamic range images the main insights behind 2sdq are the use of two quantization step sizes that approximate wavelet coefficients with more or less precision depending on their density and a rate distortion optimization technique that adjusts the distortion decreases produced when coding 2sdq indexes the integration of 2sdq in current codecs is straightforward the applicability and efficiency of 2sdq are demonstrated within the framework of jpeg2000

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

types and full abstraction for polyadic π calculus a type system for terms of the monadic p calculus is introduced and used to obtain a full abstraction result for the translation of the polyadic p calculus into the monadic calculus well sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent

trellis based scalar vector quantization of sources with memory the trellis based scalar vector quantizer tb svq can achieve the rate distortion performance bound for memoryless sources this paper extends the scope of this quantizer to coding of sources with memory first considered is a simple extension called the predictive tb svq which applies a closed loop predictive coding operation in each survivor path of the viterbi codebook search algorithm although the predictive tb svq outperforms all other known structured fixed rate vector quantizers due to practical reasons it may not approach the rate distortion limit a new quantization scheme motivated by the precoding idea of laroia et al 1993 called the precoded tb svq is also considered the granular gain is realized by the underlying trellis code while the combination of the precoder and the svq structure provides the boundary gain this new quantization scheme is asymptotically optimal and can in principle approach the rate distortion bound for markov sources

a low complexity method for fixed rate entropy constrained vector quantization this paper describes a new approach to fixed rate entropy constrained vector quantization fevq for stationary memoryless sources where the structure of codewords are derived from a variable length scalar quantizer we formulate the quantization search operation as a zero one integer optimization problem and show that the resulting integer program can be closely approximated by solving a simple linear program the result is a lagrange formulation which adjoins the constraint on the entropy codeword length to the distortion unlike the previously known methods with a fixed lagrange multiplier we use an iterative algorithm to optimize the underlying objective function while updating the lagrange multiplier until the constraint on the overall rate is satisfied the key feature of the new method is the substantial reduction in the number of iterations in comparison with previous related methods in order to achieve some packing gain we combine the process of trellis coded quantization with that of fevq this results in an iterative application of the viterbi algorithm on the underlying trellis for selecting the lagrange multiplier numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature

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

multiple description trellis coded quantization we present a construction of multiple description trellis coded quantizers we use the tensor product of trellises to build a trellis which is applicable to multiple description coding the problems of index assignment and set partitioning for the resulting trellis are considered the viterbi algorithm provides the best path for encoding and the design procedure utilizes a generalized lloyd algorithm the encoding process simultaneously generates all the transmitted sequences furthermore the complexity of the scheme is almost independent of the rate the quantizer provides remarkable performance with little encoding 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

general embedded quantization for wavelet based lossy image coding embedded quantization is a mechanism employed by many lossy image codecs to progressively refine the distortion of a transformed image currently the most common approach to do so in the context of wavelet based image coding is to couple uniform scalar deadzone quantization usdq with bitplane coding bpc usdq bpc is convenient for its practicality and has proved to achieve competitive coding performance but the quantizer established by this scheme does not allow major variations this paper introduces a multistage quantization scheme named general embedded quantization geq that provides more flexibility to the quantizer geq schemes can be devised for specific decoding rates achieving optimal coding performance practical approaches of geq schemes achieve coding performance similar to that of usdq bpc while requiring fewer quantization stages the performance achieved by geq is evaluated in this paper through experimental results carried out in the framework of modern image coding systems

new permutation codes using hadamard unscrambling corresp a new class of codes for data compression is described that combines permutations with the fast hadamard transform fht it was invented for digital speech compression based on linear predictive coding lpc but may be useful for other data compression applications one particular code with rate frac 1 2 is considered a 16 bit code for a block length of 32 samples all coding and decoding steps are fast so that real time applications with cheap hardware can be anticipated

the stretched golay and other codes for high snr finite delay quantization of the gaussian source at 1 2 bit per sample error correcting codes are considered as codebooks for high performance vector quantization vq of the iid gaussian source at fractional bit rate a family of good rate one half codes is introduced the stretched golay codes the performance of these codes is compared to other good block codes trellis coded quantization and other techniques the stretched golay codes are shown to outperform previously published results for block lengths 32 40 56 and 64 the good performance together with fast decoding make these techniques attractive for applications such as low bit rate coding of speech

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

towards a unified approach to encodability and separation results for process calculi we present a unified approach to evaluate the relative expressive power of process calculi in particular we identify a small set of criteria that have already been somehow presented in the literature that an encoding should satisfy to be considered a valid means for language comparison we argue that the combination of such criteria is a valid proposal by noting that i several well known encodings appeared in the literature satisfy them ii this notion is not trivial because some known encodings do not satisfy all the criteria we have proposed iii several well known separation results can be formulated in terms of our criteria and iv some widely believed but never formally proved separation results can be proved by using the criteria we propose moreover the criteria defined induce general proof techniques for separation results that can be easily instantiated to cover known case studies

low complexity predictive trellis coded quantization of speech line spectral frequencies low complexity block constrained trellis coded quantization bc tcq structures are studied and a predictive bc tcq encoding method is developed for quantization of line spectrum frequency lsf parameters for speech coding applications the performance is compared with the linear predictive coding lpc vector quantizers used in the amr wb itu g 722 2 and is 641 speech coding standards demonstrating reduction in spectral distortion sd and significant reduction in encoding complexity

unions of non disjoint theories and combinations of satisfiability procedures in this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability we describe a general combination method which given a procedure that decides constraint satisfiability with respect to a constraint theory t1 and one that decides constraint satisfiability with respect to a constraint theory t2 produces a procedure that semi decides constraint satisfiability with respect to the union of t1 and t2 we provide a number of model theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete with special emphasis on the case in which the signatures of the component theories are non disjoint we also describe some general classes of theories to which our combination results apply and relate our approach to some of the existing combination methods in the field

space frequency quantization for wavelet image coding a new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree structured quantization related to spatial structures has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation this paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder we consider zerotree quantization zeroing out tree structured sets of wavelet coefficients and the simplest form of scalar quantization a single common uniform scalar quantizer applied to all nonzeroed coefficients and we formalize the problem of optimizing their joint application we develop an image coding algorithm for solving the resulting optimization problem despite the basic form of the two quantizers considered the resulting algorithm demonstrates coding performance that is competitive often outperforming the very best coding algorithms in the literature

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

image coding using adaptive recursive interpolative dpcm a predictive image coder having minimal decoder complexity is presented the image coder utilizes recursive interpolative dpcm in conjunction with adaptive classification entropy constrained trellis coded quantization and optimal rate allocation to obtain signal to noise ratios snrs in the range of those provided by the most advanced transform coders

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

complexity constrained trellis quantizers a reasonable measure of quantizer complexity is the expected number of quanta per input sample for which distortion is computed given this measure a rate distortion complexity theory is obtained by extending earlier work in alphabet constrained rate distortion theory numerical results show that operation on the alphabet constrained rate distortion bound can be obtained with a complexity of two furthermore lloyd max conditions are shown to describe the minimum of a slightly constrained version of the rate distortion complexity problem complexity constrained design methods are applied first to trellis coded quantizers where they are shown to reduce arithmetic operations by at least 25 they are then used to develop model based trellis quantizers the trellises of which are derived from a markov model of the source simulation results confirm that excellent performance can be obtained with modest complexity

trellis coded modulation with multidimensional constellations trellis coded modulation schemes using four eight or 16 dimensional constellations have a number of potential advantages over the usual two dimensional schemes a smaller constituent two dimensional constellation easier tolerance to phase ambiguities and a better trade off between complexity and coding gain a number of such schemes are presented and evaluated starting with a variety of multidimensional lattices we show how to select multidimensional constellations how to partition them into subsets how to construct trellis codes using those subsets and how to map hits to constellation points simplifications of the viterbi decoding algorithm are presented we conclude that there are multidimensional trellis coded modulation schemes that perform better for the same complexity than do two dimensional schemes

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

a calculus for cryptographic protocols we introduce the spi calculus an extension of the pi calculus designed for describing and analyzing cryptographic protocols we show how to use the spi calculus particularly for studying authentication protocols the pi calculus without extension suffices for some abstract protocols the spi calculus enables us to consider cryptographic issues in more detail we represent protocols as processes in the spi calculus and state their security properties in terms of coarse grained notions of protocol equivalence

on overflow and underflow problems in buffer instrumented variable length coding of fixed rate memoryless sources corresp it is well known that variable length coding schemes can be employed in entropy encoding of finite alphabet sources to transmit these codes over a synchronous channel however requires a buffer since in practice this buffer is of finite size it is subject to both overflow and undertow the buffer behavior is studied with particular application to huffman coding of the outputs of an optimum uniform threshold quantizer driven by a memoryless gaussian source fairly general upper and lower bounds on the average terminal time are developed under certain conditions the tightness of these bounds is verified and asymptotic formulas are developed as an example an encoding scheme employing huffman codes in conjunction with uniform quantization of memoryless gaussian sources is considered and the buffer behavior as a function of the buffer size and output rate is studied

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

lossy compression of discrete sources via the viterbi algorithm we present a new lossy compressor for finite alphabet sources for coding a sequence xn the encoder starts by assigning a certain cost to each possible reconstruction sequence it then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor the cost of each sequence is a linear combination of its distance from the sequence xn and a linear function of its kth order empirical distribution the structure of the cost function allows the encoder to employ the viterbi algorithm to find the sequence with minimum cost we identify a choice of the coefficients used in the cost function which ensures that the algorithm universally achieves the optimum rate distortion performance for any stationary ergodic source in the limit of large provided that increases as o log n iterative techniques for approximating the coefficients which alleviate the computational burden of finding the optimal coefficients are proposed and studied

image subband coding using context based classification and adaptive quantization adaptive compression methods have been a key component of many proposed subband or wavelet image coding techniques this paper deals with a particular type of adaptive subband image coding where we focus on the image coder s ability to adjust itself on the fly to the spatially varying statistical nature of image contents this backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters specifically we present backward adaptive quantization using a new context based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients we couple this classification with online parametric adaptation of the quantizer applied to each class a simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate distortion performance in particular at very low rates for popular test images it is comparable or superior to most of the state of the art coders in the literature

embedded trellis coded quantization for jpeg2000 a modified embedded trellis coded quantization tcq for jpeg2000 is presented in this paper the method for approximately inverting tcq in the absence of the least significant bits is improved experimental results presented using the optimal rate control algorithm and different embedded tcq formulations show that modified embedded tcq yields significant performance improvement compared to the original one in jpeg2000

equational formulas with membership constraints we propose a set of transformation rules for first order formulae whose atoms are either equations between terms or membership constraints t can be interpreted as a regular tree language is called a sort in the algebraic specification community or as a tree language in any class of languages which satisfies some adequate closure and decidability properties this set of rules is proved to be correct terminating and complete this provides a quantifier elimination procedure for every regular tree language l the first order theory of some structure defining l is decidable this extends the results of several previously published results we also show how to apply our results to automatic inductive proofs in equational theories

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

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

duality between source coding and channel coding and its extension to the side information case we explore the information theoretic duality between source coding with side information at the decoder and channel coding with side information at the encoder we begin with a mathematical characterization of the functional duality between classical source and channel coding formulating the precise conditions under which the optimal encoder for one problem is functionally identical to the optimal decoder for the other problem we then extend this functional duality to the case of coding with side information by invoking this duality we are able to generalize the result of wyner and ziv 1976 relating to no rate loss for source coding with side information from gaussian to more arbitrary distributions we consider several examples corresponding to both discrete and continuous valued cases to illustrate our formulation for the gaussian cases of coding with side information we invoke geometric arguments to provide further insights into their duality our geometric treatment inspires the construction and dual use of practical coset codes for a large class of emerging applications for coding with side information such as distributed sensor networks watermarking and information hiding communication systems

what is a good encoding of guarded choice abstract the calculus with synchronous output and mixed guarded choices is strictly more expressive than the calculus with asynchronous output and no choice this result was recently proved by c palamidessi and as a corollary she showed that there is no fully compositional encoding from the former into the latter that preserves divergence freedom and symmetries this paper argues that there are nevertheless good encodings between these calculi in detail we present a series of encodings for languages with 1 input guarded choice 2 both input and output guarded choice and 3 mixed guarded choice and investigate them with respect to compositionality and divergence freedom the first and second encoding satisfy all of the above criteria but various good candidates for the third encoding inspired by an existing distributed implementation invalidate one or the other criterion while essentially confirming palamidessi s result our study suggests that the combination of strong compositionality and divergence freedom is too strong for more practical purposes

a generic type system for the pi calculus we propose a general powerful framework of type systems for the calculus and show that we can obtain as its instances a variety of type systems guaranteeing non trivial properties like deadlock freedom and race freedom a key idea is to express types and type environments as abstract processes we can check various properties of a process by checking the corresponding properties of its type environment the framework clarifies the essence of recent complex type systems and it also enables sharing of a large amount of work such as a proof of type preservation making it easy to develop new type systems

compact quantum groups and groupoidc algebras abstract we study simple compact matrix quantum groups in the context of groupoid c algebras and obtain explicit descriptions of the structure of the c algebra of quantum su n and a concrete formula for its haar functional

jointly optimized trellis coded residual vector quantization the union of residual vector quantization rvq and trellis coded vector quantization tcvq was considered by various authors where the emphasis was on the sequential design we consider a new jointly optimized combination of rvq and tcvq with advantages in all categories necessary conditions for optimality of the jointly optimized trellis coded residual vector quantizers tcrvq are derived a constrained direct sum tree structure is introduced that facilitates rvq codebook partitioning simulation results for jointly optimized tcrvq are presented for memoryless gaussian laplacian and uniform sources the rate distortion performance is shown to be better than rvq and sequentially designed tcrvq

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

hyperspectral image compression using entropy constrained predictive trellis coded quantization a training sequence based entropy constrained predictive trellis coded quantization ecptcq scheme is presented for encoding autoregressive sources for encoding a first order gauss markov source the mean squared error mse performance of an eight state ecptcq system exceeds that of entropy constrained differential pulse code modulation ecdpcm by up to 1 0 db in addition a hyperspectral image compression system is developed which utilizes ecptcq a hyperspectral image sequence compressed at 0 125 b pixel band retains an average peak signal to noise ratio psnr of greater than 43 db over the spectral bands

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

source coding bounds using quantizer reproduction levels corresp constraining the reproduction alphabet to be of small size in encoding continuous amplitude memoryless sources has been shown to give very small degradation from the ideal performance of the rate distortion bound the optimum fixed size reproduction alphabet and its individual letter probabilities are required in order to encode the source with performance approaching that of theory these can be found through a somewhat lengthy but convergent algorithm given reasonably chosen fixed sets of reproduction letters and or their probabilities we define new rate distortion functions which are coding bounds under these alphabet constraints we calculate these functions for the gaussian and laplacian sources and the squared error distortion measure and find that performance near the rate distortion bound is achievable using a reproduction alphabet consisting of a small number of optimum quantizer levels

coset codes i introduction and geometrical classification practically all known good constructive coding techniques for bandlimited channels including lattice codes and various trellis coded modulation schemes can be characterized as coset codes a coset code is defined by a lattice partition lambda lambda and by a binary encoder c that selects a sequence of cosets of the lattice lambda the fundamental coding gain of a coset code as well as other important parameters such as the error coefficient the decoding complexity and the constellation expansion factor are purely geometric parameters determined by c lambda lambda the known types of coset codes as well as a number of new classes that systematize and generalize known codes are classified and compared in terms of these parameters

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

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

universal trellis coded quantization a new form of trellis coded quantization based on uniform quantization thresholds and on the fly quantizer training is presented the universal trellis coded quantization utcq technique requires neither stored codebooks nor a computationally intense codebook design algorithm its performance is comparable with that of fully optimized entropy constrained trellis coded quantization ectcq for most encoding rates the codebook and trellis geometry of utcq are symmetric with respect to the trellis superset this allows sources with a symmetric probability density to be encoded with a single variable rate code rate allocation and quantizer modeling procedures are given for utcq which allow access to continuous quantization rates an image coding application based on adaptive wavelet coefficient subblock classification arithmetic coding and utcq is presented the excellent performance of this coder demonstrates the efficacy of utcq we also present a simple scheme to improve the perceptual performance of utcq for certain imagery at low bit rates this scheme has the added advantage of being applied during image decoding without the need to reencode the original image

an error control scheme for transmission of vector quantization data over noisy channels this paper presents an error control scheme for transmitting vector quantized data over noisy channels first we review a self organizing feature map sofm based approach to construct the mapping from the codebook of the quantizer to the channel signal set of the communication system this approach is robust with respect to channel noise even if we do not use any error control scheme in the communication system afterwards a new trellis type quantizer namely the trellis coded kohonen 1984 map tckm is presented the design process of the tckm which is based on the neighborhood structure of sofms is simpler than that of conventional trellis coded vector quantizers tcvqs simulation results show that the performance of tckms is comparable with that of tcvqs last we introduce the error control scheme based on the concepts of the above two applications of sofms simulation results show that the proposed error control scheme is more robust with respect to channel noise the advantage of our approaches mentioned above is that the design processes of transmission systems are predefined before the construction of the codebook thus different codebooks with the same neighborhood structure can share the same design

robust source coding of images for very noisy channels robust source coding provides the compression and noise mitigation necessary for image transmission over noisy channels two methods are compared differential pulse code modulation dpcm and predictive trellis coded quantisation ptcq incorporating linear and nonlinear filters findings show that although ptcq has better rate distortion properties dpcm provides better performance in noise additionally the nonlinear filter yields better images

a lower bound on the average error of vector quantizers corresp a lower bound is proposed for the mean squared error of an n dimensional vector quantizer with a large number of output points

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

decidability of the purely existential fragment of the theory of term algebras this paper is concerned with the question of the decidability and the complexity of the decision problem for certain fragments of the theory of free term algebras the existential fragment of the theory of term algebras is shown to be decidable through the presentation of a nondeterministic algorithm which given a quantifier free formula p constructs a solution for p if it has one and indicates failure if there are no solutions it is shown that the decision problem is in np by proving that if a quantifier free formula p has a solution then there is one that can be represented as a dag in space at most cubic in the length of p the decision problem is shown to be complete for np by reducing 3 sat to that problem thus it is established that the existential fragment of the theory of pure list structures in the language of nil cons car cdr subexpression is np complete it is further shown that even a slightly more expressive fragment of the theory of term algebras the one that allows bounded universal quantifiers is undecidable

design performance and complexity analysis of residual trellis coded vector quantizers multistage trellis coded vector quantization ms tcvq is developed as a constrained trellis source coding technique the performance of the two stage tcvq is studied for gaussian sources issues of stage by stage design output alphabet selection and complexity are addressed with emphasis on selecting and partitioning the stage codebooks for a given rate ms tcvq achieves low encoding and storage complexity compared to tcvq and comparisons with same dimensional multistage vector quantization indicate a 0 5 3 db improvement in signal to quantization noise ratio

on multiterminal source code design multiterminal mt source coding refers to separate lossy encoding and joint decoding of multiple correlated sources recently the rate region of both direct and indirect mt source coding in the quadratic gaussian setup with two encoders was determined we are thus motivated to design practical mt source codes that can potentially achieve the entire rate region in this paper we present two practical mt coding schemes under the framework of slepian wolf coded quantization swcq for both direct and indirect mt problems the first asymmetric swcq scheme relies on quantization and wyner ziv coding and it is implemented via source splitting to achieve any point on the sum rate bound in the second conceptually simpler scheme symmetric swcq the two quantized sources are compressed using symmetric slepian wolf coding via a channel code partitioning technique that is capable of achieving any point on the slepian wolf sum rate bound our practical designs employ trellis coded quantization and turbo low density parity check ldpc codes for both asymmetric and symmetric slepian wolf coding simulation results show a gap of only 0 139 0 194 bit per sample away from the sum rate bound for both direct and indirect mt coding problems

sliding block and random source coding with constrained size reproduction alphabets recent research has shown that nearly optimum ratedistortion function performance can be obtained in encoding memoryless continuous amplitude sources using a constrained size reproduction alphabet in this paper we use a four letter reproduction alphabet in encoding the gaussian and laplacian sources with the squared error distortion measure we introduce a sliding block code generator decoder and perform extensive coding simulations at a rate of one bit source symbol the average distortions in those simulations are much below the optimum quantization distortion and with much smaller search intensity are about the same or lower than distortions reported previously in comparable research the slidingblock code results are also compared to those of parallel random coding simulations with the same reproduction alphabet and rate