design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

representing ontologies using description logics description graphs and rules description logics dls are a family of state of the art knowledge representation languages and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems recent experience with dls however has shown that their expressivity is often insufficient to accurately describe structured objects objects whose parts are interconnected in arbitrary rather than tree like ways dl knowledge bases describing structured objects are therefore usually underconstrained which precludes the entailment of certain consequences and causes performance problems during reasoning to address this problem we propose an extension of dl languages with description graphs a knowledge modeling construct that can accurately describe objects with parts connected in arbitrary ways furthermore to enable modeling the conditional aspects of structured objects we also extend dls with rules we present an in depth study of the computational properties of such a formalism in particular we first identify the sources of undecidability of the general unrestricted formalism based on that analysis we then investigate several restrictions of the general formalism that make reasoning decidable we present practical evidence that such a logic can be used to model nontrivial structured objects finally we present a practical decision procedure for our formalism as well as tight complexity bounds

nonequiprobable signaling on the gaussian channel signaling schemes for the gaussian channel based on finite dimensional lattices are considered the signal constellation consists of all lattice points within a region r and the shape of this region determines the average signal power spherical signal constellations minimize average signal power and in the limit as n to infinity the shape gain of the n sphere over the n cube approaches pi e 6 approximately 1 53 db a nonequiprobable signaling scheme is described that approaches this full asymptotic shape gain in any fixed dimension a signal constellation omega is partitioned into t subconstellations omega sub 0 omega sub tau 1 of equal size by scaling a basic region r signal points in the same subconstellation are used equiprobably and a shaping code selects the subconstellation omega sub i with frequency f sub i shaping codes make it possible to achieve any desired fractional bit rate the schemes presented are compared with equiprobable signaling schemes based on voronoi regions of multidimensional lattices for comparable shape gain and constellation expansion ratio the peak to average power ratio of the schemes presented is superior furthermore a simple table lookup is all that is required to address points in the constellations it is also shown that it is possible to integrate coding and nonequiprobable signaling within a common multilevel framework

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

rotated multi d constellations in rayleigh fading mutual information improvement and pragmatic approach for near capacity performance in high rate regions this paper studies the mutual information improvement attained by rotated multidimensional multi d constellations via a unitary precoder g in rayleigh fading at first based on the symmetric cut off rate of the n d signal space we develop a design criterion with regard to the precoder g it is then demonstrated that the use of rotated constellations in only a reasonably low dimensional signal space can significantly increase the mutual information in high rate regimes based on parameterizations of unitary matrices we then construct good unitary precoder g in 4 d signal space using a simple optimization problem which involves only four real variables and it is applicable to any modulation scheme to further illustrate the potential of multi d constellation and to show the practical use of mutual information improvement we propose a simple yet powerful bit interleaved coded modulation bicm scheme in which a multi d mapping technique employed in a multi d rotated constellation is concatenated with a short memory high rate convolutional code by using extrinsic information transfer exit charts it is shown that the proposed technique provides an exceptionally good error performance in particular both exit chart analysis and simulation results indicate that a turbo pinch off and a bit error rate around 10 6 happen at a signal to noise ratio that is well below the coded modulation and bicm capacities using traditional signal sets for example with code rates ranging from 2 3 to 7 8 the proposed system can operate 0 82 db 2 93 db lower than the bicm capacity with qpsk and gray labeling the mutual information gain offered by rotated constellations can be therefore utilized to design simple yet near shannon limit systems in the high rate regions

laplace transform analysis of a multiplicative asset transfer model abstract we analyze a simple asset transfer model in which the transfer amount is a fixed fraction f of the giver s wealth the model is analyzed in a new way by laplace transforming the master equation solving it analytically and numerically for the steady state distribution and exploring the solutions for various values of f 0 1 the laplace transform analysis is superior to agent based simulations as it does not depend on the number of agents enabling us to study entropy and inequality in regimes that are costly to address with simulations we demonstrate that boltzmann entropy is not a suitable e g non monotonic measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model

multi edge type low density parity check codes for bandwidth efficient modulation a method of designing low density parity check codes for bandwidth efficient high order modulation is proposed a multi edge type ldpc code ensemble is used to improve the correspondence between modulation bit channel capacity and bit level protection in a bit interleaved coded modulation system a key innovation is the development of a multi dimensional extrinsic information transfer exit vector field technique for the analysis and design of multi edge type codes a condition sufficient for the decoder to converge is derived on the multi dimensional exit vector field and this condition is used as a constraint in code optimization code designs indicate that the proposed method produces codes matching the performance of codes designed using best available methods in ensemble threshold and is capable of achieving identical finite length error rates with shorter block lengths in addition to simplified design complexity the resulting codes allow for low complexity implementation and rate adaptivity and hence are well suited for adaptive modulation systems

group codes outperform binary coset codes on nonbinary symmetric memoryless channels typical minimum distances and error exponents are analyzed on the 8 psk gaussian channel for two capacity achieving code ensembles with different algebraic structure it is proved that the typical group code over the cyclic group of order eight achieves both the gilbert varshamov bound and the expurgated error exponent on the other hand the typical binary coset codes under any labeling is shown to be bounded away both from the gilbert varshamov bound at any rate and the expurgated exponent at low rates the reason for this phenomenon is shown to rely on the symmetry structure of the 8 psk constellation which is known to match the cyclic group of order eight but not the direct product of three copies of the binary group the presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical code performance than designing codes whose algebraic structure does not match the channel this contrasts the well known fact that the average binary coset code achieves both the capacity and the random coding error exponent of any discrete memoryless channel

on achievable rates and complexity of ldpc codes over parallel channels bounds and applications a variety of communication scenarios can be modeled by a set of parallel channels upper bounds on the achievable rates under maximum likelihood ml decoding and lower bounds on the decoding complexity per iteration of ensembles of low density parity check ldpc codes are presented the communication of these codes is assumed to take place over statistically independent parallel channels where the component channels are memoryless binary input and output symmetric the bounds are applied to ensembles of punctured ldpc codes where the puncturing patterns are either random or possess some structure our discussion is concluded by a diagram showing interconnections between the new theorems and some previously reported results

on the information loss of the max log approximation in bicm systems we present a comprehensive study of the information rate loss of the max log approximation for m ary pulse amplitude modulation pam in a bit interleaved coded modulation bicm system it is widely assumed that the calculation of l values using the max log approximation leads to an information loss we prove that this assumption is correct for all m pam constellations and labelings with the exception of a symmetric 4 pam constellation labeled with a gray code we also show that for max log l values the bicm generalized mutual information gmi which is an achievable rate for a standard bicm decoder is too pessimistic in particular it is proved that the so called harmonized gmi which can be seen as the sum of bit level gmis is achievable without any modifications to the decoder we then study how bit level channel symmetrization and mixing affect the mi and the gmi for max log l values our results show that these operations which are often used when analyzing bicm systems preserve the gmi however this is not necessarily the case when the mi is considered necessary and sufficient conditions under which these operations preserve the mi are provided

bandwidth efficient modulation codes based on nonbinary irregular repeat accumulate codes using nonbinary low density parity check ldpc codes with random coset mapping bennatan and burshtein constructed bandwidth efficient modulation codes with remarkable performance under belief propagation bp decoding however due to the random nature of ldpc codes most of the good ldpc codes found in the literature do not have a simple encoding structure thus the encoding complexity of those ldpc codes can be as high as o n 2 where n is the codeword length to reduce the encoding complexity in this paper nonbinary irregular repeat accumulate ira codes with time varying characteristic and random coset mapping are proposed for bandwidth efficient modulation schemes the time varying characteristic and random coset mapping result in both permutation invariance and symmetry properties respectively in the densities of decoder messages the permutation invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using gaussian distributions under the gaussian approximation extrinsic information transfer exit charts for nonbinary ira codes are developed and several codes of different spectral efficiencies are designed based on exit charts in addition by proper selection of nonuniform signal constellations the constructed codes are inherently capable of obtaining shaping gains even without separate shaping codes simulation results indicate that the proposed codes not only have simple encoding schemes but also have remarkable performance that is even better than that constructed using nonbinary ldpc codes

a computationally efficient multilevel coding scheme for isi channels this paper proposes a multilevel coding scheme with linear mapping for intersymbol interference isi channels and derives a low complexity receiver structure that can achieve the isi channel capacity the transmitter superimposes many layers of independent binary antipodal streams to generate a quadrature amplitude modulation qam or gaussian like channel input the receiver performs multistage decoding with decision feedback and interference cancellation within each stage is a linear minimum mean square error mmse equalizer followed by an error correcting decoder the complexity scales linearly with the channel length and the number of layers and the process is shown to be asymptotically information lossless if a fixed input power is properly distributed over a sufficiently large number of layers this framework is then extended to achieve the capacity of the isi channel using a transmitter side spectral shaping filter that converts a gaussian input sequence with a white spectrum to one with a water filling spectrum

optimization of ldpc codes for modulation and detection in layered multi antenna architectures in this paper we first perform the density evolution of ldpc codes in layered multi antenna architectures using bit interleaved coded modulation and detection based on successive decoding and interference cancellation the noise thresholds of ldpc codes are shown to be achieved within 1 2 db of the capacity for these architectures we then present a rate allocation method which optimizes the performance of a layered architecture and find good degree distributions for ldpc codes with the rates allocated by our method simulation results show that the performance for an optimized layered architecture is better by 4 db than that for the layered architecture using ldpc codes with the same rate in all layers

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

reliability based coded modulation with low density parity check codes in this letter we consider the interleaver design in bit interleaved coded modulation bicm with low density parity check ldpc codes the design paradigm is to provide more coding protection through iterative decoding to bits that are less protected by modulation and are thus less reliable at the output of the demodulator the design is carried out by an ad hoc search algorithm over the column permutations of the parity check matrix our simulations show that the proposed reliability based coded modulation scheme can improve the error rate performance of conventional bicm schemes based on regular ldpc codes by a few tenths of a decibel with no added complexity

density evolution for nonbinary ldpc codes under gaussian approximation this paper extends the work on density evolution for binary low density parity check ldpc codes with gaussian approximation to ldpc codes over gf q we first generalize the definition of channel symmetry for nonbinary inputs to include q ary phase shift keying psk modulated channels for prime q and binary modulated channels for q that is a power of 2 for the well defined q ary input symmetric output channel we prove that under the gaussian assumption the density distribution for messages undergoing decoding is fully characterized by q 1 quantities assuming uniform edge weights we further show that the density of messages computed by the check node decoder cnd is fully defined by a single number we then present the approximate density evolution for regular and irregular ldpc codes and show that the q 1 dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q 2p through application of approximate density evolution and linear programming we optimize the degree distribution of ldpc codes over gf 3 and gf 4 the optimized irregular ldpc codes demonstrate performance close to the shannon capacity for long codewords we also design gf q codes for high order modulation by using the idea of a channel adapter we find that codes designed in this fashion outperform those optimized specifically for the binary additive white gaussian noise awgn channel for a short codewords and a spectral efficiency of 2 bits per channel use b cu

ldpc code design considerations for non uniform channels irregular low density parity check ldpc code design for parallel sub channels with different qualities is investigated such channels appear in many communication systems e g orthogonal frequency division multiplexing systems when channel knowledge is available at both the transmitter and receiver following the literature we consider allotted ldpc codes which carefully assign different parts of the code to sub channels to reduce the number of design parameters and allow for efficient design semi regular allotted codes have been suggested we first formulate the design of semi regular codes as a mixed integer linear programming relaxing the semi regularity constraint broadens the search space which results in improved codes and also a more efficient design via linear programming while information theoretic results suggest that having channel state information for a fixed power assignment does not change the capacity we show that under non optimal decoding or when the maximum degree allowed in the code is small allotted codes significantly outperform conventional ones finally for the case that neither side has the channel knowledge thus capacity loss is inevitable we see that the reduced capacity can still be approached by ldpc codes

implementing the han kobayashi scheme using low density parity check codes over gaussian interference channels we focus on gaussian interference channels gics and study the han kobayashi coding strategy for the two user case with the objective of designing implementable explicit channel codes specifically low density parity check codes are adopted for use over the channel their benefits are studied and suitable codes are designed iterative joint decoding is used at the receivers where independent and identically distributed channel adapters are used to prove that log likelihood ratios exchanged among the nodes of the tanner graph enjoy symmetry when bpsk or qpsk with gray coding is employed this property is exploited in the proposed code optimization algorithm adopting a random perturbation technique code optimization and convergence threshold computations are carried out for different gics employing finite constellations by tracking the average mutual information furthermore stability conditions for the admissible degree distributions under strong and weak interference levels are determined via examples it is observed that the optimized codes using bpsk or qpsk with gray coding operate close to the capacity boundary for strong interference for the case of weak interference it is shown that nontrivial rate pairs are achievable via the newly designed codes which are not possible by single user codes with time sharing performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions where for one instance the results are compared with those of some structured designs

rotational invariance of trellis codes ii group codes and decoders for pt i see ibid vol 42 no 3 p 751 65 1996 in part i general results on rotationally invariant codes and encoders were derived assuming no algebraic structure in part ii trellis codes based on group systems are considered as a special case for which code and encoder constructions are particularly simple rotational invariance is expressed as an algebraic constraint on a group code and algebraic constructions are found for both absorbed precoder encoders and for encoders with separate differential precoders finally the various encoder forms used to achieve rotational invariance are compared based on their performance on an awgn channel

on the capacity of the gaussian channel with a finite number of input levels an analytic confirmation of an observation made by g ungerboeck 1965 that approximately optimal performance on a gaussian channel with capacity c can be obtained with about 2 sup c 1 levels is given in particular the results imply that by using about 2 sup c 1 levels a rate of nearly c 1 bit can be achieved and that by using 2 sup c 1 levels a rate of about c 0 4 bits can be achieved

multilevel codes theoretical concepts and practical design rules this paper deals with 2 sup l ary transmission using multilevel coding mlc and multistage decoding msd the known result that mlc and msd suffice to approach capacity if the rates at each level are appropriately chosen is reviewed using multiuser information theory it is shown that there is a large space of rate combinations such that mlc and full maximum likelihood decoding mld can approach capacity it is noted that multilevel codes designed according to the traditional balanced distance rule tend to fall in the latter category and therefore require the huge complexity of mld the capacity rule the balanced distances rules and two other rules based on the random coding exponent and cutoff rate are compared and contrasted for practical design simulation results using multilevel binary turbo codes show that capacity can in fact be closely approached at high bandwidth efficiencies moreover topics relevant in practical applications such as signal set labeling dimensionality of the constituent constellation and hard decision decoding are emphasized bit interleaved coded modulation proposed by caire et al see ibid vol 44 p 927 46 1998 is reviewed in the context of mlc finally the combination of signal shaping and coding is discussed significant shaping gains are achievable in practice only if these design rules are taken into account

a simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials in this paper a numerical multiscale method is proposed for computing the response of structures made of linearly non aging viscoelastic and highly heterogeneous materials in contrast with most of the approaches reported in the literature the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro scales the macroscopic constitutive law takes the form of a convolution integral containing an effective relaxation tensor to numerically identify this tensor a representative volume element rve for the microstructure is first chosen relaxation tests are then numerically performed on the rve correspondingly the components of the effective relaxation tensor are determined and stored for different snapshots in time at the macroscopic scale a continuous representation of the effective relaxation tensor is obtained in the time domain by interpolating the data with the help of spline functions the convolution integral characterizing the time dependent macroscopic stress strain relation is evaluated numerically arbitrary local linear viscoelastic laws and microstructure morphologies can be dealt with implicit algorithms are provided to compute the time dependent response of a structure at the macroscopic scale by the finite element method accuracy and efficiency of the proposed approach are demonstrated through 2d and 3d numerical examples and applied to estimate the creep of structures made of concrete

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

a robust multi level design for dirty paper coding we propose a robust close to capacity dirty paper coding dpc design framework in which multi level low density parity check ldpc codes and trellis coded quantization tcq are employed as the channel and source coding components respectively the proposed design framework is robust in the sense that it yields close to capacity solutions in the high medium and low rate regimes this is in contrast to existing practical dpc schemes that perform well only in one or two of these regimes but not all three we design codes for transmission rates of 0 5 1 0 1 5 and 2 0 bits sample b s using one two three and four ldpc levels at a block length of 2 105 the codes perform 0 95 0 58 0 55 and 0 54 db from the corresponding information theoretic limits respectively we also propose a low complexity decoding scheme that does not involve iterative message passing between the source and channel decoders the low complexity scheme performs only 1 08 0 85 and 0 79 db away from the theoretical limits at transmission rates of 1 0 1 5 and 2 0 b s respectively

on optimal shaping of multidimensional constellations a scheme for the optimal shaping of multidimensional constellations is proposed this scheme is motivated by a type of structured vector quantizer for memoryless sources and results in n sphere shaping of n dimensional cubic lattice based constellations because n sphere shaping is optimal in n dimensions shaping gains higher than those of n dimensional voronoi constellations can be realized while optimal shaping for a large n can realize most of the 1 53 db total shaping gain it has the undesirable effect of increasing the size and the peak to average power ratio of the constituent 2d constellation this limits its usefulness for many real world channels which have nonlinearities the proposed scheme alleviates this problem by achieving optimal constellation shapes for a given limit on the constellation expansion ratio or the peak to average power ratio of the constituent 2d constellation results of calderbank and ozarow 1990 on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain comparisons with forney s 1989 trellis shaping scheme are also provided

approaching v blast capacity with adaptive modulation and ldpc encoding this paper presents a practical implementation of the vertical bell laboratories layered space time v blast type system in which the multiple input multiple output mimo open loop capacity can be approached with conventional scalar coding using adaptive modulation with appropriate channel codes e g low density parity check ldpc codes and optimum successive detection osd the density evolution technique is employed to determine the maximal achievable rate of an ldpc code for each transmit antenna for a given channel realization at a given signal to noise ratio numerical results will show that the average sum rate of the adaptively modulated ldpc encoded system is quite close to the v blast capacity with both rate and power adaptations considering the performance degradation caused by error propagation due to the imperfect feedback and relatively long decoding delay in the osd we use parallel interference cancellation followed by minimum mean square error filtering in the bit error rate ber performance simulation simulation results will show that a target ber of 10 5 can be achieved by the optimally designed ldpc codes to simplify the code design we replace the ldpc codes optimally designed for each channel realization with rate compatible punctured ldpc codes at the cost of a slight sum rate loss if the fading process is nonergodic the outage capacity corresponding to a given outage probability is used to measure the channel performance as an example we design the ldpc codes for an adaptively modulated 2times2 v blast system to approach its outage capacity for a given outage probability

reasoning within expressive fuzzy rough description logics it is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge based applications description logics dls are suitable well known logics for managing structured knowledge that have gained considerable attention the last decade the current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in dls are analyzed in this paper an integration between the theories of fuzzy dls and rough dls has been attempted by providing fuzzy rough dls based on fuzzy rough set theory the syntax semantics and properties of fuzzy rough dls are given it is proved that the satisfiability subsumption entailment and abox consistency reasoning in fuzzy rough dls may be reduced to the abox consistency reasoning in the corresponding fuzzy dls

computing the minimum distance of nonbinary ldpc codes finding the minimum distance of low density parity check ldpc codes is an np hard problem different from all existing works that focus on binary ldpc codes we in this paper aim to compute the minimum distance of nonbinary ldpc codes motivated by the fact that operating in a large galois field provides one important degree of freedom to achieve both good waterfall and error floor performance our method is based on the existing nearest nonzero codeword search nncs method but several modifications are incorporated for nonbinary ldpc codes including the modified error impulse pattern the dithering method and the nonbinary decoder numerical results on the estimated minimum distances show that a code s minimum distance can be increased by careful selection of nonzero elements of the parity check matrix or by increasing the mean column weight or by increasing the size of the galois field these results support observations that have been made based on simulated performance in the literature finally we provide an upper bound on the minimum distance for nonbinary quasi cyclic ldpc codes

comparison of different numerical laplace inversion methods for engineering applications abstract laplace transform is a powerful method for enabling solving differential equation in engineering and science using the laplace transform for solving differential equations however sometimes leads to solutions in the laplace domain that are not readily invertible to the real domain by analytical means numerical inversion methods are then used to convert the obtained solution from the laplace domain into the real domain four inversion methods are evaluated in this paper several test functions which arise in engineering applications are used to evaluate the inversion methods we also show that each of the inversion methods is accurate for a particular case this study shows that among all these methods the fourier transform inversion technique is the most powerful but also the most computationally expensive stehfest s method which is used in many engineering applications is easy to implement and leads to accurate results for many problems including diffusion dominated ones and solutions that behave like e t type functions however this method fails to predict e t type functions or those with an oscillatory response such as sine and wave functions

optimal nonuniform signaling for gaussian channels variable rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied when the criterion is one of minimizing the average transmitted energy for a given average bit rate the best possible distribution with which to select constellations points is a maxwell boltzmann distribution in principle when constellation points are selected according to a maxwell boltzmann distribution the ultimate shaping gain pi e 6 or 1 53 db can be achieved in any dimension nonuniform signaling schemes can be designed by mapping simple variable length prefix codes onto the constellation using the huffman procedure prefix codes can be designed that approach the optimal performance these schemes provide a fixed rate primary channel and a variable rate secondary channel and are easily incorporated into standard lattice type coded modulation schemes

efficient llr calculation for non binary modulations over fading channels log likelihood ratio llr computation for non binary modulations over fading channels is complicated a measure of llr accuracy on asymmetric binary channels is introduced to facilitate good llr approximations for non binary modulations considering piecewise linear llr approximations we prove convexity of optimizing the coefficients according to this measure for the optimized approximate llrs we report negligible performance loss compared to true llrs

low complexity coded modulation for isi constrained channels we propose a low complexity pam based transmission scheme that is well suited for channels constrained by inter symbol interference isi and colored gaussian noise the scheme consists of coset codes constructed on multi dimensional lattices with a combination of low density parity check ldpc codes and classical reed solomon rs codes to approach the capacity of an isi constrained channel the code is easy to employ in conjunction with spectral shaping tomlinson harashima precoding and decision feedback equalization dfe the scheme performs within 2 2 5 db of un shaped channel capacity the sphere bound at very low ber s even with regular ldpc codes of modest block lengths we investigate dense multidimensional lattices such as the schlafli gosset barnes wall and leech lattices besides simple one dimensional lattices via the density evolution technique we show that the lattices reduce the noise threshold of belief propagation decoders we investigate the practical application of the proposed schemes to 10g base t an emerging ethernet standard over twisted pairs at 10 gbit sec a simple 1 dimensional scheme improves upon recent proposals by 0 5 1 db at ber s approaching 10 11 with half the ldpc coding complexity multi dimensional schemes are seen to reduce the complexity further

bit interleaved coded modulation with mismatched decoding metrics bit interleaved coded modulation bicm has become the de facto coding standard for communication systems recently bicm has been cast as a mismatched decoding scheme due to the assumption of independent bit metrics in addition to this inherent mismatch practical demodulators may produce mismatched decoding metrics because of implementation constraints such as clipping and metric approximation to reduce computational complexity in this paper we investigate bicm with such metrics in line with recent works on this topic we adopt the generalized mutual information gmi as the pertinent performance measure first we show that level dependent scaling of logarithmic bit metrics can improve the bicm gmi second we propose a uniform metric scaling which can lead to an improved performance of mismatched sum product symbol by symbol decoding even if the gmi is not changed third we investigate general metric mismatch correction methods and analyze their effects in terms of the gmi by means of three application examples we illustrate that metric mismatch correction including metric scaling can significantly increase bicm rates

conditions for 90 degrees phase invariant block coded qam based on v a zinoviev s 1981 generalized concatenated codes conditions for the construction of 90 degrees phase invariant qam are derived furthermore a proposal for the necessary differential encoding decoding is made the conditions for phase invariance are specialized for the case of reed muller codes as outer codes of the generalized concatenation

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

design and analysis of nonbinary ldpc codes for arbitrary discrete memoryless channels we present an analysis under the iterative decoding of coset low density parity check ldpc codes over gf q designed for use over arbitrary discrete memoryless channels particularly nonbinary and asymmetric channels we use a random coset analysis to produce an effect that is similar to output symmetry with binary channels we show that the random selection of the nonzero elements of the gf q parity check matrix induces a permutation invariance property on the densities of the decoder messages which simplifies their analysis and approximation we generalize several properties including symmetry and stability from the analysis of binary ldpc codes we show that under a gaussian approximation the entire q 1 dimensional distribution of the vector messages is described by a single scalar parameter like the distributions of binary ldpc messages we apply this property to develop extrinsic information transfer exit charts for our codes we use appropriately designed signal constellations to obtain substantial shaping gains simulation results indicate that our codes outperform multilevel codes at short block lengths we also present simulation results for the additive white gaussian noise awgn channel including results within 0 56 db of the unrestricted shannon limit i e not restricted to any signal constellation at a spectral efficiency of 6 bits s hz

on the error probability of signals in additive white gaussian noise a new upper bound to the probability of error in detecting one of m equally probable signals in additive white gaussian noise is presented this bound is easy to calculate can be applied to any signal set it is always better than the union and minimum distance bounds examples demonstrate the use of the bound

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

block coded modulation optimized for finite error rate on the white gaussian noise channel this correspondence examines the performance of block coded modulation bcm at finite decoded bit error rates ber we consider the optimum geometric structure to optimize coding gain at finite ber rather than asymptotic coding gain we introduce the concept of the row ber and show that this structure may be implemented by a bcm scheme in which the row bit error rates are equalized we present a design procedure for such schemes and show that significant improvements over conventional schemes are possible

on punctured trellis coded modulation punctured convolutional codes result in some savings in the complexity of viterbi decoders compared to other codes of the same rate however in general use of the punctured structure in the decoder results in a performance loss for trellis codes due to difficulties in assigning metrics we provide constructions for punctured rate 2 3 codes based on decomposition of the metric into orthogonal components these show no loss in performance for trellis coded qam and psk we also provide 180 spl deg and 90 spl deg rotationally invariant punctured tcm for qam signaling

computing upper bounds to error probability of coded modulation schemes to evaluate an upper bound on error probabilities of signal constellations used for transmission over the additive white gaussian noise awgn channel enumeration of all the constellation intradistances is required these may be infinite in number for example when convolutional codes are used and the constellations are lattices truncation of the series does not necessarily provide a bound anymore and must be done with care yet the union bound is very simple as it does not require any further knowledge about the signal constellation than the distance enumerator in this paper we describe some methods that can be used to evaluate error probabilities of infinite signal constellations and that require only a finite number of terms these methods are applicable for example to convolutional codes decoded with a finite depth viterbi algorithm and to signal constellations carved from lattices coded modulations based on lattices and convolutional or block codes can also be dealt with as an example of application we analyze a variable rate 3 stage coded modulation encoder decoder which has been built and is based on a combination of convolutional codes with a single parity check block code

adaptive modulation and coding schemes based on ldpc codes with irregular modulation in this paper we propose an adaptive modulation and coding amc scheme which uses only a single low density parity check ldpc encoder decoder with irregular modulation two gray mapped quadrature amplitude modulations are employed within a codeword so that the transmission rates of the proposed amc can be controlled even though the rate of the employed ldpc code is fixed the rate and degree distribution of the employed ldpc code are selected properly for the proposed scheme we also optimize the bit to symbol mapping for the ldpc code over irregular modulation at each transmission rate the performance of the proposed scheme is compared with that of the amc scheme with a dedicated ldpc code at each transmission rate numerical results show that the proposed scheme has a performance comparable to that of the amc scheme with dedicated ldpc codes

trellis coding with multidimensional qam signal sets trellis coding using multidimensional quadrature amplitude modulation qam signal sets is investigated finite size 2d signal sets are presented that have minimum average energy are 90 degrees rotationally symmetric and have from 16 to 1024 points the best trellis codes using the finite 16 qam signal set with two four six and eight dimensions are found by computer search the multidimensional multi d signal set is constructed from the 2 d signal set the best moderate complexity trellis codes for infinite lattices with two four six and eight dimensions are also found the minimum free squared euclidean distance and number of nearest neighbors for these codes were used as the selection criteria many of the multi d codes are fully rotationally invariant and give asymptotic coding gains up to 6 0 db from the infinite lattice codes the best codes for transmitting j j 1 4 j 1 3 j 1 2 j 2 3 and j 3 4 b sym j an integer are presented

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

answering regular path queries in expressive description logics via alternating tree automata expressive description logics dls have been advocated as formalisms for modeling the domain of interest in various application areas including the semantic web data and information integration peer to peer data management and ontology based data access an important requirement there is the ability to answer complex queries beyond instance retrieval taking into account constraints expressed in a knowledge base we consider this task for positive 2 way regular path queries p2rpqs over knowledge bases in the expressive dl ziq p2rpqs are more general than conjunctive queries union of conjunctive queries and regular path queries from the literature they allow regular expressions over roles and data joins that require inverse paths the dl ziq extends the core dl alc with qualified number restrictions inverse roles safe boolean role expressions regular expressions over roles and concepts of the form s self in the style of the dl sriq using techniques based on two way tree automata we first provide as a stepping stone an elegant characterization of tbox and abox satisfiability testing which gives us a tight exptime bound for this problem under unary number encoding we then establish a double exponential upper bound for answering p2rpqs over ziq knowledge bases this bound is tight our result significantly pushes the frontier of 2exptime decidability of query answering in expressive dls both with respect to the query language and the considered dl furthermore by reducing the well known dl sriq to ziq with an exponential blow up in the size of the knowledge base we also provide a tight 2exptime upper bound for knowledge base satisfiability in sriq and establish the decidability of query answering for this significant fragment of the new owl 2 standard

invariance properties of binary linear codes over a memoryless channel with discrete input this work studies certain properties of the probability density function pdf of the bit log likelihood ratio llr for binary linear block codes over a memoryless channel with discrete input and discrete or continuous output we prove that under a set of mild conditions the pdf of the bit llr of a specific bit position is independent of the transmitted codeword it is also shown that the pdf of a given bit llr when the corresponding bit takes the values of zero and one are symmetric with respect to each other reflection of one another with respect to the vertical axis for the case of channels with binary input a sufficient condition for two bit positions to have the same pdf is presented

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

baseband trellis codes with a spectral null at zero a method is described for modifying classical n dimensional trellis codes to provide baseband codes that combine a spectral null at dc with significant coding gain the information rate of the classical code is decreased by one bit and this extra redundancy is used to keep the running digital sum bounded equivalently if the rate is held constant then twice as many signal points are needed causing a power penalty of 6 n db baseband trellis codes are presented for several information rates together with complete spectral plots and performance comparisons a method of constructing baseband codes with multiple spectral nulls is also described

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

low density lattice codes low density lattice codes ldlc are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white gaussian noise awgn channel in ldlc a codeword x is generated directly at the n dimensional euclidean space as a linear transformation of a corresponding integer message vector b i e x gb 1 where h g 1 is restricted to be sparse the fact that h is sparse is utilized to develop a linear time iterative decoding scheme which attains as demonstrated by simulations good error performance within 0 5 db from capacity at block length of n 100 000 symbols the paper also discusses convergence results and implementation considerations

llr approximation for wireless channels based on taylor series and its application to bicm with ldpc codes a new approach for the approximation of the channel log likelihood ratio llr for wireless channels based on taylor series is proposed the approximation is applied to uncorrelated flat fading channels with unknown channel state information at the receiver it is shown that the proposed approximation greatly simplifies the calculation of channel llrs and yet provides results almost identical to those based on the exact calculation of channel llrs the results are obtained in the context of bit interleaved coded modulation bicm schemes with low density parity check ldpc codes and include threshold calculations and error rate performance of finite length codes compared to the existing approximations the proposed method is either significantly less complex or considerably more accurate

density evolution for asymmetric memoryless channels density evolution de is one of the most powerful analytical tools for low density parity check ldpc codes and graph codes with message passing decoding algorithms with channel symmetry as one of its fundamental assumptions density evolution has been widely and successfully applied to different channels including binary erasure channels becs binary symmetric channels bscs binary additive white gaussian noise biawgn channels etc this paper generalizes density evolution for asymmetric memoryless channels which in turn broadens the applications to general memoryless channels e g z channels composite white gaussian noise channels etc the central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree a new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed several properties of the new density evolution method are explored including stability results for general asymmetric memoryless channels simulations code optimizations and possible new applications suggested by this new density evolution method are also provided this result is also used to prove the typicality of linear ldpc codes among the coset code ensemble when the minimum check node degree is sufficiently large it is shown that the convergence to perfect projection is essential to the belief propagation bp algorithm even when only symmetric channels are considered hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels

binary intersymbol interference channels gallager codes density evolution and code performance bounds we study the limits of performance of gallager codes low density parity check ldpc codes over binary linear intersymbol interference isi channels with additive white gaussian noise awgn using the graph representations of the channel the code and the sum product message passing detector decoder we prove two error concentration theorems our proofs expand on previous work by handling complications introduced by the channel memory we circumvent these problems by considering not just linear gallager codes but also their cosets and by distinguishing between different types of message flow neighborhoods depending on the actual transmitted symbols we compute the noise tolerance threshold using a suitably developed density evolution algorithm and verify by simulation that the thresholds represent accurate predictions of the performance of the iterative sum product algorithm for finite but large block lengths we also demonstrate that for high rates the thresholds are very close to the theoretical limit of performance for gallager codes over isi channels if c denotes the capacity of a binary isi channel and if c sub i i d denotes the maximal achievable mutual information rate when the channel inputs are independent and identically distributed i i d binary random variables c sub i i d spl les c we prove that the maximum information rate achievable by the sum product decoder of a gallager coset code is upper bounded by c sub i i d the last topic investigated is the performance limit of the decoder if the trellis portion of the sum product algorithm is executed only once this demonstrates the potential for trading off the computational requirements and the performance of the decoder

design of multi input multi output systems based on low density parity check codes we design serial concatenated multi input multi output systems based on low density parity check ldpc codes we employ a receiver structure combining the demapper detector and the decoder in an iterative fashion we consider the a posteriori probability app demapper as well as a suboptimal demapper incorporating interference cancellation with linear filtering extrinsic information transfer exit chart analysis is applied to study the convergence behavior of the proposed schemes we show that exit charts match very well with the simulated decoding trajectories and they help explain the impact of different mappings and different demappers it is observed that if the app demapper transfer characteristics are almost flat the ldpc codes optimized for binary input channels are good enough to achieve performance close to the channel capacity we also present a simple code optimization method based on exit chart analysis and we design a rate 1 2 ldpc code that achieves very low bit error rates within 0 15 db of the capacity of a two input two output rayleigh fading channel with 4 pulse amplitude modulation we next propose to use a space time block code as an inner code of our serial concatenated coding scheme by means of a simple example scheme using an alamouti inner code we demonstrate that the design optimization of the outer code e g ldpc code is greatly simplified

decidability of shiq with complex role inclusion axioms motivated by medical terminology applications we investigate the decidability of an expressive and prominent description logic dl shiq extended with role inclusion axioms of the form r s t it is well known that a naive such extension leads to undecidability and thus we restrict our attention to axioms of the form r s r or s r r which is the most important form of axioms in the applications that motivated this extension surprisingly this extension is still undecidable however it turns out that by restricting our attention further to acyclic sets of such axioms we regain decidability we present a tableau based decision procedure for this dl and report on its implementation which promises to behave well in practice and provides important additional functionality in a medical terminology application

determining and approaching achievable rates of binary intersymbol interference channels using multistage decoding by examining the achievable rates of a multistage decoding system on stationary ergodic channels we derive lower bounds on the mutual information rate corresponding to independent and uniformly distributed i u d inputs also referred to as the i u d information rate for binary intersymbol interference isi channels we show that these bounds become tight as the number of decoding stages increases our analysis which focuses on the marginal conditional output densities at each stage of decoding provides an information rate corresponding to each stage these rates underlie the design of multilevel coding schemes based upon low density parity check ldpc codes and message passing that in combination with multistage decoding approach the i u d information rate for binary isi channels we give example constructions for channel models that have been commonly used in magnetic recording these examples demonstrate that the technique is very effective even for a small number of decoding stages

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

trellis coded multidimensional phase modulation a 2l dimensional multiple phase shift keyed l mpsk signal set is obtained by forming the cartesian product of l two dimensional mpsk signal sets a systematic approach to partitioning l mpsk signal sets that is based on block coding is used an encoder system approach is developed it incorporates the design of a differential precoder a systematic convolutional encoder and a signal set mapper trellis coded l 4psk l 8psk and l 16psk modulation schemes are found for 1

capacity approaching bandwidth efficient coded modulation schemes based on low density parity check codes we design multilevel coding mlc and bit interleaved coded modulation bicm schemes based on low density parity check ldpc codes the analysis and optimization of the ldpc component codes for the mlc and bicm schemes are complicated because in general the equivalent binary input component channels are not necessarily symmetric to overcome this obstacle we deploy two different approaches one based on independent and identically distributed i i d channel adapters and the other based on coset codes by incorporating i i d channel adapters we can force the symmetry of each binary input component channel by considering coset codes we extend the concentration theorem based on previous work by richardson et al see ibid vol 47 p 599 618 feb 2001 and kavc spl caron ic spl acute et al see ibid vol 49 p 1636 52 july 2003 we also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior next we jointly optimize the code rates and degree distribution pairs of the ldpc component codes for the mlc scheme the optimized irregular ldpc codes at each level of mlc with multistage decoding msd are able to perform well at signal to noise ratios snr very close to the capacity of the additive white gaussian noise awgn channel we also show that the optimized bicm scheme can approach the parallel independent decoding pid capacity as closely as does the mlc pid scheme simulations with very large codeword length verify the accuracy of the analytical results finally we compare the simulated performance of these coded modulation schemes at finite codeword lengths and consider the results from the perspective of a random coding exponent analysis

design of low density parity check codes for modulation and detection a coding and modulation technique is studied where the coded bits of an irregular low density parity check ldpc code are passed directly to a modulator at the receiver the variable nodes of the ldpc decoder graph are connected to detector nodes and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder the code is optimized by performing a curve fitting on extrinsic information transfer charts design examples are given for additive white gaussian noise channels as well as multiple input multiple output mimo fading channels where the receiver but not the transmitter knows the channel for the mimo channels the technique operates within 1 25 db of capacity for various antenna configurations and thereby outperforms a scheme employing a parallel concatenated turbo code by wide margins when there are more transmit than receive antennas

numerical inversion of a laplace transform solution of a diffusion equation with a mixed derivative term we consider a diffusion equation with a mixed derivative term modelling the transient flow of a second grade fluid the same diffusion equation with a mixed derivative term also comes up in the modelling of heat conduction in which the history of the temperature gradient is included the equations differ in the sign of the coefficient of the mixed derivative term we show that the method of lines solution is stable for the transient flow of a second grade fluid and unstable for heat conduction with the temperature gradient history included a laplace transform solution for the heat conduction case is then investigated the laplace transform solution is inverted numerically using a fourier based method a stable solution is obtained the solutions are compared and discussed

attributive concept descriptions with complements abstract we investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages it is shown that deciding coherence and subsumption of such descriptions are pspace complete problems that can be decided with linear space

techniques of bounding the probability of decoding error for block coded modulation structures two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented the first bound which is applicable to the additive white gaussian noise awgn channel is tighter than the well known union bound and the minimum distance bound especially for low signal to noise ratio it is shown that for the leech lattice this upper bound is very close to a sphere lower bound for the second upper bound which is applicable to any memoryless channel not necessarily awgn a method of random coset coding is presented for the awgn channel a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code which is required for the computation of the first upper bound

design of bandwidth efficient unequal error protection ldpc codes this paper presents a strategy for the design of bandwidth efficient ldpc codes with unequal error protection bandwidth efficiency is obtained by appropriately designing the codes for higher order constellations assuming an awgn channel the irregularities of the ldpc code are designed using the gaussian approximation of the density evolution to enhance the unequal error protection property of the code as well as account for the different bit error probabilities given by the higher order constellation the proposed code design algorithm is flexible in terms of the number and proportions of protection classes it also allows arbitrary modulation schemes our method combines the design of unequal error protection ldpc codes for the binary input awgn channel with the code design for higher order constellations by dividing the variable node degree distribution into sub degree distributions for each protection class and each level of protection from the modulation the results show that appropriate code design for higher order constellations reduces the overall bit error rate significantly furthermore the unequal error protection capability of the code is increased especially for high snr