a novel method for solving the inverse scattering problem for time harmonic acoustic waves in the resonance region ii in a previous paper siam j appl math 1985 pp 1039 1053 we presented a new method for determining the shape of an acoustically soft obstacle from a knowledge of the time harmonic incident wave and the far field pattern of the scattered wave the method given there was based on knowing the far field pattern for an interval of values of the square of the wave number k such that this interval contained the first eigenvalue lambda 1 of the interior dirichlet problem the purpose of this paper is to extend the methods of our earlier paper to treat the case when the far field pattern is only known for a single value of the wave number such that k 2 is not equal to lambda 1 in addition we show how to combine the results of this paper with the first to obtain a method that is valid for any fixed value of k independent of whether or not k 2 is an eigenvalue we also extend our analysis to include the case of the impedance boundary value problem numerical examples are given showing the pra

an inversion algorithm in two dimensional elasticity abstract in this paper scattering problems for the rigid body and the cavity in two dimensional linear elasticity are considered in each case the corresponding far field scattering amplitudes are presented and the herglotz condition and herglotz wavefunctions are introduced a pair of integral equations are constructed in the far field region the properties of the herglotz functions are used to derive solvability conditions and to built approximate far field equations a method for solving inverse scattering problems is proposed and the support of the scattering obstacle is found by noting the unboundedness of the l2 norm of the herglotz densities as an interior point approaches the boundary of the scattering object from inside the scatterer illustration of the unboundedness property on the boundary is carried out for rigid circular cylinders and cavities numerical results for rigid bodies are also given showing the applicability of this method

a fast encoding method for lattice codes and quantizers in an earlier paper the authors described a very fast method which for the root lattices a n d n e n their duals and certain other lattices finds the closest lattice point to an arbitrary point of the underlying space if the lattices are used as codes for a gaussian channel the algorithm provides a fast decoding procedure or if they are used as vector quantizers the algorithm performs the analog to digital conversion efficiently the present paper offers a solution to the inverse problem for the same lattices the encoding problem for channel codes or the digital to analog part of quantizing namely given an integer k to find the kth code vector and to the closely related problem of finding the index k of a given code vector

signal space characterization of iterative decoding by tracing the flow of computations in the iterative decoders for low density parity check codes we formulate a signal space view for a finite number of iterations in a finite length code on a gaussian channel maximum a posteriori map codeword decoding or maximum likelihood decoding decodes to the codeword signal that is closest to the channel output in euclidean distance in contrast we show that iterative decoding decodes to the pseudosignal that has highest correlation with the channel output the set of pseudosignals corresponds to pseudocodewords only a vanishingly small number of which correspond to codewords we show that some pseudocodewords cause decoding errors but that there are also pseudocodewords that frequently correct the deleterious effects of other pseudocodewords

a useful lemma for capacity analysis of fading interference channels this paper presents a simple new expression for the exact evaluation of averages of the form e ln 1 x1 xn y1 ym 1 where x1 xn y1 ym are arbitrary non negative random variables in terms of the joint moment generating functions of these random variables application examples are given for the ergodic capacity evaluation of some multiuser wireless communication systems which are difficult to solve by the known classical methods

tables of sphere packings and spherical codes the theta function of a sphere packing gives the number of centers at each distance from the origin the theta functions of a number of important packings a n d n e n the leech lattice and others and tables of the first fifty or so of their coefficients are given in this paper

channel coding with quadrature quadrature phase shift keying q sup 2 psk signals channel coding due to trellis modulation has been proved to be useful for bandlimited channels however these modulations mostly designed with n use of 2d signals are primarily aimed at coding gain only it is pointed out that utilization of all available signal dimensions which is limited by the time bandwidth product may improve the bandwidth efficiency and simultaneously bring an additional coding gain trellis coding with a spectrally efficient 4d signal set based on q sup 2 psk is addressed without any expansion of the q sup 2 psk signal set a simple hand designed 16 state trellis code provides a coding gain of 6 02 db with the same number of states in g ungergoeck s 1982 8 psk trellis the gain is 4 1 db in low intersymbol interference situations the bandwidth efficiency of this coded q sup 2 psk is twice that of coded 8 psk if both operate at 2 b s hz and p sub b e 10 sup 5 the coded q sup 2 psk provides a saving of about 4 db over the coded 8 psk some fully connected trellises with an expanded signal due to 2 use of q sup 2 psk signals are also presented two such codes ar rate 7 8 achieve a gain of 5 45 db with only eight states

a fast method for acoustic imaging of multiple three dimensional objects this paper is concerned with the inverse problem for imaging multiple three dimensional objects using the information of the far field pattern of the scattered wave a spatially dependent function which has noticeably different values inside and outside the obstacle is derived a numerical method based on the characterization is developed to obtain a visualization of the obstacle the most remarkable advantage of this method is that it does not need any prior knowledge about the geometry and physical properties of the scatterer and requires only the information of the far field measurements for a finite number of directions of incidence and observation distributed over a limited range furthermore the scheme is very simple and fast since it avoids the use of the iterative procedure and requires only the solution of a linear system some numerical examples with synthetic far field data are given showing the practicality and efficiency of this scheme

the covering radius of the leech lattice we investigate the points in 24 dimensional space that are at maximal distance from the leech lattice i e the deep holes in that lattice the distance of such a point from the leech lattice is 1 sqrt 2 times the minimal distance between the lattice points furthermore there are 23 inequivalent types of deep hole one for each of the 23 even unimodular 24 dimensional lattices found by niemeier

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

on block coded modulation with interblock memory block coded modulation with interblock memory bcmim is a variation of block coded modulation bcm which is designed for multilevel coding by providing interblock memory between adjacent blocks the coding rate of a bcmim scheme can be increased without decreasing the minimum squared euclidean distance msed as compared to the original bcm in an early version of bcmim interblock coding is provided only between the first two coding levels of adjacent blocks in this paper we design bcmim with a more general form for which interblock coding can be introduced among many coding levels in this way we can further increase the coding rate of bcmim without decreasing the msed we provide many examples to show the advantages of bcmim with the general form most of the examples are designed based on multidimensional signal sets since a multidimensional signal set can provide more coding levels than a two dimensional 2 d signal set

some implications of tcm for optical direct detection channels consideration is given to the optical direct detection channel and it is shown how simple trellis coded modulation tcm can be used to improve performance or increase throughput in bits per second without bandwidth expansion or performance loss in fact a modest performance gain can be achieved although the approach can be used with other signal constellations the authors concentrate on signals derived from the pulse position modulation ppm format by allowing overlap theoretical motivation for using this signal set known as overlapping ppm oppm was recently given by i bar david and g kaplan 1984 who showed a capacity gain when overlap is introduced

the no response test a sampling method for inverse scattering problems we describe a novel technique which we call the no response test to locate the support of a scatterer from knowledge of a far field pattern of a scattered acoustic wave the method uses a set of sampling surfaces and a special test response to detect the support of a scatterer without a priori knowledge of the physical properties of the scatterer specifically the method does not depend on information about whether the scatterer is penetrable or impenetrable nor does it depend on any knowledge of the nature of the scatterer absorbing reflecting etc in contrast to previous sampling algorithms the techniques described here enable one to locate obstacles or inhomogeneities from the far field pattern of only one incident field the no response test is a one wave method we investigate the theoretical basis for the no response test and derive a one wave uniqueness proof for a region containing the scatterer we show how to find the object within this region we demonstrate the applicability of the method by reconstructing sound soft sound hard impedance and inhomogeneous medium scatterers in two dimensions from one wave with full and limited aperture far field data

a parallel algorithm for solving the inverse scattering moment problem abstract a plane incident wave impinges upon an unknown acoustically soft scatterer it is assumed that the scatterer has a polynomial boundary it is star shaped and its characteristic dimension is much less than the wavelength of the incident field an analytic procedure is proposed to reduce the shape reconstruction process to the evaluation of certain expansion coefficients and the solution of a linear algebraic system then a parallel numerical algorithm is constructed which recovers the exact shape of the scatterer from the knowledge of a finite number of generalized low frequency moments generated by the leading low frequency approximation the efficiency of the proposed algorithm as well as the detailed parametric influence on the performance of the algorithm are extensively investigated

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

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

performance of pll based optical oppm communication systems the power spectral density psd of a direct detected optical signal with overlapping pulse position modulation oppm scheme is derived it is demonstrated that this spectrum contains a strong periodic component at the signal symbol frequency thereby enabling a simple pll device to provide joint symbol and slot synchronization the variance of the timing error for a linearized pll synchronizer is shown to be mainly dominated by and is inversely proportional to the product of the pll closed loop bandwidth and symbol duration of the oppm signal the performance of a shot noise limited pll based optical oppm communication system is then assessed in terms of the overall system symbol error rate

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

modulation and coding for throughput efficient optical systems optical direct detection systems are currently being considered for some high speed intersatellite links where data rates of a few hundred megabits per second are envisioned under power and pulsewidth constraints the authors investigate the capacity cutoff rate and error probability performance of uncoded and trellis coded systems for various modulation schemes and under throughput and power constraints modulation schemes considered are on off keying pulse position modulation ppm overlapping ppm and multipulse combinatorial ppm

a lower bound on the minimum euclidean distance of trellis coded modulation schemes a lower bound on the minimum free euclidean distance of trellis coded modulation tcm is derived that guarantees the existence of good tcm codes of any complexity the bound is used to compare trellis codes combined with phase shift keying pulse amplitude modulation and quadratic amplitude shift keying modulation this random coding bound is the first lower bound on the free distance of trellis codes is tighter than any upper bound for large constraint lengths and predicts the asymptotic performance of tcm when the complexity of the code becomes large the bound can be used with any code rate and any modulation scheme and shows that the free distance increases linearly with the constraint length for large values of the constraint length

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

probabilistic construction of large constraint length trellis codes for sequential decoding probabilistic algorithms are given for constructing good large constraint length trellis codes for use with sequential decoding that can achieve the channel cutoff rate bound at a bit error rate ber of 10 sup 5 10 sup 6 the algorithms are motivated by the random coding principle that an arbitrary selection of code symbols will produce a good code with high probability one algorithm begins by choosing a relatively small set of codes randomly the error performance of each of these codes is evaluated using sequential decoding and the code with the best performance among the chosen set is retained another algorithm treats the code construction as a combinatorial optimization problem and uses simulated annealing to direct the code search trellis codes for 8 psk and 16 qam constellations with constraint lengths v up to 20 are obtained simulation results with sequential decoding show that these codes reach the channel cutoff rate bound at a ber of 10 sup 5 10 sup 6 and achieve 5 0 6 35 db real coding gains over uncoded systems with the same spectral efficiency and up to 2 0 db real coding gains over 64 state trellis codes using viterbi decoding

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

a tractable framework for the analysis of dense heterogeneous cellular networks this paper investigates the downlink performance of dense k tier heterogeneous cellular networks hcns under general settings first gaussian approximation bounds for the standardized aggregate wireless interference awi in dense k tier hcns are obtained for when base stations bss in each tier are distributed over the plane according to a spatial and general poisson point process the kolmogorov smirnov ks distance is used to measure deviations of the distribution of the standardized awi from the standard normal distribution an explicit and analytical expression bounding the ks distance between these two distributions is obtained as a function of a broad range of network parameters such as per tier transmission power levels per tier bs intensity bs locations general fading statistics and general bounded path loss models bounds achieve a good statistical match between the standardized awi distribution and its normal approximation even for moderately dense hcns second various spatial performance metrics of interest such as outage capacity ergodic capacity and area spectral efficiency in the downlink of k tier hcns for general signal propagation models are investigated by making use of the derived distribution approximation results considering two specific bs association policies it is shown that the derived performance bounds track the actual performance metrics reasonably well for a wide range of bs intensities with the gap among them becoming negligibly small for denser hcn deployments finally both analytical and numerical results on the area spectral efficiency reveal a non linear growth trend with diminishing returns of hcn performance hence the sf sir invariance property does not hold under bounded path loss models which is a critical finding from the hcn design perspective in particular it points out a critical bs density beyond which the hcn performance starts to decline due to excessive wireless interference

exact sinr statistics in the presence of heterogeneous interferers we derive new results for the higher order moments of signal to interference plus noise ratio sinr in the presence of an arbitrary poisson point process ppp based heterogeneous interference field the analysis leverages on a moment generating function mgf methodology which only requires the statistics of intended signal and aggregate interference thus eliminating the need for the exact distribution of sinr we extend the existing results on interference statistics by deriving a generalized closed form expression of the interference mgf considering nakagami m fading channels with exclusion region in certain special cases explicit expressions for the averages of different functions of sinr are found which also lead to closed form solutions for the probability distributions of aggregate interference reciprocal and signal to interference ratio we prove that in such cases the effect of total ppp based interference power on useful transmission is mathematically equivalent to the severe fluctuations from a one sided gaussian fading channel as an application example the proposed methodology is used together with stochastic geometry theory to characterize the average sinr and rate in heterogeneous cellular networks the validity of our analytical derivations is confirmed via monte carlo simulations for various system settings we show that with cellular network densification there exists a tradeoff between the average sinr and rate performance

series expansion for interference in wireless networks the spatial correlations in transmitter node locations introduced by common multiple access protocols make the analysis of interference outage and other related metrics in a wireless network extremely difficult most works therefore assume that nodes are distributed either as a poisson point process ppp or a grid and utilize the independence properties of the ppp or the regular structure of the grid to analyze interference outage and other metrics but the independence of node locations makes the ppp a dubious model for nontrivial macs which intentionally introduce correlations e g spatial separation while the grid is too idealized to model real networks in this paper we introduce a new technique based on the factorial moment expansion of functionals of point processes to analyze functions of interference in particular outage probability we provide a taylor series type expansion of functions of interference wherein increasing the number of terms in the series provides a better approximation at the cost of increased complexity of computation various examples illustrate how this new approach can be used to find outage probability in both poisson and non poisson wireless networks

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

frame synchronization for optical overlapping pulse position modulation systems the maximum likelihood rules for locating data frames in direct detection optical communication systems utilizing overlapping pulse position modulation oppm are derived under two distinct assumptions of symbol and chip synchronization respectively various approximations to the optimal rules are identified as well as upper and lower bounds on the probability of correct synchronization further the problem of sequence design based on a maximum peak to sidelobe distance criterion is studied and upper bounds on peak to sidelobe distance for sequences of oppm symbols are derived some good sequences are obtained through a computer search

elastic herglotz functions solutions of the spectral navier equation in the linearized theory of elasticity that satisfy the herglotz boundness condition at infinity are introduced the leading asymptotic terms in a neighborhood of infinity provide the far field patterns and the herglotz norm is expressed as the sum of the l 2 norms of these patterns over the unit sphere basic integral representations that connect the solid spherical navier eigenvectors to the vector spherical harmonics over the unit sphere are utilized to prove the fundamental representation theorem for the elastic herglotz solutions in full space it is shown that the longitudinal and the transverse herglotz kernels are exactly the corresponding far field patterns of the irrotational and the solenoidal parts of the displacement field particular methods to obtain the displacement field from the far field patterns and vice versa are also described

trellis complexity and minimal trellis diagrams of lattices this paper presents results on trellis complexity and low complexity trellis diagrams of lattices we establish constructive upper bounds on the trellis complexity of lattices these bounds both improve and generalize the similar results of tarokh and vardy see ibid vol 43 p 1294 1300 1997 we also construct trellis diagrams with minimum number of paths for some important lattices such trellises are called minimal the constructed trellises which are novel in many cases can be employed to efficiently decode the lattices via the viterbi algorithm in particular a general structure for minimal trellis diagrams of d sub n lattices is obtained this structure corresponds to a new code formula for d sub n moreover we develop some important duality results which are used in both deriving the upper bounds and finding the minimal trellises all the discussions are based on a universal approach to the construction and analysis of trellis diagrams of lattices using their bases

average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

using nu ssga to reduce the searching time in inverse problem of a buried metallic object we describe an inverse scattering problem with the aim of reducing the computation time for recovering the details of a perfectly conducting cylindrical object buried in a half space first we use fourier series or cubic spline methods to describe the shape and reformulate the inverse problem into an optimization one then we solved it by the improved steady state genetic algorithm ssga and simple genetic algorithm sga respectively and compare the cost time in finding out the global extreme solution of the objective function it is found the searching ability of ssga is much powerful than that of the sga even when the initial guess is far away from the exact one the cost time for converging to a global extreme solution using by ssga is much less than that by sga numerical results are given to show that the inverse problem by using ssga is much better than sga in time costing

distance spectra and upper bounds on error probability for trellis codes the problem of estimating error probability for trellis codes is considered the set of all squared euclidean distances between code sequences is presented as a countable set this representation is used for calculating the generating functions for upper bounding error probability and bit error probability for trellis codes satisfying some symmetry conditions the generating functions of squared euclidean distances distance spectra are obtained by inversion of a matrix of order 2 sup spl nu it is shown that the generating functions are defined in terms of one formal variable for qam and uniform am and in terms of q 4 formal variables for q ary psk q 2 sup m where m spl ges 2 is an integer for small spl nu the generating functions may be found in closed form for larger spl nu a numerical technique for obtaining some initial terms of the power series expansion is proposed this algorithm is based on the recurrent matrix equations and the chinese remainder theorem

properties of the far field operator for a multilayered scatterer in acoustic scattering theory in this paper we consider the inverse scattering problem which is to determine the shape of a multilayered scatterer the adjoint of the far field operator is found in scattering theory the boundary data are given by the traces of plane waves the closure of the span of the images of these plane waves under the far field operator is characterized furthermore taking the affine hull instead of the span of the plane waves on the boundary some results are obtained

rate gains in block coded modulation systems with interblock memory this paper examines the performance gains achievable by adding interblock memory to and altering the mapping of coded bits to symbols in block coded modulation systems the channel noise considered is additive gaussian and the twin design goals are to maximize the asymptotic coding gain and to minimize the number of apparent nearest neighbors in the case of the additive white gaussian noise channel these goals translate into the design of block codes of a given weighted or normalized distance whose rate is as high as possible and whose number of codewords at minimum normalized distance is low the effect of designing codes for normalized distance rather than hamming distance is to ease the problem of determining the best codes for given parameters in the cases of greatest interest and many such best codes are given

design modeling and performance analysis of multi antenna heterogeneous cellular networks this paper presents a stochastic geometry based framework for the design and analysis of downlink multi user multiple input multiple output mimo heterogeneous cellular networks with linear zero forcing transmit precoding and receive combining assuming rayleigh fading channels and perfect channel state information the generalized tiers of base stations may differ in terms of their poisson point process spatial density number of transmit antennas transmit power artificial biasing weight and number of user equipments served per resource block the spectral efficiency of a typical user equipped with multiple receive antennas is characterized using a non direct moment generating function based methodology with closed form expressions of the useful received signal and aggregate network interference statistics systematically derived in addition the area spectral efficiency is formulated under different space division multiple access and single user beamforming transmission schemes we examine the impact of different cellular network deployments propagation conditions antenna configurations and mimo setups on the achievable performance through theoretical and simulation studies based on the state of the art system parameters the results highlight the inherent limitations of baseline single input single output transmission and conventional sparse macro cell deployment as well as the promising potential of multi antenna communications and small cell solution in interference limited cellular environments

the inverse scattering problem for time harmonic acoustic waves in an inhomogeneous medium with complex refraction index abstract the inverse scattering problem of determining the complex refraction index of a compact inhomogeneous medium from a knowledge of the far field patterns of the scattered fields corresponding to many incident time harmonic plane acoustic waves is solved by using the colton monk method again by using the same method the analogue of karp s theorem for the scattering of acoustic waves through an inhomogeneous medium with compact support is proven

information rates of photon limited overlapping pulse position modulation channels a direct detection photon limited optical communication channel that uses pulse position modulation ppm under a pulsewidth constraint is considered overlapping ppm oppm allows multiple positions per pulsewidth as well as fractional modulation indices number of pulsewidths per frame requiring more refined timing than that needed for conventional disjoint ppm djppm it is shown that even at moderate values of the expected photon count per pulse q such as needed for high data rates oppm outperforms on off keying ook in both capacity and cutoff rate even though ook is uniformly superior to djppm moreover efficient use of oppm is possible with equiprobable input symbols whereas ook requires inconvenient asymmetrical inputs to achieve capacity and high cutoff rate efficiencies nats photon at lower data rates where capacity efficiency is the prime criterion a significant advantage 20 percent over djppm can be achieved up to efficiencies of about 0 7 nats photon the m ary photon limited oppm channel can be viewed as an ambiguity and erasure channel in the sense that some channel outputs are ambiguous in only some input symbols and only if no photons are counted is there ambiguity in all input symbols for large m ambiguities cause bursts of erasures of data symbols massey s interlaced encoding as well as conventional encoding followed by interleaving are adaptable to this bursty channel and effect an increase in its cutoff rate comparable to the increase obtainable with djppm by the same techniques

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

the three dimensional inverse scattering problem for acoustic waves abstract we consider the inverse scattering problem for an acoustically soft obstacle in r 3 by assuming a priori that the unknown scattering obstacle is starlike and has its boundary lying in a compact family of holder continuously differentiable surfaces it is shown that an optimal solution can be constructed which depends continuously on the measured far field data remarks are made on the numerical approximation of the optimal solution

image reconstruction of perfectly conducting objects by a cascaded method in this paper we propose a method which combines a particle swarm optimization pso algorithm with a newton kantorovitch algorithm for image reconstruction of perfectly conducting objects first the inverse problem is recast as a global nonlinear optimization problem which is solved by a pso then the solution obtained by the pso is taken as an initial guess for the newton kantorovitch algorithm to obtain the more accuracy solution in a few iterations the inversion algorithm which is based on the rigorous mathematics makes use of the received scattered field and appropriate boundary condition to derive a set of nonlinear integral equations the moment method is used to transform the nonlinear integral equations into matrix form then the pseudoinverse transformation is employed to overcome the ill posedness to obtain a convergent and stable solution the particle swarm optimization algorithm is employed to find out the global extreme solution of the object function numerical results show that the performance of this cascaded method is better than the individual pso and the individual newton kantorovitch algorithm satisfactory reconstruction has been obtained by using this cascaded method

sphere bound achieving coset codes and multilevel coset codes a simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array l and its error probability on an additive white gaussian noise awgn channel it is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding including certain binary lattices these codes have structure of the kind that has been found to be useful in practice capacity curves and design guidance for practical codes are given exponential error bounds for coset codes are developed generalizing poltyrev s 1994 bounds for lattices these results are based on the channel coding theorems of information theory rather than the minkowski hlawka theorem of lattice theory

rate 5 6 trellis coded 8 psk some new short constraint length codes are described for satellite channels which are constant envelope and which have spectral and energy efficiencies intermediate to other recent coded techniques namely r 2 3 coded 8 psk and r 3 4 coded 16 psk we use two intervals of 8 psk transmission to form a modulation base for r 5 6 trellis codes a particularly attractive design is an eight state code producing 6 2 db gain on the gaussian channel over uncoded 8 psk yet sacrificing only 16 percent in spectral efficiency

the cutoff rate for on off keying it is well known that on off keying ook i e the transmission of a pulse for a data one mark and transmission of no signal for a data zero space exhibits a 3 db inferiority to antipodal signalling in terms of the signal to noise ratio required to achieve a specified bit error probability when the channel is characterized by the cutoff rate r sub 0 this 3 db inferiority persists in the sense that the required e sub b n sub 0 to operate at a given value of r sub 0 is 3 db greater for the ook channel than for the antipodal channel however it is shown that if the definition of cutoff rate is generalized in an appropriate way to reflect the fact that signal energy is expended only in the transmission of marks part of this penalty is recovered in fact it is shown that in the limit of low r sub 0 there is no penalty in signal to noise ratio even at rates of realistic interest the penalty is significantly less than the expected 3 db

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

graphs tessellations and perfect codes on flat tori quadrature amplitude modulation qam like signal sets are considered in this paper as coset constellations placed on regular graphs on surfaces known as flat tori such signal sets can be related to spherical block and trellis codes and may be viewed as geometrically uniform gu in the graph metric in a sense that extends the concept introduced by forney homogeneous signal sets of any order can then be labeled by a cyclic group induced by translations on the euclidean plane we construct classes of perfect codes on square graphs including lee spaces and on hexagonal and triangular graphs all on flat tori extension of this approach to higher dimensions is also considered

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

maximum likelihood symbol synchronization for the direct detection optical on off keying channel the maximum likelihood symbol synchronization statistic is derived from noisy observations of randomly modulated on off keying data for the direct detection optical channel a similar statistic for the case when the transmitter sends a special pattern of alternating o s and 1 s for synchronization purposes only is also derived various approximations to the optimal statistic are introduced and their performance compared to the optimal one under a new criterion believed to be more appropriate for the poisson channel than the mean square error criterion routinely used with other channels it is shown that although the variable associated with symbol transitions is continuous the possible values of it that maximize the maximum likelihood ml statistic belong to a discrete set with relatively few elements

finite state codes a class of codes called finite state fs codes is defined and investigated the codes which generalize both block and convolutional codes are defined by their encoders which are finite state machines with parallel inputs and outputs a family of upper bounds on the free distance of a given fs code is derived a general construction for fs codes is given and it is shown that in many cases the fs codes constructed in this way have a free distance that is the largest possible catastrophic error propagation cep for fs codes is also discussed it is found that to avoid cep one must solve the graph theoretic problem of finding a uniquely decodable edge labeling of the state diagram

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

discrete multiple tone modulation with coset coding for the spectrally shaped channel a discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference isi and additive gaussian noise multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete fourier transform dft code vectors and high gain coset or trellis codes symbol blocks from an inverse dft idft are cyclically extended to generate isi free channel output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels asymptotic performance of this system is derived and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample this discrete multiple tone technique is linear in both the modulation and the demodulation and is free from the effects of error propagation that often afflict systems employing bandwidth optimized decision feedback plus coset codes

studying the sinr process of the typical user in poisson networks using its factorial moment measures based on a stationary poisson point process a wireless network model with random propagation effects shadowing and or fading is considered in order to examine the process formed by the signal to interference plus noise ratio sinr values experienced by a typical user with respect to all the base stations in the down link channel this sinr process is completely characterized by deriving its factorial moment measures which involve numerically tractable explicit integral expressions this novel framework naturally leads to expressions for the k coverage probability including the case of random sinr threshold values considered in multi tier network models while the k coverage probabilities correspond to the marginal distributions of the order statistics of the sinr process a more general relation is presented connecting the factorial moment measures of the sinr process to the joint densities of these order statistics this gives a way for calculating the exact values of the coverage probabilities arising in a general scenario of signal combination and interference cancellation between base stations the presented framework consisting of the mathematical representations of sinr characteristics with respect to the factorial moment measures holds for the whole domain of sinr and is amenable to considerable model extension

a two step method in inverse scattering problem for a crack in this paper we present a method for solving a time harmonic acoustic inverse scattering problem for a sound soft crack in r2 based on the integral equation method our method splits the nonlinear severely ill posed inverse problem into a linear well posed direct problem and a nonlinear ill posed problem at this setting not only the regularized newton s method can still be used to solve the inverse problem numerically but also with the advantage of keeping the structure of the algorithm simple and efficient

capacity and cutoff rate for optical overlapping pulse position modulation channels upper and lower bounds on the capacity and cutoff rate for direct detection optical overlapping pulse position modulation channels are derived it is shown that these bounds are asymptotically tight in the sense that the difference between the upper and lower bounds converges to zero as the pulse position multiplicity m and or the average photon count per pulse q goes to infinity the tightness of these bounds for finite values of m and and is investigated by providing some numerical examples orders of magnitude of the rate of convergence of the difference between the bounds are also estimated

shannon theoretic approach to a gaussian cellular multiple access channel we obtain shannon theoretic limits for a very simple cellular multiple access system in our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor spl alpha 0 spl les spl alpha spl les 1 times the sum of the signals transmitted from the adjacent cells plus ambient gaussian noise although this simple model is scarcely realistic it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems we consider both a one dimensional linear cellular array and the familiar two dimensional hexagonal cellular pattern the discrete time channel is memoryless we assume that n contiguous cells have active transmitters in the one dimensional case and that n sup 2 contiguous cells have active transmitters in the two dimensional case there are k transmitters per cell most of our results are obtained for the limiting case as n spl rarr spl infin the results include the following 1 we define c sub n c spl circ sub n as the largest achievable rate per transmitter in the usual shannon theoretic sense in the one and two dimensional cases respectively assuming that all signals are jointly decoded we find expressions for limn spl rarr spl infin c sub n and limn spl rarr spl infin c spl circ sub n 2 as the interference parameter spl alpha increases from 0 c sub n and c spl circ sub n increase or decrease according to whether the signal to noise ratio is less than or greater than unity 3 optimal performance is attainable using tdma within the cell but using tdma for adjacent cells is distinctly suboptimal 4 we suggest a scheme which does not require joint decoding of all the users and is in many cases close to optimal

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n

a bounded distance decoding algorithm for the leech lattice with generalizations an algorithm is given that decodes the leech lattice with not much more than twice the complexity of soft decision decoding of the golay code the algorithm has the same effective minimum distance as maximum likelihood decoding and increases the effective error coefficient by less than a factor or two the algorithm can be recognized as a member of the class of multistage algorithms that are applicable to hierarchical constructions it is readily generalized to lattices that can be expressed in terms of binary code formulas and in particular to construction b lattices

the inverse scattering problem for time harmonic acoustic waves the inverse scattering problem we are considering in this paper is to determine the shape of a sound soft bounded connected obstacle from a knowledge of the time harmonic incident wave with frequency in the resonance region and the far field pattern of the scattered wave after some introductory remarks we begin by describing the method of integral equations and the null field method for solving the direct scattering problem this enables us to define an operator t mapping the boundary of the scattering obstacle and the incident field onto the far field pattern the inverse scattering problem is to invert this operator in order to do this we first must examine the range of t i e to characterize the class of far field patterns and to establish the existence of t on the range of t i e to show the uniqueness of the solution to the inverse scattering problem this analysis shows that for a given measured far field pattern in general no solution exists to the inverse scattering problem and if a solution does exist it does not depend continuously on the measured data i e the problem is improperly posed this motivates us to consider a linearized model and to examine various methods for studying linearized improperly posed problems based on the ideas of a priori assumptions and compactness arguments we then consider a simple model problem that focuses on the nonlinear character of the inverse scattering problem and motivated by our study of the linearized model reformulate the inverse scattering problem as a problem in constrained optimization we conclude by considering the numerical solution of this nonlinear optimization problem approach your problems from the right end and begin with the answers then one day perhaps you will find the final question from the hermit clad in crane feathers in the chinese maze murders by r van gulik

optimization of signal sets for partial response channels i numerical techniques given a linear time invariant discrete time channel the problem of constructing n input signals of finite length k that maximize minimum l sub 2 distance between pairs of outputs is considered two constraints on the input signals are considered a power constraint on each of the n inputs hard constraint and an average power constraint over the entire set of inputs soft constraint the hard constraint problem is equivalent to packing n points in an ellipsoid in min k n 1 dimensions to maximize the minimum euclidean distance between pairs of points gradient based numerical algorithms and a constructive technique based on dense lattices are used to find locally optimal solutions to the preceding signal design problems two numerical examples are shown for which the average spectrum of an optimized signal set resembles the water pouring spectrum that achieves shannon capacity assuming additive white gaussian noise

on the numerical solution of the three dimensional inverse obstacle scattering problem abstract the inverse problem under consideration is to determine the shape of an impenetrable sound soft obstacle from the knowledge of a time harmonic incident plane acoustic wave and far field or near field measurements of the scattered wave we present a method for the approximate solution which avoids the solution of the corresponding direct problem and stabilizes the ill posed inverse problem by reformulating it as a nonlinear optimization problem the numerical implementation of the method is described and some three dimensional examples of reconstructions are given

a new non iterative singular sources method for the reconstruction of piecewise constant media we describe a novel non iterative method for the reconstruction of a piecewise constant inhomogeneous medium in acoustic scattering which we call the singular sources method the basic idea of the method is to use the behaviour of the scattered field for singular incident fields multipoles to calculate the size of the refractive index n at some point z0 on the boundary of the support of the scatterer and then eliminate this value from the data by subtracting a known piecewise constant background medium the paper includes the theory for the singular sources method to locate the unknown support of an inhomogeneous medium for a known inhomogeneous background medium also we give a new uniqueness proof for the reconstruction of a piecewise constant medium in two or three dimensions using techniques that differ from those used to prove previous well known results

performance evaluation of coded modulation schemes based on binary lattices we describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding these techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary lattice is based multilevel coded modulation schemes can also be described through a trellis by combining with this the trellis structure of the lattice constellation we obtain a single trellis that can be used for maximum likelihood decoding using the viterbi algorithm and for computing the error probability an upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels and is applicable to both maximum likelihood and staged decoding

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

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

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

bounds on the capacity of a spectrally constrained poisson channel an upper bound is derived on the capacity of a poisson channel that has a stationary input process of a given spectrum and is subjected to peak and average power constraints the bound is shown to be asymptotically tight with the relaxation of the spectral constraints its maximization over a given set of admissible spectra is closely related to an analogous problem in the awgn regime the results are used for bounding the capacity of a poisson channel under a second moment bandwidth constraint as well as the capacity under a strict bandwidth constraint asymptotically tight lower bounds on the channel capacity for the above two cases are also presented the approach for lower bounding the capacity for the latter case yields as a by product improved bounds on the bit error probability in uncoded amplitude shift keying and on off modulation as a special case operating over a poisson channel impaired by intersymbol interference

a modified design of trellis coded mpsk for the fading channel it is shown that the classical additive white gaussian noise awgn channel design can be retained for the fading channel with any degree of fading if carried out with the appropriate signal set size m m sub min the size of the signal set m sub min is shown to depend upon the number of parallel transitions between a given pair of states and the throughput rate in the proposed multiple trellis coded modulation mtcm scheme with a modified design mtcm md the output bits from a rate m m 1 trellis encoder are assigned multiple signals from an m sub min psk signal set compared to the mtcm with set partitioning proposed for the fading channel spf design the mtcm md scheme provides the same signal diversity and the same or increased values of the branch distance product and always leads to increased value of d sup 2 free as a result the performance is always improved on the rician fading channel due to the increased d sup 2 free and is improved on any fading channel when an increase in branch distance produce p takes place when compared to the mtcm with the set partitioning optimum for the awgn channel spa design the mtcm md scheme under certain conditions provides the same value of d sup 2 free as the mtcm spa design and is then asymptotically optimum for both the awgn channel and the fading channels

a new description of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of real or complex numbers that are input to a noisy transmission channel ungerboeck has constructed simple trellis codes that provide the same noise immunity as is given by increasing the power of uncoded transmission by factors ranging from two to four his method is to specify an underlying convolutional code and a rule mapping by set partitioning that maps the output of this code onto a fixed signal constallation a new description of a trellis code is given that combines these two steps into one the new description is analytic rather than graphical many practical codes can be described very simply and strict bounds on performance can be obtained a method for differential encoding trellis codes is presented that was suggested by the authors representation

the limited aperture problem of inverse acoustic scattering dirichlet boundary conditions let d be a bounded simply connected domain in the plane and let f theta k underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l be the far field pattern arising from the scattering of a time harmonic acoustic plane wave u l underset raise0 3em hbox smash scriptscriptstyle thicksim x exp ik underset raise0 3em hbox smash scriptscriptstyle thicksim x cdot underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l where underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l is a unit vector and k is the wave number and the time harmonic factor e i omega t has been factored out it is assumed in addition that the total field satisfies homogeneous dirichlet boundary conditions on partial d in this paper a method is presented for recovering partial d given the far field patterns f theta k underset raise0 3em hbox smash scriptscriptstyle thicksim alpha l

a unified mgf based capacity analysis of diversity combiners over generalized fading channels unified exact ergodic capacity results for l branch coherent diversity combiners including equal gain combining egc and maximal ratio combining mrc are not known this paper develops a novel generic framework for the capacity analysis of l branch egc mrc over generalized fading channels the framework is used to derive new results for the gamma shadowed generalized nakagami m fading model which can be a suitable model for the fading environments encountered by high frequency 60 ghz and above communications the mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework

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

suboptimal decoding of linear codes partition technique general symmetric channels are introduced and near maximum likelihood decoding in these channels is studied first we define a class of suboptimal decoding algorithms based on an incomplete search through the code trellis it is proved that the decoding error probability of suboptimal decoding is bounded above for any q ary code of length n and code rate r by twice the error probability of its maximum likelihood decoding and tends to the latter as n grows second we design a suboptimal trellis like algorithm which reduces the known decoding complexity of the order of q sup n min r 1 r operations to that of q sup nr i r operations for all cyclic codes and virtually all long linear codes we also consider the corresponding bounds for concatenated codes an important corollary is that this suboptimal decoding can provide complexity below the lower bounds on trellis complexity at a negligible expense in terms of decoding error probability

inverse scattering for conductors by the equivalent source method the inverse scattering for two dimensional conductors is investigated assume that an incident wave is incident upon conducting cylinders of unknown shape and the scattered field is measured outside by properly processing the scattering data the position and shape of the conducting scatterers can then be reconstructed the proposed theory of inverse scattering is a combination of the diffraction tomography and the equivalent source method to overcome the ill posedness the condition of the measured scattered field and the boundary condition on the conductor surfaces are combined and recast into an optimization problem using the least squares concept by comparing the reconstructed and the prescribed results the inversion algorithms are numerically examined note that if a priori information of the shape is sufficient and the equivalent sources are properly placed the algorithms can be flexibly applied to the cases of multiple conductors also the effects of noise contamination and multiple scattering on the reconstruction result are numerically investigated

inverse scattering via low frequency moments an acoustically soft scatterer defined by a closed and star shape polynomial surface of any degree disturbs the propagation of a time harmonic plane incident wave it is demonstrated that under the hypotheses of schiffer s uniqueness theorem all the generalized low frequency moments corresponding to the capacity potential can be obtained from the scattering amplitude an analytic algorithm is proposed that recovers the geometry of the body whenever a finite number of generalized moments generated by the leading low frequency approximation are given what is striking here is the fact that a surface measure generated by a potential problem is enough to recover the geometry of the scatterer the idea here is to relate the given moments to a set of particular combined spherical moments that appear as coefficients of an algebraic linear system whose solution provides the coefficients of the scattering surface in spherical harmonics this is done with the help of an inner product defined over the surface of

a coded modulation scheme with interblock memory proposes a coded modulation scheme with interblock memory the proposed scheme has a multi stage coding structure however at some coding stage the coding designs for every two adjacent blocks are related compared to coded modulation schemes for which each block is independent of the others the introduction of interblock coding provides additional flexibility in the design in this way for the proposed scheme one can achieve a large minimum euclidean distance while the number of nearest neighbors is not too large the authors also design a multi stage decoding algorithm which is optimum in each stage and has low decoding complexity three specific examples are provided to demonstrate the advantages of the proposed scheme

trellis codes for the optical direct detection channel it is observed that the reduced complexity minimum distance search method of zehavi and wolf 1987 can be extended from codes designed using the squared euclidean distance measure to any measure which is additive over the code branches c n georghiades 1989 has derived such a metric for codes for the direct detection optical channel the search method is applied to find codes for four and eight point overlapping pulse position modulation oppm with large minimum distance and a small number of codewords at that distance

multidimensional mappings for iteratively decoded bicm on multiple antenna channels multidimensional binary mappings for bit interleaved coded modulations bicms on ergodic multiple antenna channels with iterative decoding are presented after derivation of a closed form expression for the pairwise error probability under ideal maximum likelihood ml decoding the design criterion for mapping optimization is established from the ml performance of the ideally interleaved channel it coincides with the figure of merit derived from the genie condition when the iterative receiver converges to perfect a priori information multidimensional mapping constructions that exhibit high signal to noise ratio snr gains without increasing the complexity of the a posteriori probability app detection are proposed they allow for a reduced decoding complexity as they achieve near turbo code performance with a single convolutional code