faulty successive cancellation decoding of polar codes for the binary erasure channel in this paper the faulty successive cancellation decoding of polar codes for the binary erasure channel is studied to this end a simple erasure based fault model is introduced to represent errors in the decoder and it is shown that under this model polarization does not happen meaning that fully reliable communication is not possible at any rate furthermore a lower bound on the frame error rate of polar codes under faulty successive cancellation decoding is provided which is then used along with a well known upper bound in order to choose a blocklength that minimizes the erasure probability under faulty decoding finally an unequal error protection scheme that can re enable asymptotically erasure free transmission at a small rate loss and by protecting only a constant fraction of the decoder is proposed the same scheme is also shown to significantly improve the finite length performance of the faulty successive cancellation decoder by protecting as little as 1 5 of the decoder

max matching diversity in ofdma systems this paper considers the problem of optimal subcarrier allocation in ofdma systems to achieve the minimum outage probability while guaranteeing fairness the optimal subcarrier allocation algorithm and the maximum frequency diversity gain are both analyzed through the maximum matching method based on the random bipartite graph theory accordingly a surprising result is found which shows that the maximum frequency diversity gain in subcarrier sharing ofdma systems is the same as that in point to point ofdm systems that serve only one user by using n subcarriers it is then demonstrated that this maximum frequency diversity gain can be achieved by a proposed random vertex rotation based hopcroft karp rvrhk algorithm with the time complexity of o n2 5 where n is the number of subcarriers because the theoretical analysis and the rvrhk algorithm are both based on the maximum matching method the maximum frequency diversity in ofdma systems is referred to as the max matching diversity in this paper

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

exact pairwise error probability of space time codes we describe a simple technique for the numerical calculation within any desired degree of accuracy of the pairwise error probability pep of space time codes over fading channels this method applies also to the calculation of e q spl radic spl xi for any nonnegative random variable spl xi whose moment generating function spl phi sub spl xi s e exp s spl xi is known its application to the multiple antenna independent rayleigh fading channel and to the rayleigh block fading channel is discussed and illustrated by two simple examples

transmit beamforming for space frequency coded mimo ofdm systems with spatial correlation feedback this paper addresses the problem of joint optimization of transmit beamforming and space frequency sf coding for mimo ofdm systems with spatial correlation feedback in broadband communications this problem is challenging in the sense that the transmitter should be designed to beamform across multiple eigenspaces associated with the multipath environment simultaneously with arbitrary transmit spatial correlation the performance analysis for sf coded mimo ofdm systems with beamforming is provided and a general optimization problem for the beamforming design is formulated three suboptimal approaches to design the beamformer based on the derived design criteria are proposed i eigenvalue selection scheme ii eigenspace selection scheme and iii per subcarrier approach based on decoding at each subcarrier the proposed schemes take into account the multiple eigenspace information associated with the multipath delay channel improvement in the performance over sf coding without beamforming is shown through simulations in terms of bit error rate the eigenvalue selection scheme provides the best performance among the proposed algorithms this scheme locates the subspace associated with the largest eigenvalues in the eigenspace of the covariance matrices with the eigenvalue selection scheme the performance improvement is about 3 db over the sf coding without beamforming for highly correlated channels as shown in our simulations

adaptive mimo ofdm based on partial channel state information relative to designs assuming no channel knowledge at the transmitter considerably improved communications become possible when adapting the transmitter to the intended propagation channel as perfect knowledge is rarely available transmitter designs based on partial statistical channel state information csi are of paramount importance not only because they are more practical but also because they encompass the perfect and no knowledge paradigms in this paper we first provide a partial csi model for orthogonal frequency division multiplexed ofdm transmissions over multi input multi output mimo frequency selective fading channels we then develop an adaptive mimo ofdm transmitter by applying an adaptive two dimensional 2 d coder beamformer we derived recently on each ofdm subcarrier along with an adaptive power and bit loading scheme across ofdm subcarriers relying on the available partial csi at the transmitter our objective is to maximize the transmission rate while guaranteeing a prescribed error performance under the constraint of fixed transmit power numerical results confirm that the adaptive 2 d space time coder beamformer with two basis beams as the two strongest eigenvectors of the channel s correlation matrix perceived at the transmitter combined with adaptive ofdm power and bit loaded with m ary quadrature amplitude modulated qam constellations improves the transmission rate considerably

interpolation based unitary precoding for spatial multiplexing mimo ofdm with limited feedback spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm systems linear precoding requires channel state information for each ofdm subcarrier which can be achieved using feedback to reduce the amount of feedback this paper proposes a limited feedback architecture that combines precoder quantization with a special matrix interpolator in the proposed system the receiver sends information about a fraction of the precoding matrices to the transmitter and the transmitter reconstructs the precoding matrices for all the subcarriers a new interpolator is proposed inspired by spherical interpolation that respects the orthogonal columns of the precoding matrices and the performance invariance to right multiplication by a unitary matrix the interpolator is parameterized by a set of unitary matrices a construction of a suitable set is briefly described simulations illustrate the performance of limited feedback precoding with coding estimation or prediction error and time variation for bit error rate ber mutual information and mean squared error mse

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

computing linear transformations with unreliable components we consider the problem of computing a binary linear transformation when all circuit components are unreliable two models of unreliable components are considered probabilistic errors and permanent errors we introduce the encoded technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy by deriving a lower bound we show that in some cases the computational complexity of the encoded technique achieves the optimal scaling in error probability further we examine the gain in energy efficiency from the use of a voltage scaling scheme where gate energy is reduced by lowering the supply voltage we use a gate energy reliability model to show that tuning gate energy appropriately at different stages of the computation dynamic voltage scaling in conjunction with encoded can lead to orders of magnitude energy savings over the classical uncoded approach finally we also examine the problem of computing a linear transformation when noiseless decoders can be used providing upper and lower bounds to the problem

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

stochastic belief propagation a low complexity alternative to the sum product algorithm the belief propagation bp or sum product algorithm is a widely used message passing method for computing marginal distributions in graphical models at the core of the bp message updates when applied to a graphical model involving discrete variables with pairwise interactions lies a matrix vector product with complexity that is quadratic in the state dimension d and requires transmission of a d 1 dimensional vector of real numbers messages to its neighbors since various applications involve very large state dimensions such computation and communication complexities can be prohibitively complex in this paper we propose a low complexity variant of bp referred to as stochastic belief propagation sbp as suggested by the name it is an adaptively randomized version of the bp message updates in which each node passes randomly chosen information to each of its neighbors the sbp message updates reduce the computational complexity per iteration from quadratic to linear in d without assuming any particular structure of the potentials and also reduce the communication complexity significantly requiring only log2d bits transmission per edge moreover we establish a number of theoretical guarantees for the performance of sbp showing that it converges almost surely to the bp fixed point for any tree structured graph and for any graph with cycles satisfying a contractivity condition in addition for these graphical models we provide nonasymptotic upper bounds on the convergence rate showing that the l norm of the error vector decays no slower than o 1 t with the number of iterations t on trees and the normalized mean squared error decays as o 1 t for general graphs this analysis also supported by experimental results shows that sbp can provably yield reductions in computational and communication complexities for various classes of graphical models

the multitone channel the maximum bit rate of multitone qam quadrature amplitude modulation over a general linear channel is found first the overall bit rate for an awgn channel with a two level transfer function is maximized using a multitone qam system the power distribution between the tones and the number of bits symbol per tone is optimized for a given symbol error rate extending these results to the general channel it is shown that the optimum power division for multitone signals is similar to the water pouring solution of information theory furthermore multitone qam performance is about 9 db worse than the channel capacity independent of the channel characteristics the multitone results throughout are compared to those of an equivalent single tone linearly equalized system the comparison shows that the multitone system is useful for some channels e g those with deep nulls in the transfer function the maximum bit error rate over a twisted pair channel which is performance dominated by near end crosstalk next is also found

a robust maximin approach for mimo communications with imperfect channel state information based on convex optimization this paper considers a wireless communication system with multiple transmit and receive antennas i e a multiple input multiple output mimo channel the objective is to design the transmitter according to an imperfect channel estimate where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy the robust transmission scheme is composed of an orthogonal space time block code ostbc whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them at the receiver the signal is detected assuming a perfect channel knowledge the optimization problem corresponding to the design of the power allocation among the estimated eigenmodes whose goal is the maximization of the signal to noise ratio snr is transformed to a simple convex problem that can be easily solved different sources of errors are considered in the channel estimate such as the gaussian noise from the estimation process and the errors from the quantization of the channel estimate among others for the case of gaussian noise the robust power allocation admits a closed form expression finally the benefits of the proposed design are evaluated and compared with the pure ostbc and nonrobust approaches

asymptotic capacity of multicarrier transmission with frequency selective fading and limited feedback we study the capacity of multicarrier transmission through a slow frequency selective fading channel with limited feedback which specifies channel state information our results are asymptotic in the number of subchannels we first assume independent and identically distributed i i d subchannel gains and show that for a large class of fading distributions a uniform power distribution over an optimized subset of subchannels or on off power allocation gives the same asymptotic growth in capacity as optimal water filling e g with rayleigh fading furthermore the growth in data rate can be achieved with a feedback rate as if the number of active subchannels is bounded the capacity grows only as with the feedback rate of we then consider correlated subchannels modeled as a markov process and study the savings in feedback assuming a fixed ratio of coherence bandwidth to the total bandwidth the ratio between minimum feedback rates with correlated and i i d subchannels converges to zero with e g as for rayleigh fading subchannels satisfying a first order autoregressive process we also show that adaptive modulation or rate control schemes in which the rate on each subchannel is selected from a quantized set achieves the same asymptotic growth rates in capacity and required feedback finally our results are extended to cellular uplink and downlink channel models

gallager b ldpc decoder with transient and permanent errors this paper studies the performance of a noisy gallager b decoder for regular ldpc codes we assume that the noisy decoder is subject to both transient processor errors and permanent memory errors we permit different error rates at different functional components in addition for the sake of generality we allow asymmetry in the permanent error rates of component outputs and thus we model error propagation in the decoder via a suitable asymmetric channel we then develop a density evolution type analysis on this asymmetric channel the recursive expression for the bit error probability is derived as a function of the code parameters node degrees codeword weight transmission error rate and the error rates of the permanent and the transient errors based on this analysis we then derive the residual error of the gallager b decoder for the regime where the transmission error rate and the processing error rates are small in this regime we further observe that the residual error rate can be well approximated by a suitable combination of the transient error rate and the permanent error rate at variable nodes provided that the check node degree is large enough based on this insight we then propose and analyze a scheme for detecting permanent errors and correcting detected residual errors the scheme exploits the parity check equations of the code and reuses the existing hardware to locate permanent errors in memory blocks performance analysis and simulation results show that with high probability the detection scheme discovers correct locations of permanent memory errors while with low probability it mislabels the functional memory as being defective the proposed error detection and correction scheme can be implemented in circuit and is useful in combating failures arising from aging

optimal resource allocation in the ofdma downlink with imperfect channel knowledge previous research efforts on ofdma resource allocation have typically assumed the availability of perfect channel state information csi unfortunately this is unrealistic primarily due to channel estimation errors and more importantly channel feedback delay in this paper we develop optimal resource allocation algorithms for the ofdma downlink assuming the availability of only partial imperfect csi we consider both continuous and discrete ergodic weighted sum rate maximization subject to total power constraints and average bit error rate constraints for the discrete rate case we approach these problems using a dual optimization framework allowing us to solve these problems with o mk complexity per symbol for an ofdma system with k used subcarriers and m active users while achieving relative optimality gaps of less than 10 5 for continuous rates and less than 10 3 for discrete rates in simulations based on realistic parameters

channel adaptive quantization for limited feedback mimo beamforming systems multiple input multiple output mimo wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques in the absence of full channel knowledge at the transmitter the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low rate feedback channel in the literature quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution commonly the uncorrelated rayleigh distribution when the channel is not uncorrelated rayleigh however these quantization strategies result in a degradation of the receive signal to noise ratio snr in this paper switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution the codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel the convergence properties of the codebook selection algorithm are studied assuming a block stationary model for the channel in the case of a nonstationary channel it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in snr simulation results show that in the case of correlated channels the snr performance of the link can be significantly improved by adaptation compared with nonadaptive quantization strategies designed for uncorrelated rayleigh fading channels

density evolution and functional threshold for the noisy min sum decoder this paper investigates the behavior of the min sum decoder running on noisy devices our aim is to evaluate the robustness of the decoder to computation noise caused by the faulty logic in the processing units this type of noise represents a new source of errors that may occur during the decoding process to this end we first introduce probabilistic models for the arithmetic and logic units of the finite precision min sum decoder and then carry out the density evolution analysis of the noisy min sum decoder we show that in some particular cases the noise introduced by the device can help the min sum decoder to escape from fixed points attractors and may actually result in an increased correction capacity with respect to the noiseless decoder we also point out a specific threshold phenomenon referred to as functional threshold which accurately describes the convergence behavior of noisy decoders the behavior of the noisy ms is demonstrated in the asymptotic limit of the code length through a noisy version of density evolution and is also verified in the finite length case by monte carlo simulations

a more accurate one dimensional analysis and design of irregular ldpc codes we introduce a new one dimensional 1 d analysis of low density parity check ldpc codes on additive white gaussian noise channels which is significantly more accurate than similar 1 d methods our method assumes a gaussian distribution in message passing decoding only for messages from variable nodes to check nodes compared to existing work which makes a gaussian assumption both for messages from check nodes and from variable nodes our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence similar to previous work the problem of designing irregular ldpc codes reduces to a linear programming problem however our method allows irregular code design in a wider range of rates without any limit on the maximum variable node degree we use our method to design irregular ldpc codes with rates greater than 1 4 that perform within a few hundredths of a decibel from the shannon limit the designed codes perform almost as well as codes designed by density evolution

interpolation based transmit beamforming for mimo ofdm with limited feedback transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm system optimal beamforming requires channel state information in the form of the beamforming vectors for each ofdm subcarrier this paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation in the proposed system the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation a new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors the beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter the proposed quantization system provides only a moderate increase in complexity versus over comparable approaches numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate

belief propagation algorithms on noisy hardware the wide recognition that emerging nano devices will be inherently unreliable motivates the evaluation of information processing algorithms running on noisy hardware as well as the design of robust schemes for reliable performance against hardware errors of varied characteristics in this paper we investigate the performance of a popular statistical inference algorithm belief propagation bp on probabilistic graphical models implemented on noisy hardware and we propose two robust implementations of the bp algorithm targeting different computation noise distributions we assume that the bp messages are subject to zero mean transient additive computation noise we focus on graphical models satisfying the contraction mapping condition that guarantees the convergence of the noise free bp we first upper bound the distances between the noisy bp messages and the fixed point of noise free bp as a function of the iteration number next we propose two implementations of bp namely censoring bp and averaging bp that are robust to computation noise censoring bp rejects incorrect computations to keep the algorithm on the right track to convergence while averaging bp takes the average of the messages in all iterations up to date to mitigate the effects of computation noise censoring bp works effectively when with high probability the computation noise is exactly zero and averaging bp although having a slightly larger overhead works effectively for general zero mean computation noise distributions sufficient conditions on the convergence of censoring bp and averaging bp are derived simulations on the ising model demonstrate that the two proposed implementations successfully converge to the fixed point achieved by noise free bp additionally we apply averaging bp to a bp based image denoising algorithm and as a bp decoder for ldpc codes in the image denoising application averaging bp successfully denoises an image even when nominal bp fails to do so in the presence of computation noise in the bp ldpc decoder application the power of averaging bp is manifested by the reduction in the residual error rates compared with the nominal bp decoder

representation of similarity in three dimensional object discrimination how does the brain represent visual objects in simple perceptual generalization tasks the human visual system performs as if it represents the stimuli in a low dimensional metric psychological space shepard 1987 in theories of three dimensional 3d shape recognition the role of feature space representations as opposed to structural biederman 1987 or pictorial ullman 1989 descriptions has long been a major point of contention if shapes are indeed represented as points in a feature space patterns of perceived similarity among different objects must reflect the structure of this space the feature space hypothesis can then be tested by presenting subjects with complex parameterized 3d shapes and by relating the similarities among subjective representations as revealed in the response data by multidimensional scaling shepard 1980 to the objective parameterization of the stimuli the results of four such tests accompanied by computational simulations support the notion that discrimination among 3d objects may rely on a low dimensional feature space representation and suggest that this space may be spanned by explicitly encoded class prototypes

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

predictive coding of bit loading for time correlated mimo channels with a decision feedback receiver in this paper we consider variable rate transmission over a slowly varying multiple input multiple output mimo channel with a decision feedback receiver the transmission rate is adapted to the channel by dynamically assigning bits to the subchannels of the mimo system predictive quantization is used for the feedback of bit loading to take advantage of the time correlation inherited from the temporally correlated channel due to the use of decision feedback at the receiver the bit loading is related to the cholesky decomposition of the channel gram matrix assuming the channel is modeled by a slowly varying gauss markov process we show that the nested submatrices generated during the process of cholesky decomposition can be updated as time evolves based on the update we derive the optimal predictor of the next bit loading for predictive quantization furthermore we derive the statistics of the prediction error which are then exploited to design the quantizer to achieve a smaller quantization error simulations are given to demonstrate that the proposed predictive quantization gives a good approximation of the desired transmission rate with a low feedback rate

the extraction and complexity limits of graphical models for linear codes two broad classes of graphical modeling problems for codes can be identified in the literature constructive and extractive problems the former class of problems concern the construction of a graphical model in order to define a new code the latter class of problems concern the extraction of a graphical model for a fixed given code the design of a new low density parity check code for some given criteria e g target block length and code rate is an example of a constructive problem the determination of a graphical model for a classical linear block code that implies a decoding algorithm with desired performance and complexity characteristics is an example of an extractive problem this work focuses on extractive graphical model problems and aims to lay out some of the foundations of the theory of such problems for linear codes the primary focus of this work is a study of the space of all graphical models for a fixed given code the tradeoff between cyclic topology and complexity in this space is characterized via the introduction of a new bound the forest inducing cut set bound fi csb the proposed bound provides a more precise characterization of this tradeoff than that which can be obtained using existing tools e g the csb and can be viewed as a generalization of the square root bound for tail biting trellises to graphical models with arbitrary cyclic topologies searching the space of graphical models for a given code is then enabled by introducing a set of basic graphical model transformation operations that are shown to span this space finally heuristics for extracting novel graphical models for linear block codes using these transformations are investigated

visual recognition and categorization on the basis of similarities to multiple class prototypes one of the difficulties of object recognition stems from the need to overcome the variability in object appearance caused by pose and other factors such as illumination the influence of these factors can be countered by learning to interpolate between stored views of the target object taken under representative combinations of viewing conditions difficulties of another kind arise in daily life situations that require categorization rather than recognition of objects although categorization cannot rely on interpolation between stored examples we show that knowledge of several representative members or prototypes of each of the categories of interest can provide the necessary computational substrate for the categorization of new instances we describe a system that represents input shapes by their similarities to several prototypical objects and show that it can recognize new views of the familiar objects discriminate among views of previously unseen shapes and attribute the latter to familiar categories

performance of ldpc codes under faulty iterative decoding departing from traditional communication theory where decoding algorithms are assumed to perform without error a system where noise perturbs both computational devices and communication channels is considered here this paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low density parity check ldpc codes concentration of decoding performance around its average is shown to hold when noise is introduced into message passing and local computation density evolution equations for simple faulty iterative decoders are derived in one model computing nonlinear estimation thresholds shows that performance degrades smoothly as decoder noise increases but arbitrarily small probability of error is not achievable probability of error may be driven to zero in another system model the decoding threshold again decreases smoothly with decoder noise as an application of the methods developed an achievability result for reliable memory systems constructed from unreliable components is provided

pinning synchronization in t s fuzzy complex networks with partial and discrete time couplings communication constraints which may lead to the degradation of performance are common and unavoidable in a real world network in this paper two kinds of communication constraints are considered during the process of information transmission in takagi sugeno ts fuzzy complex network 1 partial couplings where only some part of nodes state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon and 2 discrete time couplings where the nodes information are sampled at certain time instants this is the first time when both communication constraints are simultaneously considered in fuzzy complex networks compared with the perfect communication much less information is available for synchronization to overcome this difficulty a regrouping method is employed to reconstruct the fuzzy network the concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete time couplings simulation examples are also provided to demonstrate the effectiveness of the theoretical results

convergence analysis of reweighted sum product algorithms markov random fields are designed to represent structured dependencies among large collections of random variables and are well suited to capture the structure of real world signals many fundamental tasks in signal processing e g smoothing denoising segmentation etc require efficient methods for computing approximate marginal probabilities over subsets of nodes in the graph the marginalization problem though solvable in linear time for graphs without cycles is computationally intractable for general graphs with cycles this intractability motivates the use of approximate ldquomessage passingrdquo algorithms this paper studies the convergence and stability properties of the family of reweighted sum product algorithms a generalization of the widely used sum product or belief propagation algorithm in which messages are adjusted with graph dependent weights for pairwise markov random fields we derive various conditions that are sufficient to ensure convergence and also provide bounds on the geometric convergence rates when specialized to the ordinary sum product algorithm these results provide strengthening of previous analyses we prove that some of our conditions are necessary and sufficient for subclasses of homogeneous models but not for general models the experimental simulations on various classes of graphs validate our theoretical results

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

similarity connectionism and the problem of representation in vision a representational scheme under which the ranking between represented similarities is isomorphic to the ranking between the corresponding shape similarities can support perfectly correct shape classification because it preserves the clustering of shapes according to the natural kinds prevailing in the external world this article discusses the computational requirements of representation that preserves similarity ranks and points out the relative straightforwardness of its connectionist implementation

sufficient conditions for convergence of the sum product algorithm novel conditions are derived that guarantee convergence of the sum product algorithm also known as loopy belief propagation or simply belief propagation bp to a unique fixed point irrespective of the initial messages for parallel synchronous updates the computational complexity of the conditions is polynomial in the number of variables in contrast with previously existing conditions our results are directly applicable to arbitrary factor graphs with discrete variables and are shown to be valid also in the case of factors containing zeros under some additional conditions the conditions are compared with existing ones numerically and if possible analytically for binary variables with pairwise interactions sufficient conditions are derived that take into account local evidence i e single variable factors and the type of pair interactions attractive or repulsive it is shown empirically that this bound outperforms existing bounds

channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels a method is proposed called channel polarization to construct code sequences that achieve the symmetric capacity i w of any given binary input discrete memoryless channel b dmc w the symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability channel polarization refers to the fact that it is possible to synthesize out of n independent copies of a given b dmc w a second set of n binary input channels wn i 1 les i les n such that as n becomes large the fraction of indices i for which i wn i is near 1 approaches i w and the fraction for which i wn i is near 0 approaches 1 i w the polarized channels wn i are well conditioned for channel coding one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining codes constructed on the basis of this idea are called polar codes the paper proves that given any b dmc w with i w 0 and any target rate r i w there exists a sequence of polar codes cfrn nges1 such that cfrn has block length n 2n rate ges r and probability of block error under successive cancellation decoding bounded as pe n r les o n 1 4 independently of the code rate this performance is achievable by encoders and decoders with complexity o n logn for each