constrained capacities for faster than nyquist signaling this paper deals with capacity computations of faster than nyquist ftn signaling it shows that the capacity of ftn is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc ftn signals can in fact achieve the ultimate capacity for the signal power spectral density psd the paper lower and upper bounds the ftn capacity under the constraint of finite input alphabet it is often higher than the capacity for comparable orthogonal pulse systems sometimes it is superior to all forms of orthogonal signaling with the same psd

capacity and performance of mimo bicm with zero forcing receivers this work considers multiple input multiple output bit interleaved coded modulation mimo bicm with linear zero forcing zf receivers we derive the link level capacity llc under ideal fast fading conditions and show that it approaches the maximum likelihood ml llc as the number of receive antennas approach infinity we also derive tight analytical bounds on the coded bit error rate and prove that with n sub t transmit and n sub r receive antennas the diversity order is n sub r n sub t 1 multiplied by the free hamming distance of the convolutional code for the case of a ml receiver we show that a tight bound is not possible in general our analysis provides insights to explain the relative performance of the zf and ml receivers finally we validate the analytical results and assess the performance in a practical environment with orthogonal frequency division multiplexing and channel estimation

bounds on the information rate of intersymbol interference channels based on mismatched receivers we consider the problem of bounding the information rate of intersymbol interference channels via simulation based algorithms the adopted approach which is based on a general class of reduced complexity receivers that includes several previously studied receivers as special cases leads to provable upper and lower bounds on the information rate of interest as a by product of the information theoretic investigations novel insights on the design of efficient reduced complexity receivers are also provided since the proposed lower bounds are known to be achievable by practical receivers in many scenarios our novel approach significantly outperforms the existing ones for all practical values of the signal to noise ratio

capacity and decoding rules for classes of arbitrarily varying channels the capacity of an arbitrarily varying channel avc is considered for deterministic codes with the average probability of error criterion and typically subject to at state constraint first sufficient conditions are provided that enable relatively simple decoding rules such as typicality maximum mutual information and minimum distance to attain capacity then the possibly noisy or channels and group adder channels are studied in detail for the former the capacity is explicitly determined and shown to be attainable by minimum distance decoding next for a large class of addictive avcs in addition to providing an intuitively suggestive simplification of the general avc capacity formula it is proven that capacity can be attained by a universal decoding rule finally the effect of random state selections on capacity is studied the merits and limitations of a previous mutual information game approach are also discussed

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

a reduced state ungerboeck type map receiver with bidirectional decision feedback for m ary quasi orthogonal signaling in this paper we propose a generic receiver based on optimum maximum likelihood sequence estimation mlse employing a generalized ungerboeck metric with significantly reduced complexity for the general class of m ary quasi orthogonal signaling mos in severe multipath fading channels first by using the factor graph fg of the obtained generalized ungerboeck metric for mos and sum product algorithm spa framework a highly efficient reduced state sequence estimation rsse algorithm is proposed that operates on forward and backward directions and is directly applied to unwhitened channel matched filter cmf and code matched filter outputs at symbol rate the proposed structure generating the a posteriori probabilities app by bidirectional rsse recursions are substantiated with symbol rate bidirectional decision feedback bdf based on surviving paths in order to eliminate the post and pre cursor inter symbol interference isi as well as multi code interference mci due to the non ideal properties of the signaling waveforms and multipath channel it appears as the unification of ungerboeck type reduced trellis equalization framework for mos and achieves near optimum performance especially for channels with large dispersion second we identify a bias term through an error probability analysis which helps us improve the proposed receiver s performance furthermore a tight approximation for the bit error rate ber of the proposed receiver is derived these analyses lead to significant insight on the selection of system parameters and clearly demonstrate the high performance and efficiency of the proposed scheme by a proper choice of the signaling parameters

mixed finite element methods for quasilinear second order elliptic problems a mixed finite element method is developed to approximate the solution of a quasilinear second order elliptic partial differential equation the existence and uniqueness of the approximation are demonstrated and optimal rate error estimates are derived

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

on approximability of optimization problems related to red blue split graphs abstract an edge bicolored graph g v r b is called red blue split graph if there exists a partition i b and i r of v such that i b and i r are independent sets in v b and v r respectively red blue split graphs generalize several well studied graph classes including split graphs bipartite graphs and konig egervary graphs in this paper we consider the algorithmic complexity of various optimization problems like minimum edge or vertex deletion and maximum edge or vertex induced subgraph related to red blue split graphs all these problems are np hard and thus we look at them from algorithmic paradigms that are meant for coping with np hardness we obtain various hardness as well as algorithmic results for these problems in the realm of approximation algorithms and parameterized complexity the main tool we use to obtain all our results is polynomial time transformations between appropriate problems on the way we also resolve some problems related to inapproximability about certain optimization problems mentioned by korach et al 2006 17

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

efficiently computed reduced parameter input aided mmse equalizers for ml detection a unified approach a unified approach for computing the optimum settings of a length n sub f input aided equalizer that minimizes the mean square error between the equalized channel impulse response and a target impulse response of a given length n sub b is presented this approach offers more insight into the problem easily accommodates correlation in the input and noise sequences leads to significant computational savings and allows us to analyze a variety of constraints on the target impulse response besides the standard unit tap constraint in particular we show that imposing a unit energy constraint results in a lower mean square error at a comparable computational complexity furthermore we show that under the assumed constraint of finite length filters the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance we describe a new characterization of the optimum delay and show how to compute it finally we derive reduced parameter pole zero models of the equalizer that achieve the high performance of a long all zero equalizer at a much lower implementation cost

mixed covolume methods for quasi linear second order elliptic problems we consider covolume methods for the mixed formulations of quasi linear second order elliptic problems covolume methods for the mixed formulations of linear elliptic problem was first considered by russell rigorous block centered discretizations on irregular grids improved simulation of complex reservoir systems tech report 3 project report reservoir simulation research corporation tulsa ok 1995 and tested extensively in cai et al comput geosci 1 1997 pp 289 315 jones a mixed finite volume element method for accurate computation of fluid velocities in porous media ph d thesis university of colorado denver 1995 the analysis was carried out by chou and kwak siam j numer anal 37 2000 pp 758 771 for linear symmetric problems where they showed optimal error estimates in l2 norm for the pressure and in h div norm for the velocity in this paper we extend their results to quasi linear problems by following milner s argument math comp 44 1985 pp 303 320 through an adaptation of the duality argument of douglas and roberts math comp 44 1985 pp 39 52 for mixed covolume methods

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

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

optimal transmit filters for isi channels under channel shortening detection we consider channels affected by intersymbol interference with reduced complexity mutual information optimized channel shortening detection for such settings we optimize the transmit filter taking into consideration the reduced receiver complexity constraint as figure of merit we consider the achievable information rate of the entire system and with functional analysis we establish a general form of the optimal transmit filter which can then be optimized by standard numerical methods as a corollary to our main result we obtain some insight of the behavior of the standard waterfilling algorithm for intersymbol interference channels with only some minor changes the general form we derive can be applied to multiple input multiple output channels with intersymbol interference to illuminate the practical use of our results we provide applications of our theoretical results by deriving the optimal shaping pulse of a linear modulation transmitted over a bandlimited additive white gaussian noise channel which has possible applications in the faster than nyquist time packing technique

an expanded mixed finite element method for two dimensional sobolev equations abstract in this paper we provide an expanded mixed finite element method for a class of two dimensional sobolev equations the optimal error estimates for a semi discrete scheme and a fully discrete scheme are obtained also numerical examples are stated to verify our theoretical results

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

computing the sign or the value of the determinant of an integer matrix a complexity survey computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods we survey the complexity of existing methods to solve these problems when the input is an n n matrix a with integer entries we study the bit complexities of the algorithms asymptotically in n and the norm of a existing approaches rely on numerical approximate computations on exact computations or on both types of arithmetic in combination

mixed finite element methods for nonlinear second order elliptic problems mixed finite element methods are developed to approximate the solution of the dirichlet problem for the most general quasi linear second order elliptic operator in divergence form existence and uniqueness of the approximation are proved and optimal error estimates in l 2 are demonstrated for both the scalar and vector functions approximated by the method error estimates are also derived in l q 2 leq q leq infty newton s method is presented and analyzed to solve the nonlinear algebraic equations

a two grid algorithm for expanded mixed finite element approximations of semi linear elliptic equations a semi linear elliptic problem with variable coefficient is approximated by expanded mixed formulation based on the rtn and bdm mixed finite elements in order to solve the nonlinear approximation system of equations efficiently a two grid algorithm is considered and discussed in this paper the work includes a small nonlinear system on a coarse grid space with mesh size h and a linear system on a fine grid space with mesh size h it follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy h o h 1 2 in the l 2 norm some numerical examples are presented to illustrate the theoretical results

maximum multipath diversity with linear equalization in precoded ofdm systems in wireless communications the fading multipath channel attenuates and distorts the transmitted signal to decode the transmitted symbols and take advantage of the full multipath diversity that the channel has to offer computationally complex maximum likelihood ml decoding is often employed we show that a linear equalizer followed by a hard decision is capable of benefiting from maximum multipath diversity in linearly precoded orthogonal frequency division multiplexing ofdm systems where the information symbols are mapped through a matrix transformation before the inverse fast fourier transform ifft at the ofdm transmitter as far as we are aware this is the first proof of a linear equalization scheme achieving maximum multipath diversity over single input single output wireless links we can conclude from this result that at sufficiently high signal to noise ratios snr precoded ofdm systems will perform better over channels with more taps even with linear equalization due to the increase in diversity order

bit interleaved coded modulation revisited a mismatched decoding perspective we revisit the information theoretic analysis of bit interleaved coded modulation bicm by modeling the bicm decoder as a mismatched decoder the mismatched decoding model is well defined for finite yet arbitrary block lengths and naturally captures the channel memory among the bits belonging to the same symbol we give two independent proofs of the achievability of the bicm capacity calculated by caire et al where bicm was modeled as a set of independent parallel binary input channels whose output is the bitwise log likelihood ratio our first achievability proof uses typical sequences and shows that due to the random coding construction the interleaver is not required the second proof is based on the random coding error exponents with mismatched decoding where the largest achievable rate is the generalized mutual information moreover the generalized mutual information of the mismatched decoder coincides with the infinite interleaver bicm capacity we show that the error exponent and hence the cutoff rate of the bicm mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite interleaved model for binary reflected gray mapping in gaussian channels the loss in error exponent is small we also consider the mutual information appearing in the analysis of iterative decoding of bicm with extrinsic information transfer exit charts if the symbol metric has knowledge of the transmitted symbol exit mutual information admits a representation as a pseudo generalized mutual information which is in general not achievable a different symbol decoding metric for which the extrinsic side information refers to the hypothesized symbol induces a generalized mutual information lower than the coded modulation capacity in this case perfect extrinsic side information turns the mismatched decoder error exponent into that of coded modulation

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

optimization of information rate upper and lower bounds for channels with memory we consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete time channels with memory the channels we consider can have a finite number of states such as partial response channels or they can have an infinite state space such as time varying fading channels we optimize recently proposed information rate bounds for such channels which make use of auxiliary finite state machine channels fsmcs our main contribution in this paper is to provide iterative expectation maximization em type algorithms to optimize the parameters of the auxiliary fsmc to tighten these bounds we provide an explicit iterative algorithm that improves the upper bound at each iteration we also provide an effective method for iteratively optimizing the lower bound to demonstrate the effectiveness of our algorithms we provide several examples of partial response and fading channels where the proposed optimization techniques significantly tighten the initial upper and lower bounds finally we compare our results with results obtained by the conjugate gradient optimization algorithm and an improved variation of the simplex algorithm called soblex while the computational complexities of our algorithms are similar to the conjugate gradient method and less than the soblex algorithm our algorithms robustly find the tightest bounds interestingly from a channel coding decoding perspective optimizing the lower bound is related to increasing the achievable mismatched information rate i e the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel and not to the original channel

nearest neighbor decoding for additive non gaussian noise channels we study the performance of a transmission scheme employing random gaussian codebooks and nearest neighbor decoding over a power limited additive non gaussian noise channel we show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white gaussian noise channel with signal and noise power equal to those of the original channel the results are presented for single user channels as well as multiple access channels and are extended to fading channels with side information at the receiver

space time block coding for doubly selective channels in this paper we present a new space time block code for time and frequency selective doubly selective channels it can be interpreted as the extension of the alamouti code to doubly selective channels and relies on a joint time frequency reversal of the transmitted sequences under certain channel conditions the proposed space time block code belongs to the class that achieves full spatial delay and doppler diversity using a maximum likelihood ml receiver as well as a linear zero forcing lzf or linear minimum mean squared error lmmse receiver for realistic doubly selective channels a real valued linear data model is presented for which different receiver structures can be developed

performance analysis of turbo equalized partial response channels the performance of maximum likelihood decoding of a serial concatenation comprising a high rate block code convolutional code or a turbo code a uniform interleaver and a partial response channel with additive white gaussian noise is addressed the effect of a channel precoder on the system performance is also considered bit and word error rate estimates based upon properties of the average euclidean distance spectrum of the coded partial response channel are derived the estimates are compared to computer simulation results and implications for system design are discussed

gaussian codes and weighted nearest neighbor decoding in fading multiple antenna channels we investigate the fading multiple antenna channel the decoder is assumed to possess imperfect channel fading information a modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information gmi the achievable rate is obtained we show that under certain conditions the achievable rate is equivalent to that of a fading multiple antenna gaussian channel where fading is known to the receiver and is equal to the channel estimation and where noise is due to both the channel noise and the channel estimation error we show that for our communication scheme the minimum mean square error mmse channel estimator is optimal in the sense that it achieves the highest value of gmi and hence the highest communication rate additionally a training based multiple input multiple output mimo scheme in a block fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal to noise ratio snr

variations on the gallager bounds connections and applications there has been renewed interest in deriving tight bounds on the error performance of specific codes and ensembles based on their distance spectrum we discuss many reported upper bounds on the maximum likelihood ml decoding error probability and demonstrate the underlying connections that exist between them in addressing the gallager bounds and their variations we focus on the duman and salehi see ieee trans commun vol 46 p 717 723 1998 variation which originates from the standard gallager bound a large class of efficient bounds or their chernoff versions is demonstrated to be a special case of the generalized second version of the duman and salehi bounds implications and applications of these observations are pointed out including the fully interleaved fading channel resorting to either matched or mismatched decoding the proposed approach can be generalized to geometrically uniform nonbinary codes finite state channels bit interleaved coded modulation systems and it can be also used for the derivation of upper bounds on the conditional decoding error probability

a converse coding theorem for mismatched decoding at the output of binary input memoryless channels an upper bound on the maximal transmission rate over binary input memoryless channels provided that the decoding decision rule is given is derived if the decision rule is equivalent to the maximum likelihood decoding matched decoding then the bound coincides with the channel capacity otherwise mismatched decoding it coincides with a known lower bound

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

a counter example to the mismatched decoding converse for binary input discrete memoryless channels this paper studies the mismatched decoding problem for binary input discrete memoryless channels an example is provided for which an achievable rate based on superposition coding exceeds the csiszar korner hui rate thus providing a counter example to a previously reported converse result both numerical evaluations and theoretical results are used in establishing this claim

time frequency packing for linear modulations spectral efficiency and practical detection schemes we investigate the spectral efficiency achievable by a low complexity symbol by symbol receiver when linear modulations based on the superposition of uniformly time and frequency shifted replicas of a base pulse are employed although orthogonal signaling with gaussian inputs achieves capacity on the additive white gaussian noise channel we show that when finite order constellations are employed by giving up the orthogonality condition thus accepting interference among adjacent signals we can considerably improve the performance even when a symbol by symbol receiver is used we also optimize the spacing between adjacent signals to maximize the achievable spectral efficiency moreover we propose a more involved transmission scheme consisting of the superposition of two independent signals with suitable power allocation and a two stage receiver showing that it allows a further increase of the spectral efficiency finally we show that a more involved equalization algorithm based on soft interference cancellation allows to achieve an excellent bit error rate performance even when error correcting codes designed for the gaussian noise limited channel are employed and thus does not require a complete redesign of the coding scheme

harmonic mean and end to end performance of transmission systems with relays closed form expressions for the statistics of the harmonic mean of two independent and identically distributed gamma variates are presented the probability density function of the harmonic mean of two f variates is also derived these statistical results are then applied to study the performance of wireless communication systems with nonregenerative relays over flat nakagami fading channels more specifically outage probability formulas for noise limited systems as well as systems affected by interference are obtained furthermore general expressions for average bit error rates are also derived finally comparisons between regenerative and nonregenerative systems are presented numerical results show that the former systems clearly outperform the latter ones for low average signal to noise ratios snrs they also show that the two systems have similar performance at high average snrs

characteristic mixed discontinuous finite element methods for advection dominated diffusion problems abstract in this paper three characteristic mixed discontinuous finite element methods are introduced for time dependent advection dominated diffusion problems namely the diffusion term in these problems is discretized using mixed discontinuous finite elements and the temporal differentiation and advection terms are treated by a characteristic tracking scheme the first method is based on the standard modified method of characteristics it is simple to set up and analyze but fails to preserve an integral identity satisfied by the solution of the differential problems the second method is formulated using the modified method of characteristics with adjusted advection and preserves the integral identity globally the third method is defined in terms of a local eulerian lagrangian technique and preserves the identity locally these three methods not only preserve the conceptual and computational merits of both characteristics based procedures and discontinuous finite element schemes they also possess new features such as they are more stable are more accurate and can handle the case where the diffusion coefficient is zero stability and convergence properties are studied for all three methods unconditionally stable results and sharp error estimates are established their relationships to standard characteristics based methods such as mmoc mmocaa ellam and cmfem are described in detail numerical results are presented

diversity analysis for linear equalizers over isi channels it has been shown in the literature that with zero padding prefix zpp the optimum diversity gain of frequency selective channels can be obtained by uncoded signals and zero forcing zf equalizers in this paper we derive two important results about linear equalizers over frequency selective channels 1 with cyclic prefix and any rate 1 unitary precoding which includes the uncoded coded ofdm scfdma systems as special cases linear equalizers can only obtain order 1 diversity and 2 although linear equalizers can achieve the optimum diversity order with zero padding prefix and uncoded signals the required snr signal to noise ratio is an increasing function of the symbol length the second result implies that we may not be able to take advantage of the diversity gain in practice due to the high snr requirements special cases are also investigated to gain some physical insights about the effects of different prefixes on the performance of linear equalizers the results in this paper can be utilized in the design of up down link lte systems with linear equalizers

diversity multiplexing tradeoff in isi channels the optimal diversity multiplexing tradeoff curve for the intersymbol interference isi channel is computed and various equalizers are analyzed using this performance metric maximum likelihood signal decoding mlsd and decision feedback equalization dfe equalizers achieve the optimal tradeoff without coding but zero forcing zf and minimum mean square error mmse equalizers do not however if each transmission block is ended with a period of silence lasting the coherence time of the channel both zf and mmse equalizers become diversity multiplexing optimal this suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency division multiplexing ofdm or viterbi can be realized in much simpler fashion with a small modification to the transmit scheme

arbitrarily varying channels with general alphabets and states previous results of csiszar and narayan 1988 1989 1991 on the capacity of discrete arbitrarily varying channels with input and state constraints are extended to the case of arbitrary alphabets and state sets for channels with scalar or vector inputs and additive interference consisting of a deterministic part and noise both arbitrarily varying subject to power constraints the capacity for deterministic codes is shown to be equal to the random coding capacity if the input power exceeds the power of the deterministic interference and zero otherwise explicit capacity formulas are also given

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

integer metrics for binary input symmetric output memoryless channels consider a coded communication system where antipodal signaling is used over symmetric memoryless channels a mismatch decoder employing metrics which assume values in a finite set of integers is used two performance measures for achievable rates are considered the generalized cutoff rate and the mismatch capacity two different integer metric assignments which maximize these criteria are found the optimal metric assignment holds for any binary input symmetric output memoryless channels it is calculated explicitly for the faded additive white gaussian noise channel with and without diversity an interference channel model and the additive cauchy channel the difference in terms of achievable rates between decoding using the optimal continuous metric and integer metric is calculated for these channels the degradation for fairly low number of quantization levels is found to be small e g for nine quantization levels degradation is less than 0 3 db for all analyzed channels the sensitivity of the generalized cutoff rate and the mismatch capacity to the exact location of the quantization levels is rather mild the difference between the mismatch capacity corresponding to the optimal integer quantization and the mismatch capacity obtained by the quantization which optimizes the generalized cutoff rate is found to be quite small

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

a rate splitting approach to fading channels with imperfect channel state information as shown by medard the capacity of fading channels with imperfect channel state information can be lower bounded by assuming a gaussian channel input x with power p and by upper bounding the conditional entropy h x y hat h by the entropy of a gaussian random variable with variance equal to the linear minimum mean square error in estimating x from y hat h we demonstrate that using a rate splitting approach this lower bound can be sharpened by expressing the gaussian input x as the sum of two independent gaussian variables x 1 and x 2 and by applying medard s lower bound first to bound the mutual information between x 1 and y while treating x 2 as noise and by applying it a second time to the mutual information between x 2 and y while assuming x 1 to be known we obtain a capacity lower bound that is strictly larger than medard s lower bound we then generalize this approach to an arbitrary number l of layers where x is expressed as the sum of l independent gaussian random variables of respective variances p ell ell 1 dotsc l summing up to p among all such rate splitting bounds we determine the supremum over power allocations p ell and total number of layers l this supremum is achieved for l rightarrow infty and gives rise to an analytically expressible capacity lower bound for gaussian fading this novel bound is shown to converge to the gaussian input mutual information as the signal to noise ratio snr grows provided that the variance of the channel estimation error h hat h tends to zero as the snr tends to infinity

simulation based computation of information rates for channels with memory the information rate of finite state source channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence followed by a forward sum product recursion on the joint source channel trellis this method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite state approximations further upper and lower bounds can be computed by reduced state methods

suboptimal and optimal convergence in mixed finite element methods an elliptic partial differential equation may be formulated in different but equivalent ways and the mixed finite element methods derived from these formulations have different properties we give general error estimates for two such methods which are always optimal for the raviart thomas elements but which are suboptimal for the brezzi douglas marini elements in one of the methods computational experiments show that this suboptimal estimate is sharp

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

multiscale mortar expanded mixed discretization of nonlinear elliptic problems abstract we consider the discretization of nonlinear second order elliptic partial differential equations by multiscale mortar expanded mixed method this is a domain decomposition method in which the model problem is restricted to the small pieces by dividing the computational domain into the non overlapping subdomains an unknown lagrange multiplier is introduced on the interfaces which serve as pressure dirichlet boundary condition for local subdomain problems a finite element space is defined on interface to approximate the pressure boundary such that the normal fluxes match weakly on interface we demonstrated solvability of discretization and established a priori l2 error estimates for both vector and scalar approximations we proved the optimal order convergence rates by an appropriate choice of mortar space and polynomial degree of approximation the uniqueness of discrete problem is shown for sufficiently small values of mesh size an error estimate for the mortar pressure is derived via linear interface formulation with pressure dependent coefficient we also present the analysis of the linear second order elliptic problem and prove the similar results the computational experiments are presented to validate theory

performance of single carrier block transmissions over multipath fading channels with linear equalization we study uncoded bit error rate ber performances of single carrier block transmissions zero padded zp and cyclic prefixed cp transmission when linear equalizers are applied and the bers are averaged over one block we show analytically that the ber of zp transmission with linear equalization degrades as the bandwidth efficiency increases i e there is a tradeoff between ber and bandwidth efficiency in zp transmission it is also proven that when minimum mean squared error mmse equalization is adopted zp transmission outperforms cp transmission and uncoded orthogonal frequency division multiplexing ofdm on the average over random channels however the difference between the zp and the cp transmission becomes smaller as the block size gets larger since the average ber performance of the zp transmission degrades while the average ber performance of cp transmission improves as a function of the block size numerical examples are provided to validate our theoretical findings and to compare the block transmission systems

on performance of vector ofdm with linear receivers vector orthogonal frequency division multiplexing ofdm for single transmit antenna systems is a general transmission scheme where ofdm and single carrier frequency domain equalization sc fde can be treated as two special extreme cases due to its flexibility it has drawn more and more attention recently so far all the studies about vector ofdm assume the maximum likelihood ml receiver in this paper we investigate the performance of vector ofdm with linear receivers i e the zero forcing zf and minimum mean square error mmse receivers we first show that the detection snr gap between the mmse and zf receivers increases with both channel snr and the vector blocks vb size defined in vector ofdm then it is proved that for both zf and mmse receivers all the transmitted symbols have equal performance this is different from the vector ofdm with ml receiver where different vbs may have different coding gain and thus may have different performances we analyze the diversity order for vector ofdm with mmse receiver and show that regardless of the vector ofdm symbol length n the diversity order can be represented as min m2 r d 1 where m is the vb size r is the spectrum efficiency in bits symbol and d is the maximum delay of the multipath channel for vector ofdm with zf receiver we show that the diversity order equals 1 and the performance is the same as the conventional ofdm at high snr

a soft output mimo detector with achievable information rate based partial marginalization in this paper we propose a soft output detector for multiple input multiple output mimo channels that utilizes achievable information rate air based partial marginalization pm the proposed air based pm air pm detector has superior performance compared to previously proposed pm designs and other soft output detectors such as k best while at the same time yielding lower computational complexity a detection latency that is independent of the number of transmit layers and straightforward inclusion of soft input information using a tree representation of the mimo signal the key property of the airpm is that the connections among all child layers are broken therefore least square ls estimates used for marginalization are obtained independently and in parallel which have better quality than the zero forcing decision feedback zf df estimates used in previous pm designs such a property of the airpm detector is designed via a mismatched detection model that maximizes the air furthermore we show that the chain rule holds for the air calculation which facilitates an information theoretic characterization of the air pm detector less

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

dual capacity upper bounds for binary input single tap isi channels the capacity of noisy channels with memory and finite input has been difficult to characterize explicitly in many cases in this paper we consider single tap binary input gaussian channels with inter symbol interference isi the dual capacity method is used to obtain upper bounds using markov test distributions the bound expressed as a single letter optimization problem is solved numerically for higher memory the notion of cycle basis is used to provide an exponential reduction in the computational complexity of the optimization problem bounds were obtained for the important case of the dicode channel and these are better than the previously known upper bounds and are close to achievable rates over a wide range of snrs

design and analysis of successive decoding with finite levels for the markov channel this paper proposes a practical successive decoding scheme with finite levels for the finite state markov channels fsmcs where there is no a priori state information at the transmitter or the receiver the design employs either a random interleaver or a deterministic interleaver with an irregular pattern and an optional iterative estimation and decoding procedure within each level the interleaver design criteria may be the achievable rate or the extrinsic information transfer exit chart depending on the receiver type for random interleavers the optimization problem is solved efficiently using a pilot utility function while for deterministic interleavers a good construction is given using empirical rules simulation results demonstrate that the new successive decoding scheme combined with irregular low density parity check ldpc codes can approach the identically and uniformly distributed i u d input capacity on the markov fading channel using only a few levels

orthogonal codes for robust low cost communication orthogonal coding schemes known to asymptotically achieve the capacity per unit cost cpuc for single user ergodic memoryless channels with a zero cost input symbol are investigated for single user compound memoryless channels which exhibit uncertainties in their input output statistical relationships a minimax formulation is adopted to attain robustness first a class of achievable rates per unit cost arpuc is derived and its utility is demonstrated through several representative case studies second when the uncertainty set of channel transition statistics satisfies a convexity property optimization is performed over the class of arpuc through utilizing results of minimax robustness the resulting cpuc lower bound indicates the ultimate performance of the orthogonal coding scheme and coincides with the cpuc under certain restrictive conditions finally still under the convexity property it is shown that the cpuc can generally be achieved through utilizing a so called mixed strategy in which an orthogonal code contains an appropriate composition of different nonzero cost input symbols

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

finite element approximation of a nonlinear heat conduction problem in anisotropic media abstract this paper is a survey of results which we have obtained in solving a stationary nonlinear heat conduction problem by the finite element method in particular we present uniqueness theorems for the classical and weak solutions a comparison theorem existence theorems for the weak and finite element solutions approximation of a curved boundary and numerical integration a discrete maximum principle convergence without any regularity assumptions a priori error estimates nonlinear boundary conditions and numerical algorithms

domain decomposition algorithms for mixed methods for second order elliptic problems domain decomposition algorithms for mixed finite element methods for linear second order elliptic problems in r 2 and r 3 are developed a convergence theory for two level and multilevel schwarz methods applied to the algorithms under consideration is given it is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems numerical experiments are presented to illustrate the present techniques

a general framework for transmission with transceiver distortion and some applications a general theoretical framework is presented for analyzing information transmission over gaussian channels with memoryless transceiver distortion which encompasses various nonlinear distortion models including transmit side clipping receive side analog to digital conversion and others the framework is based on the so called generalized mutual information gmi and the analysis in particular benefits from the setup of gaussian codebook ensemble and nearest neighbor decoding for which it is established that the gmi takes a general form analogous to the channel capacity of undistorted gaussian channels with a reduced effective signal to noise ratio snr that depends on the nominal snr and the distortion model when applied to specific distortion models an array of results of engineering relevance is obtained for channels with transmit side distortion only it is shown that a conventional approach which treats the distorted signal as the sum of the original signal part and a uncorrelated distortion part achieves the gmi for channels with output quantization closed form expressions are obtained for the effective snr and the gmi and related optimization problems are formulated and solved for quantizer design finally super nyquist sampling is analyzed within the general framework and it is shown that sampling beyond the nyquist rate increases the gmi for all snr values for example with binary symmetric output quantization information rates exceeding one bit per channel use are achievable by sampling the output at four times the nyquist rate

multiuser random coding techniques for mismatched decoding this paper studies multiuser random coding techniques for channel coding with a given possibly suboptimal decoding rule for the mismatched discrete memoryless multiple access channel an error exponent is obtained that is tight with respect to the ensemble average and positive within the interior of lapidoth s achievable rate region this exponent proves the ensemble tightness of the exponent of liu and hughes in the case of maximum likelihood decoding an equivalent dual form of lapidoth s achievable rate region is given and the latter is shown to immediately extend to channels with infinite and continuous alphabets in the setting of single user mismatched decoding similar analysis techniques are applied to a refined version of superposition coding which is shown to achieve rates at least as high as standard superposition coding for any set of random coding parameters

on the low rate shannon limit for binary intersymbol interference channels for a discrete time binary input gaussian channel with finite intersymbol interference we prove that reliable communication can be achieved if and only if e sub b n sub 0 log2 g sub opt for some constant g sub opt that depends on the channel to determine this constant we consider the finite state machine which represents the output sequences of the channel filter when driven by binary inputs we then define g sub opt as the maximum output power achieved by a simple cycle in this graph and show that no other cycle or asymptotically long sequence can achieve an output power greater than this we provide examples where the binary input constraint leads to a suboptimality and other cases where binary signaling is just as effective as real signaling at very low signal to noise ratios

enhanced cell centered finite differences for elliptic equations on general geometry we present an expanded mixed finite element method for solving second order elliptic partial differential equations on geometrically general domains for the lowest order raviart thomas approximating spaces we use quadrature rules to reduce the method to cell centered finite differences possibly enhanced with some face centered pressures this substantially reduces the computational complexity of the problem to a symmetric positive definite system for essentially only as many unknowns as elements our new method handles general shape elements triangles quadrilaterals and hexahedra and full tensor coefficients while the standard mixed formulation reduces to finite differences only in special cases with rectangular elements as in other mixed methods we maintain the local approximation of the divergence i e local mass conservation in contrast galerkin finite element methods facilitate general element shapes at the cost of achieving only global mass conservation our method is shown to be as accurate as the standard mixed method for a large class of smooth meshes on nonsmooth meshes or with nonsmooth coefficients one can add lagrange multiplier pressure unknowns on certain element edges or faces this enhanced cell centered procedure recovers full accuracy with little additional cost if the coefficients or mesh geometry are piecewise smooth theoretical error estimates and numerical examples are given illustrating the accuracy and efficiency of the methods

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

ratio list decoding we extend the notion of list decoding to ratio list decoding which involves a list decoder whose list size is specified as a function of the number of messages m n and the block length n we present the necessary and sufficient conditions on m n for the existence of code sequences which enable reliable list decoding with respect to the desired list size l m n n it is shown that the ratio capacity defined as the supremum of achievable normalized logarithms of the ratio r m n n m n l m n n is equal to the shannon channel capacity c for both stochastic and deterministic encoding allowing for random list size we are able to deduce some properties of identification codes where the decoder s output can be viewed as a list of messages corresponding to decision regions that include the channel output we further address the regime of mismatched list decoding in which the list constitutes of the codewords that accumulate the highest score values jointly with the channel output according to some given function we study the case of deterministic encoding and mismatched ratio list decoding we establish similar necessary and sufficient conditions for the existence of code sequences which enable reliable mismatched list decoding with respect to the desired list size l m n n and we show that the ratio capacity with mismatched decoding is equal to the mismatch capacity focusing on the case of an exponential list size l n e n theta its comparison with ordinary mismatched decoding shows that the increase in capacity is by theta bits per channel used for all channels and decoding metrics several properties of the average error probability in the setup of mismatched list decoding with deterministic list size are provided

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

an effective implementation for stokes equation by the weak galerkin finite element method abstract in this paper we introduce and analyze the schur complement technique to a weak galerkin wg for short finite element method for solving stokes equation due to the special structure of the weak functions the main idea of schur decomposition method is to express the interior velocity functions defined inside partition elements in terms of the velocity functions defined on the partition boundary and the pressure functions this can largely reduce the degree of freedom of the derived discrete linear system we investigate the well posedness of the solution generated from schur complement and its coincidence with the standard wg method finally we exhibit some numerical experiments to illustrate the theoretical analysis

the strong ergodic theorem for densities generalized shannon mcmillan breiman theorem let xi x2 be a stationary process with probability densities f x1 x2 xn with respect to lebesgue measure or with respect to a markov measure with a stationary transition measure it is shown that the sequence of relative entropy densities 1 n log f xi x2 x0 converges almost surely this long conjectured result extends the l convergence obtained by moy perez and kieffer and generalizes the shannon mcmillanbreiman theorem to nondiscrete processes the heart of the proof is a new martingale inequality which shows that logarithms of densities are l dominated

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

generalized tangential sphere bound on the ml decoding error probability of linear binary block codes in awgn interference the error probability of maximum likelihood ml soft decision decoded binary block codes rarely accepts nice closed forms in addition for long codes ml decoding becomes prohibitively complex nevertheless bounds on the performance of ml decoded systems provide insight into the effect of system parameters on the overall system performance as well as a measure of goodness of the suboptimum decoding methods used in practice using the so called gallager s first bounding technique involving a so called gallager region and within the framework of tangential sphere bound tsb of poltyrev we develop a general bound referred to as the generalized tsb gtsb the gallager region is chosen to be a general hyper surface of revolution hsr which is optimized to tighten the bound the search for the optimal gallager region is a classical problem dating back to gallager s thesis in the early 1960s for the random coding case gallager provided the optimal solution in a closed form while for the nonrandom case the problem has been an active area of research in information theory for many years we prove that for a sphere code the optimal hsr within the proposed gtsb is a hyper cone this will climax to the tsb of poltyrev one of the tightest bounds ever developed for binary block codes and therefore terminates the search for a better gallager region in the groundwork of the gtsb

on achievable rates and error exponents for channels with mismatched decoding the problem of characterizing achievable rates and error exponents for discrete memoryless channels with mismatched decoding is addressed a mismatched cognitive multiple access channel is introduced and an inner bound on its capacity region is derived using two alternative encoding methods 1 superposition coding and 2 random binning the inner bounds are derived by analyzing the average error probability of the code ensemble for both methods and by a tight characterization of the resulting error exponents random coding converse theorems are also derived a comparison of the achievable regions shows that in the matched case random binning performs as well as superposition coding i e the region achievable by random binning is equal to the capacity region the achievability results are further specialized to obtain a lower bound on the mismatch capacity of the single user channel by investigating a cognitive multiple access channel whose achievable sum rate serves as a lower bound on the single user channel s capacity while the achievable rate presented here may not improve the rate achieved by lapidoth s scheme in optimizing over the parameters of the random coding scheme it can improve the achieved rate for given parameters and thereby may reduce the computational complexity required to find a good code

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

on the hardness of approximating minimum vertex cover we prove the minimum vertex cover problem to be np hard to approximate to within a factor of 1 3606 extending on previous pcp and hardness of approximation technique to that end one needs to develop a new proof framework and to borrow and extend ideas from several fields

achievable rates for nonlinear volterra channels random coding theorems and achievable rates for nonlinear additive noise channels are presented modeling the channel s nonlinear behavior as a causal stationary volterra system upper bounds on the average error probability are obtained for maximum likelihood and weakly typical set decoding the proposed bounds are deduced by treating correct decoding regions as subspaces of high concentration measure and deploying exponential martingale inequalities due to the union bound effect and the i i d assumption imposed on the codewords components the deduced exponents constitute only lower bounds on the true random coding exponents of nonlinear channels cubic and fourth order nonlinearities are used as examples to illustrate the relation of the random coding exponents and achievable rates with respect to the channel s parameters

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

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

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

matched information rate codes for partial response channels in this paper we design capacity approaching codes for partial response channels the codes are constructed as concatenations of inner trellis codes and outer low density parity check ldpc codes unlike previous constructions of trellis codes for partial response channels we disregard any algebraic properties e g the minimum distance or the run length limit in our design of the trellis code our design is purely probabilistic in that we construct the inner trellis code to mimic the transition probabilities of a markov process that achieves a high capacity approaching information rate hence we name it a matched information rate mir design we provide a set of five design rules for constructions of capacity approaching mir inner trellis codes we optimize the outer ldpc code using density evolution tools specially modified to fit the superchannel consisting of the inner mir trellis code concatenated with the partial response channel using this strategy we design degree sequences of irregular ldpc codes whose noise tolerance thresholds are only fractions of a decibel away from the capacity examples of code constructions are shown for channels both with and without spectral nulls

bdm mixed methods for a linear elliptic problem abstract a new mixed formulation is introduced to approximate the solution of a nonlinear elliptic problem based on the brezzi douglas marini mixed finite elements the existence and uniqueness of solutions of the mixed formulation and its discretization are demonstrated optimal error estimates in l 2 l and h s are derived numerical results are presented to compare the present approach with the standard one and to justify the theoretical results obtained here

a general formula for the mismatch capacity the fundamental limits of channels with mismatched decoding are addressed a general formula is established for the mismatch capacity of a general channel defined as a sequence of conditional distributions with a general decoding metrics sequence we deduce an identity between the verdu han general channel capacity formula and the mismatch capacity formula applied to maximum likelihood decoding metric furthermore several upper bounds on the capacity are provided and a simpler expression for a lower bound is derived for the case of a non negative decoding metric the general formula is specialized to the case of finite input and output alphabet channels with a type dependent metric the closely related problem of threshold mismatched decoding is also studied and a general expression for the threshold mismatch capacity is obtained as an example of threshold mismatch capacity we state a general expression for the erasures only capacity of the finite input and output alphabet channel we observe that for every channel there exists a matched threshold decoder which is capacity achieving in addition necessary and sufficient conditions are stated for a channel to have a strong converse

exploiting faster than nyquist signaling faster than nyquist signaling introduces intersymbol interference but increases the bit rate while preserving the signaling bandwidth for sinc pulses it has been established that with a small increase in the signaling rate beyond the nyquist rate there is no reduction in the minimum euclidean distance for binary signaling we generalize these observations to the family of raised cosine pulses the structure of the error events that reduce the minimum distance is examined and constrained coding ideas are suggested that theoretically allow even faster signaling then we propose ways of achieving these gains practically by designing appropriate constrained codes and through equalization and iterative joint equalization and decoding turbo equalization