on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

on clusterings good bad and spectral we motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures a simple recursive heuristic is shown to have poly logarithmic worst case guarantees under the new measure the main result of the article is the analysis of a popular spectral algorithm one variant of spectral clustering turns out to have effective worst case guarantees another finds a good clustering if one exists

a local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning we study the design of local algorithms for massive graphs a local graph algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph we present a local clustering algorithm our algorithm finds a good cluster a subset of vertices whose internal connections are significantly richer than its external connections near a given vertex the running time of our algorithm when it finds a nonempty local cluster is nearly linear in the size of the cluster it outputs the running time of our algorithm also depends polylogarithmically on the size of the graph and polynomially on the conductance of the cluster it produces our clustering algorithm could be a useful primitive for handling massive graphs such as social networks and web graphs as an application of this clustering algorithm we present a partitioning algorithm that finds an approximate sparsest cut with nearly optimal balance our algorithm takes time nearly linear in the number edges of the graph

large scale mimo detection using mcmc approach with blockwise sampling in this paper a low complexity approach for the large scale underdetermined multiple input multiple output mimo detection is proposed using the markov chain monte carlo mcmc algorithm in conjunction with blockwise sampling klein s algorithm is employed in each sub system to draw multidimensional samples for an mcmc detector in iterative detection and decoding idd from analysis we find that the lattice reduction lr technique cannot improve the performance of the proposed mcmc based approach under low correlated channel environment in addition due to blockwise sampling the proposed method exhibits a faster convergence speed when running a markov chain and provides a near optimal performance for the detection of underdetermined mimo systems complexity analysis and simulation results show that the proposed approach outperforms the conventional lr based klein randomized successive interference cancellation sic detection with a relatively low complexity

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

o sqrt logn approximation to sparsest cut in tilde o n 2 time this paper shows how to compute o sqrt log n approximations to the sparsest cut and balanced separator problems in tilde o n 2 time thus improving upon the recent algorithm of arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231 their algorithm uses semidefinite programming and requires tilde o n 9 5 time our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs the existence of expander flows was also established by arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231

transport behavior of a passive solute in continuous time random walks and multirate mass transfer 1 we consider the transport behavior of a passive solute in a heterogeneous medium modeled by continuous time random walks ctrw and linear multirate mass transfer mrmt within the ctrw framework we formulate a transport model which is formally equivalent to mrmt in both approaches the total concentration is divided into mobile and immobile parts the immobile concentration is given by the convolution in time of the mobile concentration and a memory function the memory function is a functional of the distribution of transition and trapping times for the ctrw and the mrmt approach respectively and determines the transport behavior of the solute based on different expressions for the memory function in the two frameworks we derive conditions for which both approaches describe the same transport behavior we focus on anomalous transport behavior that can arise if the transition and trapping time distributions behave algebraically in a given time regime using an expansion of the laplace transform of the memory function we develop explicit expressions for the time behavior of the flux concentration as well as for the center of mass velocity and the macro dispersion coefficients of the solute distribution we observe anomalous power law as well as normal fickian transport behavior depending on the exponents that dominate the trapping and transition time distributions respectively the results show that the character of the anomalous transport does not depend on the details of the transport model but only on the exponents dominating the transition or trapping time distributions the unified transport framework presented here comprising ctrw and mrmt shows new aspects and opens new perspectives for the modeling of transport in heterogeneous media

improved linear soft input soft output detection via soft feedback successive interference cancellation we propose an improved minimum mean square error mmse vertical bell labs layered space time v blast detection technique called a soft input soft output and soft feedback siof v blast detector for turbo multi input multioutput turbo mimo systems we derive a symbol estimator by minimizing the power of the interference plus noise given a priori probabilities of undetected layer symbols and a posteriori probabilities for past detected layer symbols for a low complexity implementation an approximate siof algorithm is presented which allows for a time invariant realization of the symbol ordering and an mmse filtering process another implementation referred to as the iterative siof algorithm is introduced which decides on symbol detection order based on a posteriori symbol probabilities to improve the detection performance simulations performed on a space time bit interleaved coded modulation stbicm architecture over quasi static mimo fading channels demonstrate that the siof v blast detector provides performance gains over previous turbo blast detectors most notably when more transmit antennas are used

lattice reduction based approximate map detection with bit wise combining and integer perturbed list generation for iterative detection and decoding idd in multiple input multiple output mimo systems the log likelihood ratio llr of each coded bit can be found by an optimal bit wise maximum a posteriori probability map detector however since this map detector requires a prohibitively high computational complexity low complexity suboptimal detectors are desirable in this paper lattice reduction lr based mimo detection is investigated to derive a low complexity detector that can achieve near map performance for idd in order to approximate llr values incorporating the extrinsic information provided by a soft input soft output siso decoder bit wise lr based minimum mean square error mmse filters are derived furthermore in order to minimize the performance degradation due to quantization or rounding errors in the lr based detection a low complexity integer perturbed list generation method is proposed where no tree search is used by taking advantage of a near orthogonal channel basis obtained by lr through a complexity analysis and simulations it is shown that the proposed approach achieves near optimal performance while the complexity is comparable with that of the mmse soft cancellation method which is known to be computationally efficient as a bit wise detector a parallel implementation of the proposed method would be straightforward which lowers the detection delay

almost optimal local graph clustering using evolving sets spectral partitioning is a simple nearly linear time algorithm to find sparse cuts and the cheeger inequalities provide a worst case guarantee for the quality of the approximation found by the algorithm a local graph partitioning algorithm finds a set of vertices with small conductance i e a sparse cut by adaptively exploring part of a large graph g starting from a specified vertex for the algorithm to be local its complexity must be bounded in terms of the size of the set that it outputs with at most a weak dependence on the number n of vertices in g previous local partitioning algorithms find sparse cuts using random walks and personalized pagerank spielman and teng 2013 andersen et al 2006 in this article we introduce a simple randomized local partitioning algorithm that finds a sparse cut by simulating the volume biased evolving set process which is a markov chain on sets of vertices we prove that for any 0 and any set of vertices a that has conductance at most for at least half of the starting vertices in a our algorithm will output with constant probability a set of conductance o we prove that for a given run of the algorithm the expected ratio between its computational complexity and the volume of the set that it outputs is vol a 1 2polylog n where vol a v ad v is the volume of the set a this gives an algorithm with the same guarantee up to a constant factor as the cheeger s inequality that runs in time slightly superlinear in the size of the output this is the first sublinear in the size of the input time algorithm with almost the same guarantee as the cheeger s inequality in comparison the best previous local partitioning algorithm by andersen et al 2006 has a worse approximation guarantee of o log n and a larger ratio of 1 polylog n between the complexity and output volume as a by product of our results we prove a bicriteria approximation algorithm for the expansion profile of any graph for 0 0 finds a set s of volume vol s o k1 and expansion s o k as a new technical tool we show that for any set s of vertices of a graph a lazy t step random walk started from a randomly chosen vertex of s will remain entirely inside s with probability at least 1 s 2 t this itself provides a new lower bound to the uniform mixing time of any finite state reversible markov chain

mean field analysis of personalized pagerank with implications for local graph clustering we analyse a mean field model of personalized pagerank ppr on the erd s renyi er random graph containing a denser planted er subgraph we investigate the regimes where the values of ppr concentrate around the mean field value we also study the optimization of the damping factor the only parameter in ppr our theoretical results help to understand the applicability of ppr and its limitations for local graph clustering

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

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

iterative receivers with bit level cancellation and detection for mimo bicm systems the multiple input multiple output mimo detection in the iterative receiver is investigated for a modulation of square constellation for computationally efficient mimo detection we employ the hard decision bit level cancellation blc to reduce the dimension of the mimo detection as it has advantages over the symbol level cancellation 1 it can provide better performance and 2 the extrinsic bit information can be directly used for the blc a set of reliably decoded bits from the channel decoder in iterations is used for hard decision blc to approximate the maximum a posteriori probability map detection under the partial map detection principle for the bits that are not canceled the nulling using projection is employed to approximate the map detection this approach is applicable for a lower order modulation for a higher order modulation the minimum mean square error mmse filtering with soft decision cancellation sc is applied to further mitigate the bits that are not canceled

numerical simulation of non fickian transport in geological formations with multiple scale heterogeneities 1 we develop a numerical method to model contaminant transport in heterogeneous geological formations the method is based on a unified framework that takes into account the different levels of uncertainty often associated with characterizing heterogeneities at different spatial scales it treats the unresolved small scale heterogeneities residues probabilistically using a continuous time random walk ctrw formalism and the large scale heterogeneity variations trends deterministically this formulation leads to a fokker planck equation with a memory term fpme and a generalized concentration flux term the former term captures the non fickian behavior arising from the residues and the latter term accounts for the trends which are included with explicit treatment at the heterogeneity interfaces the memory term allows a transition between non fickian and fickian transport while the coupling of these dynamics with the trends quantifies the unique nature of the transport over a broad range of temporal and spatial scales the advection dispersion equation ade is shown to be a special case of our unified framework the solution of the ade is used as a reference for the fpme solutions for the same formation structure numerical treatment of the equations involves solution for the laplace transformed concentration by means of classical finite element methods and subsequent inversion in the time domain we use the numerical method to quantify transport in a two dimensional domain for different expressions for the memory term the parameters defining these expressions are measurable quantities the calculations demonstrate long tailing arising principally from the memory term and the effects on arrival times that are controlled largely by the generalized concentration flux term

iterative tree search detection for mimo wireless systems this paper presents a reduced complexity soft input soft output detection scheme called iterative tree search detection for multiple input multiple output wireless communication systems employing turbo processing at the receiver in this scheme a reduced search space is selected with the aid of the m algorithm and qam signal constellations with block partitionable labels are used in order to make the detection complexity per bit almost independent of the modulation order as well as asymptotically linear in the number of transmit antennas results from computer simulations are presented which demonstrate the capability of the scheme to approach optimal performance at considerably reduced complexity

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

non fickian dispersion of groundwater age 1 we expand the governing equation of groundwater age to account for non fickian dispersive fluxes using continuous random walks groundwater age is included as an additional fifth dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions the general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non fickian age distributions when the transition densities diverge previously published transition densities are then used to show how the added dimension in age affects the governing differential equations depending on which transition densities diverge the resulting models may be nonlocal in time space or age and can describe asymptotic or preasymptotic dispersion a joint distribution function of time and age transitions is developed as a conditional probability and a natural result of this is that time and age must always have identical transition densities this implies that a transition density defined for age can substitute for a density in time and this has implications for transport model parameter estimation we present examples of simulated age distributions from a geologically based heterogeneous domain that exhibit non fickian behavior and show that the non fickian model provides better descriptions of the distributions than the fickian model

low complexity soft output decoding with lattice reduction aided detectors lattice reduction lr techniques have been introduced to enhance the performance of linear equalizers by collecting diversity with low complexity for many transmission systems although lr aided linear detectors may collect the same diversity as that collected by the maximum likelihood ml detector there still exists a performance gap between lr aided and ml equalizers one approach to fill this gap is to adopt soft output detectors soft output detectors enable iterative decoding when error control codes are employed for a system in this paper we propose three lr aided soft output detectors with different methods to generate the candidate lists we compare the performance and complexity of our algorithms with the existing alternatives and show that our methods achieve better performance with lower complexity the performance complexity tradeoffs of our proposed algorithms are also studied iterative decoders are performed based on these soft output detectors in the simulations to validate the effectiveness of our algorithms

lll reduction achieves the receive diversity in mimo decoding diversity order is an important measure for the performance of communication systems over multiple input multiple output mimo fading channels in this correspondence we prove that in mimo multiple access systems or mimo point to point systems with v blast transmission lattice reduction aided decoding achieves the maximum receive diversity which is equal to the number of receive antennas also we prove that the naive lattice decoding which discards the out of region decoded points achieves the maximum diversity

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

fixed complexity lll algorithm a common technique to perform lattice basis reduction is the lenstra lenstra lovasz lll algorithm an implementation of this algorithm in real time systems suffers from the problem of variable run time and complexity this correspondence proposes a modification of the lll algorithm the signal flow is altered to follow a deterministic structure which promises to obtain an easier implementation as well as a fixed execution time known in advance in the case of a maximum number of iterations as it is likely in real time systems our modification clearly outperforms the original lll algorithm as far as the quality of the reduced lattice basis is concerned

on the complexity distribution of sphere decoding we analyze the computational complexity distribution of sphere decoding sd for random infinite lattices in particular we show that under fairly general assumptions on the statistics of the lattice basis matrix the tail behavior of the sd complexity distribution is fully determined by the inverse volume of the fundamental regions of the underlying lattice particularizing this result to n x m n m i i d circularly symmetric complex gaussian lattice basis matrices we find that the corresponding complexity distribution is of pareto type with tail exponent given by n m 1 a more refined analysis reveals that the corresponding average complexity of sd is infinite for n m and finite for n m finally for i i d circularly symmetric complex gaussian lattice basis matrices we analyze sd preprocessing techniques based on lattice reduction such as the lll algorithm or layer sorting according to the v blast algorithm and regularization in particular we show that lattice reduction does not improve the tail exponent of the complexity distribution while regularization results in a sd complexity distribution with tails that decrease faster than polynomial

random walk simulation of transport in heterogeneous porous media local mass conservation problem and implementation methods the random walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity dependent dispersion tensor vary smoothly in space however in cases where sharp interfaces separate materials with contrasting hydraulic properties these quantities may be discontinuous normally velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation the use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random walk model that does not locally conserve mass unless a correction is applied at these contacts test simulations of random walk particle tracking with and without special treatment of material contacts demonstrate the problem techniques for resolving the problem including interpolation schemes and a reflection principle are reviewed and tested results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity simulations of transport in two dimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume