the differential cordic algorithm constant scale factor redundant implementation without correcting iterations the cordic algorithm is a well known iterative method for the efficient computation of vector rotations and trigonometric and hyperbolic functions basically cordic performs a vector rotation which is not a perfect rotation since the vector is also scaled by a constant factor this scaling has to be compensated for following the cordic iteration since cordic implementations using conventional number systems are relatively slow current research has focused on solutions employing redundant number systems which make a much faster implementation possible the problem with these methods is that either the scale factor becomes variable making additional operations necessary to compensate for the scaling or additional iterations are necessary compared to the original algorithm in contrast we developed transformations of the usual cordic algorithm which result in a constant scale factor redundant implementation without additional operations the resulting differential cordic algorithm dcordic makes use of on line most significant digit first redundant computation we derive parallel architectures for the radix 2 redundant number systems and present some implementation results based on logic synthesis of vhdl descriptions produced by a dcordic vhdl generator we finally prove that due to the lack of additional operations dcordic compares favorably with the previously known redundant methods in terms of latency and computational complexity

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

on the benney lin and kawahara equations abstract we establish global well posedness for the initial value problem ivp associated to the so called benney lin equation this model is a korteweg de vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics we also study the limiting behaviour of solutions to this ivp when the parameters of the perturbed terms approach 0

coded modulation in the block fading channel coding theorems and code construction we consider coded modulation schemes for the block fading channel in the setting where a codeword spans a finite number n of fading degrees of freedom we show that coded modulations of rate r bit per complex dimension over a finite signal set spl chi spl sube spl copf of size 2 sup m achieve the optimal rate diversity tradeoff given by the singleton bound spl delta n m r 1 spl lfloor n 1 r m spl rfloor for r spl isin 0 m spl rfloor furthermore we show also that the popular bit interleaved coded modulation achieves the same optimal rate diversity tradeoff we present a novel coded modulation construction based on blockwise concatenation that systematically yields singleton bound achieving turbo like codes defined over an arbitrary signal set spl chi spl sub spl copf the proposed blockwise concatenation significantly outperforms conventional serial and parallel turbo codes in the block fading channel we analyze the ensemble average performance under maximum likelihood ml decoding of the proposed codes by means of upper bounds and tight approximations we show that differently from the additive white gaussian noise awgn and fully interleaved fading cases belief propagation iterative decoding performs very close to ml on the block fading channel for any signal to noise ratio snr and even for relatively short block lengths we also show that at constant decoding complexity per information bit the proposed codes perform close to the information outage probability for any block length while standard block codes e g obtained by trellis termination of convolutional codes have a gap from outage that increases with the block length this is a different and more subtle manifestation of the so called interleaving gain of turbo codes

weakly non local solutions for capillary gravity waves fifth degree korteweg de vries equation hunter and scheurle have shown that capillary gravity water waves in the vicinity of bond number bo l 3 are consistently modelled by the korteweg de vries equation with the addition of a fifth derivative term this wave equation does not have strict soliton solutions for bo l 3 because the near solitons have oscillatory wings that extend indefinitely from the core of the wave however these solutions are arbitrarily small perturbations of solitary waves because the amplitude of the wings is exponentially small in the amplitude 6 of the core pomeau ramani and grammaticos have calculated the amplitude of the wings by applying matched asymptotics in the complex plane in the limit e 0 in this article we describe a mixed chebyshev radiation function pseudospectral method which is able to calculate the weakly non local solitons for all e we show that for fixed phase speed the solitons form a three parameter family because the linearized wave equation has three eigensolutions we also show that one may repeat the soliton with even spacing to create a three parameter of periodic solutions which we also compute because the amplitude of the wings is exponentially small these non local capillary gravity solitons are as interesting as the classical localized solitons that solve the korteweg de vries equation

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

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

exact and numerical soliton solutions of some nonlinear physical models we consider two types of variant water wave equations and the solitary wave solutions of them are constructed by using the adomian decomposition we also made a numerical comparison of the equations

the korteweg de vries kawahara equation in a bounded domain and some numerical results abstract we are concerned with the initial boundary problem associated to the korteweg de vries kawahara perturbed by a dispersive term which appears in several fluids dynamics problems we obtain local smoothing effects that are uniform with respect to the size of the interval we also propose a simple finite different scheme for the problem and prove its unconditional stability finally we give some numerical examples

a low latency pipelined 2d and 3d cordic processors the unfolded and pipelined cordic is a high performance hardware element that produces a wide variety of one and two argument functions with high throughput the reduction in delay power and area cost are of significant interest regarding this module due to its high demand for resources the linear approximation to rotation has been proposed to achieve such reductions however the schemes for rotation multiplication and vectoring division complicate the implementation in a single unit in this work we improve the linear approximation scheme leading to a unified implementation for rotation and vectoring where fully parallel tree multipliers are used instead of the second half of cordic iterations we also combine the linear approximation to rotation with the scale factor compensation so that the compensation is concurrently performed with the rotation process we then extend the method to 3d cordic such an extension is not straightforward due to the lack of existing analytical expressions for the convergence of the algorithm a comparison using a rough area time model and synthesis results shows that our proposals may achieve significant reductions in delay with no increase in area in actual implementations

coupled system of korteweg de vries equations type in domains with moving boundaries we consider the initial boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of korteweg de vries kdv type modelling strong interactions between internal solitary waves finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed we prove a global existence and uniqueness for strong solutions for the coupled system of equations of kdv type as well as the exponential decay of small solutions in asymptotically cylindrical domains finally we present a numerical scheme based on semi implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems

an explicit and numerical solutions of some fifth order kdv equation by decomposition method in this paper by considering the adomian decomposition method explicit and numerical solutions are calculated for a various fifth order korteweg de vries equations with initial condition the method does not need linearization or weak nonlinearity assumptions perturbation theory the decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self canceling noise terms where sum of components vanishes in the limit

diversity and multiplexing tradeoff in general fading channels the optimal tradeoff between diversity gain and multiplexing gain for multiple inputmultiple output mimo channels has been studied recently under the independent and identically distributed i i d rayleigh fading assumption in this correspondence this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions including different fading types nonidentical fading distributions spatial correlation and nonzero channel means our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance

analytical solution of the bagley torvik equation by adomian decomposition method abstract the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi d controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of bagley torvik equation r l bagley p j torvik on the appearance of the fractional derivative in the behavior of real materials asme j appl mech 51 1984 294 298 i podlubny fractional differential equations academic press san diego ca usa 1999 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with those available in the work of podlubny i podlubny fractional differential equations academic press san diego ca usa 1999 a good agreement of the results is observed

an explicit formula for the inverse of a pentadiagonal toeplitz matrix in this paper we mainly consider finding an explicit formula for the inverse of a pentadiagonal toeplitz matrix for that purpose we first factorize the modified form of a pentadiagonal toeplitz matrix by two tridiagonal toeplitz matrices and then use the sherman morrison woodbury inversion formula as a result an explicit inverse of a pentadiagonal toeplitz matrix is obtained under certain assumptions and numerical experiments are given to show the effectiveness of our results

the quantization effects of the cordic algorithm a detailed analysis of the quantization error encountered in the cordic coordinate rotation digital computer algorithm is presented two types of quantization error are examined an approximation error due to the quantized representation of rotation angles and a rounding error due to the finite precision representation in both fixed point and floating point arithmetic tight error bounds for these two types of error are derived the rounding error due to a scaling normalization operation in the cordic algorithm is also discussed an expression for overall quantization error is derived and several simulation examples are presented

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

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

a scale factor correction scheme for the cordic algorithm a method for the correction of scale factor of the cordic algorithm is presented in this paper the scheme requires some additional hardware for its implementation but does not require changing the elementary rotation angles or the sequence of iterations of the standard cordic algorithm upper bounds for the quantization error when using the proposed method are derived a word serial implementation of the algorithm is also given for fixed point arithmetic area and latency of the proposed implementation is compared with the standard cordic

abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method in this work we use the tanh method for solving several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk kaup kupershmidt kk and the ito forms and other related special cases abundant solitons solutions are derived two necessary criteria are established to build up reliable strategies that govern the relation between the parameters of the equation previously known solutions are recovered and entirely new bell shaped solitons are determined

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

nearest neighbor decoding in mimo block fading channels with imperfect csir this paper studies communication outages in multiple input multiple output mimo block fading channels with imperfect channel state information at the receiver csir using mismatched decoding error exponents we prove the achievability of the generalized outage probability the probability that the generalized mutual information gmi is less than the data rate and show that this probability is the fundamental limit for independent and identically distributed i i d codebooks then using nearest neighbor decoding we study the generalized outage probability in the high signal to noise ratio snr regime for random codes with gaussian and discrete signal constellations in particular we study the snr exponent which is defined as the high snr slope of the error probability curve on a logarithmic logarithmic scale we show that the maximum achievable snr exponent of the imperfect csir case is given by the snr exponent of the perfect csir case times the minimum of one and the channel estimation error diversity random codes with gaussian constellations achieve the optimal snr exponent with finite block length as long as the block length is larger than a threshold on the other hand random codes with discrete constellations achieve the optimal snr exponent with block length growing with the logarithm of the snr the results hold for many fading distributions including rayleigh rician nakagami nakagami and weibull as well as for optical wireless scintillation distributions such as lognormal rice and gamma gamma

uniform stabilization of numerical schemes for the critical generalized korteweg de vries equation with damping this work is devoted to the analysis of a fully implicit numerical scheme for the critical generalized korteweg de vries equation gkdv with p 4 in a bounded domain with a localized damping term the damping is supported in a subset of the domain so that the solutions of the continuous model issuing from small data are globally defined and exponentially decreasing in the energy space based in this asymptotic behavior of the solution we introduce a finite difference scheme which despite being one of the first order has the good property to converge in l 4 strong combining this strong convergence with discrete multipliers and a contradiction argument we show that the smallness of the initial condition leads to the uniform with respect to the mesh size exponential decay of the energy associated to the scheme numerical experiments are provided to illustrate the performance of the method and to confirm the theoretical results

the kawahara equation on bounded intervals and on a half line abstract we consider an initial boundary value problem for the kawahara equation posed on bounded intervals and on a half line we prove the existence and uniqueness of global regular and weak solutions on bounded intervals 0 l as well as a priori estimates which do not depend on l and prove that regular and weak solutions on bounded intervals converge to regular and weak solutions on the positive half line as l

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

an initial boundary value problem that approximate the quarter plane problem for the korteweg de vries equation in this paper we continue the study of the initial boundary value prob lem for the korteweg de vries equation that has been initiated in 9 we obtain global smoothing eects that are uniform with respect to the size of the interval this allows us to show that the solution of the boundary value problem converges as the size of the interval converges to infinity towards the solution of the quarter plane problem we also propose a simple finite dierents scheme for the problem on 0 1 and prove its stability

error analysis of cordic based jacobi algorithms the jacobi algorithm for eigenvalue calculation of symmetric matrices can be performed with a cordic algorithm as its basic module recently a simplified jacobi algorithm by employing approximate rotations based on cordic rotations was proposed it fully exploits the binary data structure and reduces the overall computational cost significantly in this paper an error analysis of the approximate cordic based jacobi algorithm and the conventional cordic based jacobi algorithm is performed the new algorithm behaves numerically better than the conventional cordic based jacobi algorithm for fixed as well as floating point arithmetic

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

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

existence of perturbed solitary wave solutions to a model equation for water waves abstract we prove the existence of travelling wave solutions to a fifth order partial differential equation which is a formal asymptotic approximation for water waves with surface tension these travelling waves are arbitrarily small perturbations of solitary waves but are not solitary waves themselves because they approach small amplitude oscillations for large values of the independent variable this result suggests that for bond numbers less than one third there are branches of travelling wave solutions to the water wave equations which are perturbations of supercritical elevation solitary waves and which bifurcate from froude number one and bond number one third

low density parity check codes for nonergodic block fading channels we design powerful low density parity check ldpc codes with iterative decoding for the block fading channel we first study the case of maximum likelihood decoding and show that the design criterion is rather straightforward since optimal constructions for maximum likelihood decoding do not perform well under iterative decoding we introduce a new family of full diversity ldpc codes that exhibit near outage limit performance under iterative decoding for all block lengths this family competes favorably with multiplexed parallel turbo codes for nonergodic channels

outage probability of the free space optical channel with doubly stochastic scintillation we study the asymptotic outage probability of multiple input multiple output free space optical communication with pulse position modulation in particular we consider doubly stochastic scintillation models lognormal rice and i k distributions first we consider the case when channel state information is available at the receiver only then we consider the case when it is also available at the transmitter

error analysis and reduction for angle calculation using the cordic algorithm in this paper we consider the errors appearing in angle computations with the cordic algorithm circular and hyperbolic coordinate systems using fixed point arithmetic we include errors arising not only from the finite number of iterations and the finite width of the data path but also from the finite number of bits of the input we show that this last contribution is significant when both operands are small and that the error is acceptable only if an input normalization stage is included making unsatisfactory other previous proposals to reduce the error we propose a method based on the prescaling of the input operands and a modified cordic recurrence and show that it is a suitable alternative to the input normalization with a smaller hardware cost this solution can also be used in pipelined architectures with redundant carry save arithmetic

a tight lower bound to the outage probability of discrete input block fading channels in this correspondence a tight lower bound to the outage probability of discrete input nakagami m block fading channels is proposed the approach permits an efficient method for numerical evaluation of the bound providing an additional tool for system design the optimal rate diversity tradeoff for the nakagami m block fading channel is also derived and a tight upper bound is obtained for the optimal coding gain constant

lattice boltzmann model for high order nonlinear partial differential equations in this paper a general lattice boltzmann lb model is proposed for the high order nonlinear partial differential equation with the form ensuremath partial t ensuremath phi ensuremath sum k 1 m ensuremath alpha k ensuremath partial x k mathrm ensuremath pi k ensuremath phi 0 1 ensuremath le k ensuremath le m ensuremath le 6 ensuremath alpha k are constant coefficients mathrm ensuremath pi k ensuremath phi are some known differential functions of ensuremath phi as some special cases of the high order nonlinear partial differential equation the classical m kdv equation kdv burgers equation mathrm k n n burgers equation kuramoto sivashinsky equation and kawahara equation can be solved by the present lb model compared to the available lb models the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved in addition we also conducted a detailed chapman enskog analysis and found that the high order nonlinear partial differential equation can be correctly recovered from the proposed lb model finally a large number of simulations are performed and it is found that the numerical results agree with the analytical solutions and usually the present model is also more accurate than the existing lb models h lai and c ma sci china ser g 52 1053 2009 h lai and c ma phys a amsterdam 388 1405 2009 for high order nonlinear partial differential equations

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

coded diversity on block fading channels this paper considers coded diversity schemes over block fading rician channels using random coding techniques two random coding upper bounds on the error probability of block codes are derived a new bound and a simpler but looser bound assuming binary input distribution also a new lower bound for any block code is derived using the strong converse to channel coding theorem the lower bound shows that the new random coding upper bound is quite tight furthermore it is shown that the maximum achievable diversity order in a block fading channel with finite interleaving depends not only on the number of subchannels l but also on the code rate r and that the performance can only marginally be improved by increasing the block length of the code the random coding upper bound and the lower bound are shown to converge to the capacity outage for large channel block lengths n demonstrating that the capacity outage can be used for estimating the error probability of coded diversity schemes

internal controllability of the kawahara equation on a bounded domain abstract in this paper we consider the kawahara equation posed on a bounded interval with a distributed control first we establish a carleman estimate for the kawahara equation with internal observation then applying this carleman estimate we can show that the kawahara equation is null controllable furthermore we prove the null controllability with constraints on the state for the kawahara equation