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

motion of a sphere through a fluid in stationary homogeneous flow abstract we have extended our previous analysis about the motion of a particle through a fluid in elongational flow to the case in which the fluid is in arbitrary stationary homogeneous flow expressions for the mobility in some cases of interest namely rotational elongational and simple shear flow have been derived the nonequilibrium contributions to such a quantity depend on the corresponding inverse penetration lengths

fast tcm decoding phase quantization and integer weighting tcm combining modulation and coding achieves coding gains over conventional uncoded multilevel modulation without the attendant bandwidth expansion since tcm was proposed ungerboeck 1982 1987 substantial work has done in this area a large portion of the tcm work has been in the area of high speed data transmission over voice grade modems using quadrature amplitude modulation qam qam not having a constant envelope is unattractive for employing a twt with its nonlinear behavior as the power stage additional work has been done in utilizing m ary psk with tcm simulations by taylor and chan 1981 utilizing a 4 state convolutional code demonstrated the coding gain of a rate 2 3 coded 8 psk modulation scheme wilson et al 1984 obtained results for 16 psk tcm using codes with 4 to 32 states and achieved coding gains of 3 5 to 4 8 db respectively over 8 psk and demonstrated that small memory codes achieved good gains with simple design procedures

brownian motion in a rotating flow the langevin equations for a particle of an arbitrary shape and the correlation functions for the fluctuating forces torques or force torque acting on the particle in a rotating flow are derived from the semimicroscopic level of coarse graining by using fluctuating hydrodynamics in order to obtain the solution of the navier stokes langevin equation valid over the entire flow region use is made of the method of matched asymptotic expansions in f a2 v 1 2 1 the cases of slow and rapid rotation are analyzed it is shown that the fluctuation dissipation theorems hold up to the order of f a2 v 1 2 in both slow and rapid rotation and that the diffusivity tensor depends on the angular velocity of the fluid and becomes anisotropic

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

structure optimization and realization of ffsk trellis codes the structure of combinations of l k binary trellis encoders and fast frequency shift keying ffsk modulation is studied a novel method for the optimization of these combinations is proposed it is concluded that regardless of the particular realization the best combinations can always be obtained by using a so called matched convolutional code optimum ffsk codes of rates 1 2 and 2 3 for up to 64 and 32 states respectively are reported it is shown that the best matched encoders for ffsk modulation are also matched and best for any ffsk type scheme where the pulse shape is required to satisfy nyquist s third criterion

brownian motion in a fluid in simple shear flow abstract we study brownian motion of a sphere suspended in a fluid in stationary homogeneous flow using hydrodynamic fluctuation theory we derive a langevin equation and show that the fluctuation dissipation theorem is modified by the macroscopic homogeneous flow it is found that the strength of the random force is no longer given in terms of the shear dependent friction coefficient alone as it is when the unperturbed fluid is at rest the modification originates from the tensile nature of the macroscopic flow as a special case we analyze the langevin equation for the simple shear case in detail and give the velocity autocorrelation function and the mean square displacement of the sphere for some special time regimes the possibility to defince a diffusion coefficient in these regimes is also discussed

bounds for codes over the unit circle let c be a code of length n and rate r over the alphabet a q exp 2 pi ir q r o 1 cdots q 1 and let d c be the minimum euclidean distance of c for large n the lower and upper bounds are obtained in parametric form on the achievable pairs r delta where delta d 2 c n holds to obtain these bounds the arguments leading to the gilbert bound and the elias bound respectively are applied to the alphabet a q for q rightarrow infty they are shown to be expressible in terms of the modified bessel function of the first kind the elias type bound is compared with the kabatyanskii levenshtein k l bound that holds for less restrictive alphabets it turns out that our upper bound improves the k l bound for delta leq 0 93

minimal transmitter complexity design of analytically described trellis codes g ungerboeck s 1982 design rules for a class of bandlimited codes called trellis codes are reviewed his design of the trellis is based on a set partitioning of the signal constellation and he realized these trellis codes by a convolutional encoder followed by a mapping rule from the coder output to modulation symbols r calderbank and j e mazo 1984 showed how to realize trellis codes for one dimensional signal sets in a single step easily derived nonlinear transformation with memory on a sliding block of source symbols the design rules that give a signal state specification in a trellis that yields the calderbank mazo transformation with the smallest number of terms are presented this gives a minimal transmitter complexity design it is shown how to realize the ungerboeck from the calderbank mazo form and as a result a step by step search free design procedure for trellis codes is presented two additional design rules are presented and applied to two examples by analytically designing two trellis codes a simple procedure for converting an analytic code expression to a convolutional encoder realization is discussed the analytic designs of a 4 d code and a 2 d code are presented

on the minimum length error event of minimum euclidean weight let eta denote the length of the shortest error event achieving the minimum detection distance of maximum likelihood signal detection for an impulse response having memory v a family of impulse responses where eta is of order v sup 2 is exhibited this in turn shows that some difficulty can arise in computing the minimum detection distance

on the motion and brownian motion of n spheres in a viscous fluid abstract an extension of faxen s theorem is given for the case that n spheres move with arbitrary velocities through a fluid in non uniform steady flow explicit expressions for the friction and mutual friction tensors valid to order r 3 where r is a typical distance between spheres are obtained together with this extension these expressions contain 2 3 and 4 sphere contributions brownian motion of n spheres as a consequence of fluid fluctuations is discussed on the basis of the relationships derived

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

error probability for digital transmission over nonlinear channels with application to tcm the computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered by using orthogonal volterra series the authors derive a canonical representation for discrete nonlinear systems based on a linear convolutional code and a memoryless mapper this representation shows that finite memory discrete nonlinear systems can be analyzed in much the same way as tcm trellis coded modulation schemes in particular tcm over nonlinear channels can be analyzed a technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with n branches and whose branch labels are matrices rather than scalars some examples of its application are given in particular error bounds are derived for nonlinear tcm schemes and for tcm schemes operating on nonlinear channels

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

dependence of the friction tensor on the rotation of a frame of reference abstract is is argued that the expression for the friction tensor of a sphere immerssed in a fluid depends on the choice of the frame of reference and in particular its rotation the relation between the friction tensor in the laboratory frame and the corotating frame which have been derived by different authors respectively is explicitly given memory effects are found to play a crucial role in the transformation from one frame of reference to another

tcm schemes with partially overlapped signal constellations in conventional tcm schemes for a rate of n bits per channel symbol a 2 sup n 1 point constellation is used it is shown that using constellations with less than 2 sup n 1 points one can achieve a considerable coding gain in comparison to the traditional 2 sup n 1 point constellation the increase in coding gain is due to a reduction in transmitted signal energy as a result of deleting some high power signals from the original constellation and reusing of some of the low power signals instead

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

multiple scales analysis of the fokker planck equation for simple shear flow abstract we extend the multiple time scales formalism originally introduced for the fokker planck equation by wycoff and balazs physica a 146 1987 175 to the case of simple shear flow the analysis is carried out for small values of the stokes number st a dimensionless measure of the inertia of a brownian particle the probability density is expanded in terms of hermite functions of the fluctuation velocity the difference between the actual particle velocity and the unperturbed flow velocity at its location and consequently the structure of the multiple scales hierarchy differs from the analogous equilibrium problem with a conservative forcing the multiple scales solutions are compared to a small st expansion of the exact solutions for two canonical initial conditions we also obtain the form of the smoluchowski equation correct to o st for the effects of particle inertia modifications to the scheme for hydrodynamically interacting particles are discussed

optimization of trellis codes with multilevel amplitude modulation with respect to an error probability criterion an easily computed upper bound on the error probability of a data communications system with combined trellis coding and multilevel phase modulation is derived assuming an additive white gaussian noise channel and maximum likelihood decoding this bound is used to search for codes obtained by set partitioning that minimize the bound for a fixed number of trellis states only amplitude modulated signals typically used in voiceband modem applications are considered the signal levels that minimize the error probability bound subject to an average power constraint are presented for some specific codes

error performance analysis of quadrature partial response trellis coded modulation qpr tcm in fading mobile satellite channels in order to improve the bandwidth efficiency and error performance partial response signaling prs and trellis coded modulation tcm are combined together this method is named qpr tcm whereas previous contributions have considered the performance of tcm transmitted over an additive white gaussian noise awgn channel the emphasis in this paper is on the performance of trellis coded m ary qam combined with prs in the fading environment we only consider the case where interleaving deinterleaving is employed to further combat the fading and assume that the ideal channel state information csi is available analytical upper bounds are derived using the well known transfer function bounding technique the bandwidth efficiencies are computed and the numerical results for several practical schemes are compared to each other one interesting result is that when the combined system is used on a rician fading channel the bit error probability upper bounds of the proposed 6qpr tcm and 9qpr tcm systems are better than their counterparts the 4qam tcm systems with 2 and 4 states respectively for snr values greater than a threshold which have the best error performances in the literature

coded phase frequency modulation channel coding combined with expanded signal sets has been shown 1 to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals in this paper new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented the new schemes combine fsk and psk modulation and make use of trellis coding and viterbi decoding to improve error performance over uncoded modulation the free euclidean distance is calculated for several classes of codes and upper bounds and simulation results are also presented for some simple codes the spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two dimensional modulation formats differential encoding and various extensions of the basic scheme are also discussed

uniform distance and error probability properties of tcm schemes the class of uniform trellis coded modulation tcm techniques is defined and simple explicit conditions for uniformity are derived uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning as well as on the assignment of binary labels to channel symbols the uniform distance property and uniform error property which are both derived from uniformity but are not equivalent are discussed the derived concepts are extended to encompass transmission over a not necessarily gaussian memoryless channel in which the metric used for detection may not be maximum likelihood an appropriate distance measure is defined that generalizes the euclidean distance it is proved that uniformity of a tcm scheme can also be defined under this new distance the results obtained are shown to hold for channels with phase offset or independent amplitude only fading examples are included to illustrate the applicability of the results

asymptotic upper bounds on the minimum distance of trellis codes a trellis code is a sliding window method of encoding a binary data stream as a sequence of signal points in rn when a trellis code is used to encode data at the rate of k bits channel symbol each channel input depends not only on the most recent block of k bits to enter the encoder but will also depend on a set of bits preceding this block the bits determine the state of the encoder and the most recent block of k bits generates the channel symbol conditional on the encoder state the performance of a trellis code depends on a suitably defined minimum distance property of that code this paper obtains upper bounds on this minimum distance that are better than any previously known

binary convolutional codes with application to magnetic recording calderbank heegard and ozarow 1 have suggested a method of designing codes for channels with intersymbol interference such as the magnetic recording channel these codes are designed to exploit intersymbol interference the standard method is to minimize intersymbol interference by constraining the input to the channel using run length limited sequences calderbank heegard and ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function 1 d n 2 where the channel inputs are constrained to be pm 1 this problem is considered here channel inputs are generated using a nontrivial coset of a binary convolutional code the coset is chosen to limit the zero run length of the output of the channel and so maintain clock synchronization the minimum squared euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code an interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic

the design of trellis coded mpsk for fading channels performance criteria it has been well established that the appropriate criterion for optimum trellis coded modulation design on the additive white gaussian noise channel is maximization of the free euclidean distance it is shown that when the trellis coded modulation is used on a rician fading channel with interleaving deinterleaving the design of the code of optimum performance is guided by other factors in particular the length of the shortest error event path and the product of branch distances possibly normalized by the euclidean distance of the path along the path although maximum free distance d sub free is still an important consideration it plays a less significant role the more severe the fading is on the channel these considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over rician fading channels if no interleaving deinterleaving is used then once again the design of the trellis code is guided by maximizing d sub free

norming constants for the finite mean supercritical bellman harris process let z t be a supercritical bellman harris process with offspring distribution pk and lifetime distributiong it is shown that the finiteness of the offspring mean guarantees the existence of norming constants c t such that mathop lim limits t to infty z t mathord left vphantom z t c t right kern nulldelimiterspace c t w a s for some nondegenerate random variablew c t is the quantile of the distribution function ofz t whereq 1 q being the extinction probability of the process as a byproduct of the proof z t c t is shown to be asymptotic markov the theory of weakly stable sums of i i d is used to get characterizations ofw and c t