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

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

noncoherent decorrelative detection for nonorthogonal multipulse modulation over the multiuser gaussian channel this paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser gaussian channel each user sends an m ary information symbol by transmitting one of m possibly nonorthogonal waveforms furthermore the m signals of one user are allowed to be correlated with the signals of all other users a key idea proposed here is that of a noncoherent decorrelative receiver front end like its counterpart in single pulse modulation this front end eliminates multiuser interference it therefore reduces the multiuser detection problem into decoupled single user problems over equivalent noise enhanced single user channels each equivalent single user channel is rather general and can be described as one where the waveforms employed are not only correlated but are also of unequal energies several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single user channel are obtained in the multiuser channel these detectors constitute the post decorrelative processing units for each user

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

link homotopy with one codimension two component link maps with one codimension two component are studied and an invariant of link maps modulo link homotopy is constructed using ideas from knot theory and immersion theory this invariant is used to give examples of nontrivial link homotopy classes and to show that there are infinitely many distinct link homotopy classes in many dimensions a link map with the codimension two component embedded is shown to be nullhomotopic these ideas are applied to the special case of 2 spheres in s4 to give simple examples of the failure of the whitney trick in dimension 4

nonlinear oscillations in the rolling motion of euler s disk the fixed points of the dynamical system describing the rolling motion of a uniform disk or a uniform circular hoop on a rough horizontal plane without dissipation are analyzed all fixed points of the system are stated to be steady motion states which are either saddle points or centers the spectral analysis of the sound amplitude time series emitted by a toy of the rolling disk shows that the similar nonlinear oscillations are expected in the motion with dissipation if under adiabatic approximation a finite time singularity occurs the bifurcation in the disk motion can appear

joint noncoherent demodulation and decoding for the block fading channel a practical framework for approaching shannon capacity the paper contains a systematic investigation of practical coding strategies for noncoherent communication over fading channels guided by explicit comparisons with information theoretic benchmarks noncoherent reception is interpreted as joint data and channel estimation assuming that the channel is time varying and a priori unknown we consider iterative decoding for a serial concatenation of a standard binary outer channel code with an inner modulation code amenable to noncoherent detection for an information rate of about 1 2 bit per channel use the proposed scheme using a quaternary phase shift keying qpsk alphabet provides performance within 1 6 1 7 db of shannon capacity for the block fading channel and is about 2 5 3 db superior to standard differential demodulation in conjunction with an outer channel code we also provide capacity computations for noncoherent communication using standard phase shift keying psk and quadrature amplitude modulation qam alphabets comparing these with the capacity with unconstrained input provides guidance as to the choice of constellation as a function of the signal to noise ratio these results imply that qpsk suffices to approach the unconstrained capacity for the relatively low information and fading rates considered in our performance evaluations but that qam is superior to psk for higher information or fading rates motivating further research into efficient noncoherent coded modulation with qam alphabets

multilevel codes based on partitioning following v v ginzburg 1984 a hierarchy of codes is proposed to match the geometric partitioning of a signal set the authors show that coset codes including ungerboeck lattice and binary codes and indeed any codes which rely on partitioning of the signal set are all subclasses of the proposed coding scheme the combination of such codes in a multilevel scheme often leads to reduced complexity in comparison with previously published schemes a variety of decoder structures is discussed

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

soft output decoding of rotationally invariant codes over channels with phase noise we consider rotationally invariant ri trellis coded modulations tcms transmitted over channels affected by phase noise to describe the main ideas of this paper we first concentrate as a case study on the simplest ri scheme namely the differentially encoded m ary phase shift keying m psk signal for this problem we use the framework based on factor graphs fgs and the sum product algorithm spa to derive the exact maximum a posteriori map symbol detection algorithm by analyzing its properties we demonstrate that it can be implemented by a forward backward estimator of the phase probability density function followed by a symbol by symbol completion to produce the a posteriori probabilities of the information symbols to practically implement the forward backward phase estimator we propose a couple of schemes with different complexity the resulting algorithms exhibit an excellent performance and in one case only a limited complexity increases with respect to the algorithm that perfectly knows the channel phase the properties of the optimal decoder and the proposed practical decoding schemes are then extended to the case of a generic ri code the proposed soft output algorithms can also be used in iterative decoding schemes for concatenated codes employing ri inner components among them in the numerical results we consider repeat accumulate ra codes and other serially concatenated schemes recently proposed in the technical literature

optimal joint detection estimation in fading channels with polynomial complexity the problem of sequence detection in frequency nonselective time selective fading channels when channel state information csi is not available at the transmitter and receiver is considered in this paper the traditional belief is that exact maximum likelihood sequence detection mlsd of an uncoded sequence over this channel has exponential complexity in the channel coherence time thus for slowly varying channels i e channels having coherence time on the order of the sequence length the complexity appears to be exponential in the sequence length in the first part of this work it is shown that exact mlsd can be computed with only polynomial worst case complexity in the sequence length regardless of the operating signal to noise ratio snr for equal energy signal constellations by establishing a relationship between the aforementioned complexity and the rank of the correlation matrix of the fading process an understanding of how complexity of the optimal mlsd receiver varies as the channel dynamics change is provided in the second part of this paper the problem of decoding turbo like codes in frequency nonselective time selective fading channels without receiver csi is examined using arguments similar to the ones used for the mlsd case it is shown that the exact symbol by symbol soft decision metrics sbssdms implied by the min sum algorithm can be evaluated with polynomial worst case complexity in the sequence length regardless of snr for equal energy signal constellations finally by simplifying some key steps in the polynomial complexity algorithm a family of fast approximate algorithms is derived which yield near optimal performance

noncoherent demodulation techniques for trellis coded m dpsk signals considers noncoherent decoding of trellis coded m dpsk transmission and attempts to unify and contrast the approaches to this problem which have been previously reported in the second part of the paper the maximum likelihood block decoders for the awgn channel are outlined first assuming that the decoder has no knowledge of the state of the encoder at the beginning of the block and then assuming that it knows the state because these exhaustive decoders suffer from an exponential growth in complexity with block length two simplified decoders are proposed that approach the performance of the exhaustive decoders with a much more manageable complexity through a union bound analysis and computer simulations it is shown that it is possible to achieve large gains over uncoded systems with a very reasonable decoder complexity

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

on linear structure and phase rotation invariant properties of block m psk modulation codes two important structural properties of block m 2 sup ary psk modulation codes linear structure and phase symmetry are investigated an m ary modulation code is first represented as a code with symbols from the integer group s sub m psk 0 1 2 m 1 under modulo m addition then the linear structure of block m psk modulation codes over s sub m psk with respect to modulo m vector addition is defined and conditions are derived under which a block m psk modulation code is linear once the linear structure is developed the phase symmetry of block m psk modulation codes is studied in particular a necessary and sufficient condition for a block m psk modulation code that is linear as a binary code to be invariant under 2 sup h 180 degrees m phase rotation for 1

adaptive iterative detectors for phase uncertain channels via variational bounding the problem of iterative detection decoding of data symbols transmitted over an additive white gaussian noise awgn channel in the presence of phase uncertainty is addressed in this paper by modelling the phase uncertainty either as an unknown deterministic variable process or random variable process with a known a priori probability density function a number of non bayesian and bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem in this paper a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique especially applying the generic variational bayesian vb framework efficient iterative joint estimation and detection decoding schemes are derived for the constant phase model as well as for the dynamic phase model in addition the relation of the vb based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation maximization em algorithm is provided performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors furthermore an incremental scheduling of the vb or em algorithm is shown to reduce the overall complexity of the receiver

optimal phases for a family of quadriphase cdma sequences signature sequences with good even even and odd or polyphase correlations are crucial for asynchronous code division multiple access cdma when the data sequence is random the even and odd or polyphase correlations are equally important however for most known signature sequences only their even correlations were analyzed it appears that determining the odd or the polyphase correlations is generally a very hard problem since the odd or the polyphase correlations depend on the phases of the signature sequences sole 1989 boztas hammons and kumar 1992 found a family of quadriphase sequences that are asymptotically optimal these sequences gain a factor spl radic 2 in terms of their maximum periodic even correlations when compared with the best possible binary phase shift keying bpsk sequences we find the optimal phases of these sequences the optimality is in the sense that at these phases the mean square values of the even odd and the polyphase correlations are minimal and achieve the welch 1974 bound equality simultaneously furthermore we show that at these phases the average user interference of these sequences is always smaller than that of the ideal random signature sequences comprehensive analytical and numerical results show that good phase sequences can offer a nonnegligible amount of gain over bad phase sequences at modest and high signal to noise ratios

signal sets matched to groups recently linear codes over z sub m the ring of integers mod m have been presented that are matched to m ary phase modulation the general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes a definition is given for the notion of matching it is shown that any signal set in n dimensional euclidean space that is matched to an abstract group is essentially what d slepian 1968 called a group code for the gaussian channel if the group is commutative this further implies that any such signal set is equivalent to coded phase modulation with linear codes over z sub m some further results on such signal sets are presented and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed

m ary phase coding for the noncoherent awgn channel this work considers coded m ary phase shift keying mpsk schemes with noncoherent detection a class of block codes called module phase codes is described the algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection it is shown that differential encoding may be viewed as a specific code from a particular class of module phase codes two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded mpsk are presented in the first class of module phase codes the coding gain is achieved at the expense of bandwidth expansion in the second class however the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth finally an integrated demodulation decoding technique based on a modification of information set decoding is presented it is shown that this reduced complexity suboptimal decoding strategy performs nearly as well as maximum likelihood decoding

a class of optimum block codes in signal space by using convolutional coding coupled with expanded sets of channel signals ungerboeck showed that it is possible to obtain coding gains of several decibels at a given data rate without increasing the transmission bandwidth in this paper we construct a class of optimum signal space codes using short binary block as opposed to convolutional codes our results are compared to those obtained by ungerboeck a simplified decoding procedure that is asymptotically optimum is also presented

the performance of trellis coded mdpsk with multiple symbol detection the idea of using a multiple more than two symbol observation interval to improve error probability performance is applied to differential detection of trellis coded multiple phase shift keying mpsk over an additive white gaussian noise awgn channels an equivalent euclidean distance measure per trellis branch is determined for this detection scheme this is used to define an augmented larger multiplicity trellis code whose distance measure is the conventional squared euclidean distance typical of conventional trellis coded modulation on the awgn such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis results are obtained by a combination of analysis and computer simulation it is shown that only a slight increase e g one symbol in the length of the observation interval will provide a significant improvement in bit error probability performance

stabilization and positioning control of a rolling disk by using the bogdanov takens bifurcation abstract on the basis of bogdanov takens bifurcation we obtain two nonlinear control laws for stabilization and positioning of a rolling disk on a horizontal plane at a desired set point the first control law is applied to reach a set of predetermined points from previously calculated initial conditions which unavoidably implies a small position error to overcome this problem a second procedure based on a nonlinear inverse control law is examined by using adequate leaning tilting and rolling moments the system satisfies nonholonomic constraints it is underactuated and the analysis of the bogdanov takens bifurcation provides the admissible parameter values to reach the desired set point our analysis allows stabilization and positioning of the rolling disk through small control torques neglecting the internal servomechanism dynamics with adequate reaction forces satisfying the nonholonomic conditions the results of the analytical calculations are verified by full numerical simulations

noncoherent block coded tapsk for coherent detection block coded modulation is a bandwidth efficient scheme in this paper we propose theorems about the error performance of block coded modulation using m ary phase shift keying mpsk for noncoherent detection based on these theorems we propose a novel block coded modulation scheme for noncoherent detection called noncoherent block coded mpsk the proposed scheme provides flexible designs of noncoherent block codes with different code rate block length and error performance good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes moreover noncoherent block codes of this new scheme can be decoded by multistage decoding which has the advantage of low complexity and satisfactory error performance in this paper two algorithms of multistage decoding for noncoherent detection are proposed as well the error performance of some designed codes and decoding algorithms is verified by computer simulation

lee metric bch codes and their application to constrained and partial response channels shows that each code in a certain class of bch codes over gf p specified by a code length n spl les p sup m 1 and a runlength r spl les p 1 2 of consecutive roots in gf p sup m has minimum lee distance spl ges 2r for the very high rate range these codes approach the sphere packing bound on the minimum lee distance furthermore for a given r the length range of these codes is twice as large as that attainable by berlekamp s 1984 extended negacyclic codes the authors present an efficient decoding procedure based on euclid s algorithm for correcting up to r 1 errors and detecting r errors that is up to the number of lee errors guaranteed by the designed minimum lee distance 2r bounds on the minimum lee distance for r spl ges p 1 2 are provided for the reed solomon case i e when the bch code roots are in gf p the authors present two applications first lee metric bch codes can be used for protecting against bitshift errors and synchronization errors caused by insertion and or deletion of zeros in d k constrained channels second the code construction with its decoding algorithm can be formulated over the integer ring providing an algebraic approach to correcting errors in partial response channels where matched spectral null codes are used

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

joint iterative detection and decoding in the presence of phase noise and frequency offset we present a new algorithm for joint detection and decoding of iteratively decodable codes transmitted over channels affected by a time varying phase noise pn and a constant frequency offset the proposed algorithm is obtained as an application of the sum product algorithm to the factor graph representing the joint a posteriori distribution of the information symbols and the channel parameters given the channel output the resulting algorithm employs the soft output information on the coded symbols provided by the decoder and performs forward backward recursions taking into account the joint probability distribution of phase and frequency offset we present simulation results for high order coded modulation schemes based on low density parity check codes and serially concatenated convolutional codes showing that despite its low complexity the algorithm is able to cope with a strong pn and a significant uncompensated frequency offset thus avoiding the use of complicated data aided frequency estimation schemes operating on a known preamble the robustness of the algorithm in the presence of a time varying frequency offset is also discussed

minimal trellises for block codes basic concepts in the study of trellises of block codes are defined it is shown that minimal proper trellises exists for all block codes bounds on the size of such trellises are established these bounds are shown to be exact for maximum distance separable codes and nearly so for perfect codes

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

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

iterative decoding of low density parity check codes over compound channels iterative decoding of low density parity check codes over compound channels we present a setting for decoding of low density parity check ldpc codes jointly with channel estimation suitable for transmission over memoryless compound channels we show that the performance of the combined scheme can be rigorously evaluated by means of density evolution and focus on density evolution as a tool for designing a channel estimator that matches not only to the channel but also to the ldpc ensemble as well the utility of the concept is exemplified for a compound binary symmetric channel and an unknown phase additive white gaussian channel

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

structured unitary space time autocoding constellations we previously showed that arbitrarily reliable communication is possible within a single coherence interval in rayleigh flat fading as the symbol duration of the coherence interval and the number of transmit antennas grow simultaneously this effect where the space time signals act as their own channel codes is called autocoding for relatively short e g 16 symbol coherence intervals a codebook of independent isotropically random unitary space time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error the exploitation of space time autocoding requires the creation and decoding of extraordinarily large constellations typically l 2 sup 80 we make progress on the first part of the problem through a random but highly structured constellation that is completely specified by log sub 2 l independent isotropically distributed unitary matrices the distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed thus the pairwise probability of error and hence the union bound on the block probability of error of the structured constellation is identical to that of a fully random constellation of independent signals we establish the limitations of an earlier construction through a subsidiary result that is interesting in its own right the square or for that matter any integer power greater than one of an isotropically random unitary matrix is not isotropically random with the sole exception of the one by one unitary matrix

tuning of a pid controlled gyro by using the bifurcation theory this paper concerns the control design of a pid controlled gimbals suspension gyro whose parameters are determined by using bifurcation theory the non linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes considering a pid controller with constrained integral action it is shown that depending on different values of the maximum allowed integral action a poincare andronov hopf bifurcation may appear the analysis of the stability or instability of this bifurcation from the first lyapunov value gives a procedure to adjust the parameters of the pid controller the developed control methodology is evaluated through numerical simulations 2007 elsevier b v all rights reserved

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

dynamics of an eccentric disk on a curved surface abstract this paper investigates the dynamic behavior of an eccentric disk rolling on a curve of arbitrary shape and then on a curve defined as a cubic function comparisons are made to a disk without eccentricity and the related point mass approximation the curve is subject to sinusoidal base excitation and the system is considered from the perspective of a potential well problem where escape is possible on one side the equations of motion are derived using a roll without slip constraint and the behavior is investigated by means of approximate analytical solutions numerically simulated frequency and amplitude sweeps and by considering the basins of attraction when initial conditions or forcing parameters are varied

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

noncoherent block coded tapsk and 16qam using linear component codes in this paper we derive minimum noncoherent distances of block coded tapsk twisted amplitude and phase shift keying and 16qam quadrature amplitude modulation both using linear component codes according to the derived distances noncoherent block coded tapsk nbc tapsk and noncoherent block coded 16qam nbc 16qam are proposed if the block length is very small nbc 16tapsk performs best among all noncoherent schemes and nbc 16qam performs worse due to its small minimum noncoherent distance however if the block is not short nbc 16qam has the best error performance because the codewords with small noncoherent distances are rare

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

rotationally invariant and rotationally robust codes for the awgn and the noncoherent channel the paper investigates the design and robustness of rotationally invariant ri codes first ri codes are extended to the case of serially concatenated sc trellis coded modulation tcm and several high rate powerful ri sctcm codes are designed over 8 phase shift keying and 16 quadrature amplitude modulation alphabets the investigation continues by considering more realistic channels that introduce cycle slips during phase estimation and thus rotate only part of the transmitted codeword it is proven that ri codes with small state space are robust in these channels even when traditional coherent decoders are utilized furthermore it is demonstrated through simulations that the addition of a simple stopping criterion to the coherent iterative decoding algorithm is sufficient for robustness of the more powerful ri sctcm codes when partial codeword rotations are considered finally it is investigated whether ri codes are useful for transmission in the noncoherent channel it is proved that ri codes are as good as any other good codes for this channel when the phase dynamics are low and optimal decoding is performed however it is shown that for a certain class of receivers ri codes are also robust to partial phase rotations in this channel

multiple symbol differentially detected multilevel codes for the rayleigh fading channel conventional differential detection is known to perform poorly on the fast fading rayleigh fading channel due to the rapid variation of the channel state the technique of multiple symbol differential detection msdd improves the error performance by detecting over a sequence of symbols and exploiting the inherent correlation of the fading process to further reduce the error rate we need to introduce some form of coding successful coding for the rayleigh fading channel requires interleaving to decorrelate the channel a conflicting requirement to msdd we propose a solution consisting of interleaving blocks of l m ary phase shift keying mpsk symbols that are multiple symbol differentially detected the blocks are treated as elements of an m sup l symbol alphabet over which a multilevel code based on geometrically uniform partitions is defined

noncoherent amplitude phase modulated transmission schemes for rayleigh block fading channels in this paper we investigate noncoherent transmission schemes using amplitude phase modulation for uncoded transmission schemes we derive the pairwise error probability pep and its high snr approximation for signal vectors with unequal power values using a noncoherent maximum likelihood detector under rayleigh block fading channels for coded transmission schemes we consider differential amplitude phase modulated signals and introduce a codeword interleaving strategy to improve the error performance the design criteria for the signal labelling and bit interleaving are also derived via the high snr approximation of the pep at the receiver we devise an iterative channel amplitude estimator to enhance the detection reliability with the help of a specially designed iterative receiving algorithm the designed noncoherent coded scheme can provide a significant improvement either in the error floor or the waterfall region

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

multiple phase codes for detection without carrier phase reference we consider the construction and analysis of linear block codes for m ary phase shift keying that can be decoded without carrier phase synchronization under these circumstances the function that has a significant impact on performance is the noncoherent distance analogous to the euclidean distance for the coherent case the major difficulty in constructing and analyzing such codes lies in the fact that the noncoherent distance is not a true metric for this reason prior work mainly relies on numerical approaches to search for good codes and to determine the corresponding minimum noncoherent distance we first present a theorem that links the noncoherent distance with the euclidean and lee 1958 distances this theorem allows us to construct good codes and determine their minimum noncoherent distances analytically based on this theorem we classify the codes whose duals consist of a cyclic group these codes are of minimum redundancy we further investigate codes with the flavor of hamming and shortened hamming codes many of these new codes provide significantly larger coding gains than previously known codes linear codes derived from code division multiple access cdma sequences are considered as well these codes in general provide rather large coding gains finally an algorithm is introduced that can be appended to any suboptimal decoding technique to enhance the performance

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

dimension length profiles and trellis complexity of linear block codes this semi tutorial paper discusses the connections between the dimension length profile dlp of a linear code which is essentially the same as its generalized hamming weight hierarchy and the complexity of its minimal trellis diagram these connections are close and deep dlp duality is closely related to trellis duality the dlp of a code gives tight bounds on its state and branch complexity profiles under any coordinate ordering these bounds can often be met a maximum distance separable mds code is characterized by a certain extremal dlp from which the main properties of mds codes are easily derived the simplicity and generality of these interrelationships are emphasized

pilot symbol assisted coded transmission over the block noncoherent awgn channel in this paper pilot symbol assisted transmission in conjunction with high performance coding over the block independent noncoherent additive white gaussian noise channel is investigated several approximate iterative receivers are proposed which either perform carrier phase estimation separately from detection or joint carrier phase estimation decoding in an iterative fashion the performance of the proposed receivers is analyzed using density evolution the power allocation to the pilot symbol is quantified and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal to noise ratio required for error free communication this optimal power allocation which could be utilized in code design is found to be sensitive to the channel coherence interval as well as to the particular receiver used in addition a simple upper bound on the performance of any receiver that performs joint iterative carrier phase estimation and detection is derived the obtained results are compared with the simulated performance of the proposed receivers

bit error probability for noncoherent orthogonal signals in fading with optimum combining for correlated branch diversity due to the interest in wireless personal communications there has been a lot of research on the performance of receivers with diversity most analyses assume the diversity branches are independent this paper presents an analysis of the bit error probability for receivers in which the diversity branches are correlated noncoherent orthogonal digital modulation ncodm with rician and rayleigh slow nonselective fading models are assumed through the use of the diagonalization of quadratic forms most of the calculations of the bit error probability can be reduced to a two dimensional numerical integration for some cases for dual diversity a closed form expression for the error probability is given a number of diversity combining laws including square law and maximum likelihood are considered we find that rician fading can be worse than rayleigh fading in correlated diversity environments a situation quite different from the independent diversity case also for the rayleigh fading model with correlated branch diversity we find that an equal weight square law combiner usually has the same error performance as the more complex maximum likelihood combiner however this is not the case for a rician fading model with the same correlation environment simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals

polynomial complexity noncoherent symbol by symbol detection with application to adaptive iterative decoding of turbo like codes the problem of generating symbol by symbol soft decision metrics sbssdms in the presence of unknown channel parameters is considered the motivation for this work lies in its application to iterative decoding of high performance turbo like codes transmitted over channels that introduce unknown parameters in addition to gaussian noise traditional methods for the exact evaluation of sbssdms involve exponential complexity in the sequence length a class of problems is identified for which the sbssdms can be exactly evaluated with only polynomial complexity with respect to the sequence length utilizing the close connection between symbol by symbol and sequence detection it is also shown that for the aforementioned class of problems detection of an uncoded data sequence in the presence of unknown parameters can be performed with polynomial complexity the applicability of this technique is demonstrated by considering the problem of iterative detection of low density parity check codes in the presence of unknown and time varying carrier phase offset finally based on the proposed exact schemes an ultra fast approximate algorithm for performing joint iterative decoding and phase estimation is derived that is well suited for hardware implementation

multistage decoding of multilevel block m psk modulation codes and its performance analysis multistage decoding of multilevel block multilevel phase shift keying m psk modulation codes for the additive white gaussian noise awgn channel is investigated several types of multistage decoding including a suboptimum soft decision decoding scheme are devised and analyzed upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes error probabilities of some specific multilevel block 8 psk modulation codes are evaluated and simulated the computation and simulation results for these codes show that with multistage decoding significant coding gains can be achieved with large reduction in decoding complexity in one example it is shown that the difference in performance between the proposed suboptimum multistage soft decision decoding and the single stage optimum decoding is small only a fraction of a db loss in snr at the block error probability of 10 sup 6

glrt optimal noncoherent lattice decoding this paper presents new low complexity lattice decoding algorithms for noncoherent block detection of quadrature amplitude modulation qam and pulse amplitude modulation pam signals over complex valued fading channels the algorithms are optimal in terms of the generalized likelihood ratio test glrt the computational complexity is polynomial in the block length making glrt optimal noncoherent detection feasible for implementation we also provide even lower complexity suboptimal algorithms simulations show that the suboptimal algorithms have performance indistinguishable from the optimal algorithms finally we consider block based transmission and propose to use noncoherent detection as an alternative to pilot assisted transmission pat the new technique is shown to outperform pat

the leech lattice the octacode and decoding algorithms new multilevel constructions of the golay code and the leech lattice are presented these are derived from the turyn construction and the holy construction with the octacode as the glue code further we show that the holy construction of the leech lattice with the octacode as the glue code is essentially different from the permuted turyn construction although both constructions rely on the octacode the turyn construction is based on an odd type of the octacode whereas any type of the octacode can be used in the holy construction moreover the multilevel representation of the holy construction leads to a novel lattice partition chain based on these structures we derive new bounded distance decoders for the golay code and the leech lattice whose effective error coefficient is smaller than that of any previously known bounded distance decoder we provide a general theorem for computing the effective error coefficient of coset decoding with bounded distance decoding for the subcode

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

symmetric surgery and boundary link maps in order to seperate 3 dimensional linking and knotting phenomena john milnor introduced the notion of a link homotopy 14 he allowed selfintersections but did not allow different components to cross during a link homotopy it is clear that any knot is link homotopically trivial but one of the most surprising and unintuitive see the left hand side of fig 1 results of milnor was that arbitrarily many parallel copies of a knot form a homotopically trivial link in fact one knows that any boundary link has vanishing invariants and thus it is homotopically trivial by the main result of milnor by definition in a boundary link the components bound disjointly embedded seifert surfaces for example any knot has a seifert surface and is thus a boundary link similarly parallel copies of a knot bound disjoint parallel copies of this seifert surface the notion of a link homotopy makes clearly sense for links in any dimension in fact the correct category to work in seems to be the following a link map is a continuous map such that connected components in the source are mapped disjointly into the target a link homotopy between two link maps is then an ordinary homotopy through link maps in this context a boundary link map l qi mi n is a link map which is the boundary of a link map qi wi n of oriented manifolds wi the seifert surfaces for l

quaternary quadratic residue codes and unimodular lattices we construct new self dual and isodual codes over the integers module 4 the binary images of these codes under the gray map are nonlinear but formally self dual the construction involves hensel lifting of binary cyclic codes quaternary quadratic residue codes are obtained by hensel lifting of the classical binary quadratic residue codes repeated hensel lifting produces a universal code defined over the 2 adic integers we investigate the connections between this universal code and the codes defined over z sub 4 the composition of the automorphism group and the structure of idempotents over z sub 4 we also derive a square root bound on the minimum lee weight and explore the connections with the finite fourier transform certain self dual codes over z sub 4 are shown to determine even unimodular lattices including the extended quadratic residue code of length q 1 where q spl equiv 1 mod8 is a prime power when q 23 the quaternary golay code determines the leech lattice in this way this is perhaps the simplest construction for this remarkable lattice that is known

chaotic phenomena triggering the escape from a potential well this paper explores the manner in which a driven mechanical oscillator escapes from the cubic potential well typical of a metastable system close to a fold the aim is to show how the well known atoms of dissipative dynamics saddle node folds period doubling flips cascades to chaos boundary crises etc assemble to form molecules of overall response hierarchies of cusps incomplete feigenbaum trees etc particular attention is given to the basin of attraction and the loss of engineering integrity that is triggered by a homoclinic tangle the latter being accurately predicted by a melnikov analysis after escape chaotic transients are shown to conform to recent scaling laws analytical constraints on the mapping eigenvalues are used to demonstrate that sequences of flips and folds commonly predicted by harmonic balance analysis are in fact physically inadmissible

space time autocoding prior treatments of space time communications in rayleigh flat fading generally assume that channel coding covers either one fading interval in which case there is a nonzero outage capacity or multiple fading intervals in which case there is a nonzero shannon capacity however we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable in short space time signals are their own channel codes we call this phenomenon space time autocoding and the accompanying capacity the space time autocapacity let an m transmitter antenna n receiver antenna rayleigh flat fading channel be characterized by an m spl times n matrix of independent propagation coefficients distributed as zero mean unit variance complex gaussian random variables this propagation matrix is unknown to the transmitter it remains constant during a t symbol coherence interval and there is a fixed total transmit power let the coherence interval and number of transmitter antennas be related as t spl beta m for some constant spl beta a t spl times m matrix valued signal associated with r spl middot t bits of information for some rate r is transmitted during the t symbol coherence interval then there is a positive space time autocapacity c sub a such that for all r c sub a the block probability of error goes to zero as the pair t m spl rarr spl infin such that t m spl beta the autocoding effect occurs whether or not the propagation matrix is known to the receiver and c sub a nlog 1 spl rho in either case independently of spl beta where spl rho is the expected signal to noise ratio snr at each receiver antenna lower bounds on the cutoff rate derived from random unitary space time signals suggest that the autocoding effect manifests itself for relatively small values of t and m for example within a single coherence interval of duration t 16 for m 7 transmitter antennas and n 4 receiver antennas and an 18 db expected snr a total of 80 bits corresponding to rate r 5 can theoretically be transmitted with a block probability of error less than 10 sup 9 all without any training or knowledge of the propagation matrix

on multilevel block modulation codes the multilevel technique for combining block coding and modulation is investigated a general formulation is presented for multilevel modulation codes in terms of component codes with appropriate distance measures a specific method for constructing multilevel block modulation codes with interdependency among component codes is proposed given a multilevel block modulation code c with no interdependency among the binary component codes the proposed method gives a multilevel block modulation code c that has the same rate as c a minimum squared euclidean distance not less than that of c a trellis diagram with the same number of states as that of c and a smaller number of nearest neighbor codewords than that of c finally a technique is presented for analyzing the error performance of block modulation codes for an additive white gaussian noise awgn channel based on soft decision maximum likelihood decoding error probabilities of some specific codes are evaluated by simulation and upper bounds based on their euclidean weight distributions

on the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes it was shown earlier that for a punctured reed muller rm code or a primitive bch code which contains a punctured rm code of the same minimum distance as a large subcode the state complexity of the minimal trellis diagrams is much greater than that for an equivalent code obtained by a proper permutation of the bit positions the problem of finding a permutation of the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is related to the generalized hamming weight hierarchy of a code and it is shown that for rm codes the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to v k wei 1991 the state complexity of the trellis diagram for the extended and permuted 64 24 bch code is discussed

the dynamics of group codes state spaces trellis diagrams and canonical encoders a group code c over a group g is a set of sequences of group elements that itself forms a group under a component wise group operation a group code has a well defined state space sigma sub k at each time k each code sequence passes through a well defined state sequence the set of all state sequences is also a group code the state code of c the state code defines an essentially unique minimal realization of c the trellis diagram of c is defined by the state code of c and by labels associated with each state transition the set of all label sequences forms a group code the label code of c which is isomorphic to the state code of c if c is complete and strongly controllable then a minimal encoder in controller canonical feedbackfree form may be constructed from certain sets of shortest possible code sequences called granules the size of the state space sigma sub k is equal to the size of the state space of this canonical encoder which is given by a decomposition of the input groups of c at each time k if c is time invariant and nu controllable then mod sigma sub k mod pi sub 1

on link maps and their homotopy classification is called a link map if the two spheres s p and s o have disjoint images f l s p nf2 s 0 two such link maps are called link homotopic if they are homotopic through link maps this type of equivalence relation was introduced by milnor m in the classical case m 3 p q 1 and has recently found much renewed interest see e g mr fr k i l 3 ko2 5 in this paper we study and determine in a number of cases the set lm q of link homotopy classes of link maps f as above

capacity and coding for the block independent noncoherent awgn channel communication over the noncoherent additive white gaussian noise awgn channel is considered where the transmitted signal undergoes a phase rotation unknown to the transmitter and the receiver the effects of phase dynamics are explicitly taken into account by considering a block independent model for the phase process the unknown phase is constant for a block of n complex symbols and independent from block to block in the first part of the paper the capacity achieving input distribution is characterized in particular it is shown that the maximizing density has circular symmetry is discrete in amplitude with infinite number of mass points and always has a mass point at zero furthermore asymptotic expressions and bounds for the capacity are derived based on these results the capacity is evaluated through numerical optimizations for unconstrained and modulation constrained input distributions in the second part of this paper inspired by the capacity results two classes of coding and modulation schemes are proposed for fast and moderate phase dynamics in the case of fast phase dynamics i e small n optimized modulation alphabets are designed having exponential complexity with n at the demodulator in the case of moderate phase dynamics i e moderate values of n specially designed modulation alphabets are utilized that have linear complexity with n these alphabets are used together with optimized irregular low density parity check ldpc codes simulation results show that these codes can achieve close to capacity performance with moderate complexity and outperform the best known codes so far

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

on the application of factor graphs and the sum product algorithm to isi channels in this paper based on the application of the sum product sp algorithm to factor graphs fgs representing the joint a posteriori probability app of the transmitted symbols we propose new iterative soft input soft output siso detection schemes for intersymbol interference isi channels we have verified by computer simulations that the sp algorithm converges to a good approximation of the exact marginal apps of the transmitted symbols if the fg has girth at least 6 for isi channels whose corresponding fg has girth 4 the application of a stretching technique allows us to obtain an equivalent girth 6 graph for sparse isi channels the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the bahl cocke jelinek raviv bcjr algorithm they also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction the application to joint detection and decoding of low density parity check ldpc codes is also considered and results are shown for some partial response magnetic channels also in these cases we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal serial bcjr algorithm is used for detection therefore for their parallel implementation they represent a favorable alternative to the modified parallel bcjr algorithm proposed in the literature for the application to magnetic channels

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

further results on noncoherent block coded mpsk transactions papers a novel noncoherent block coding scheme called noncoherent block coded mpsk nbc mpsk was proposed recently in this paper we present further research results on nbc mpsk we first focus on the rotational invariance ri of nbc mpsk based on the ri property of nbc mpsk with multistage decoding a noncoherent near optimal linear complexity multistage decoder for nbc mpsk is proposed then we investigate a tree search ml decoding algorithm for nbcmpsk the derived algorithm is shown to have low complexity and excellent error performance in this paper we also utilize the idea of the nbc mpsk to design noncoherent space time block codes called noncoherent space time block coded mpsk nstbc mpsk for two transmit antennas we propose a signal set with set partitioning and derive the minimum noncohent distance of nstbc mpsk with this signal set for the decoding of nstbc mpsk we modify the ml decoding algorithm of nbc mpsk and propose an iterative hard decision decoding algorithm compared with training codes and unitary space time modulation nbc mpsk and nstbc mpsk have larger minimum noncoherent distance and thus better error performance for the noncoherent ml decoder

hopf bifurcation control a new approach in this paper we find conditions to control a hopf bifurcation in a class of nonlinear systems whose linear approximation has two eigenvalues on the imaginary axis without assuming that the system is controllable we use the center manifold theorem to project the dynamics on a two dimensional manifold and design a controller that permits us to decide the stability and direction of the emerging periodic solution

energy efficient full diversity collaborative unitary space time block code designs via unique factorization of signals in this paper a novel concept called a uniquely factorable constellation pair ufcp is proposed for the systematic design of a noncoherent full diversity collaborative unitary space time block code by normalizing two alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna it is proved that such a unitary ufcp code assures the unique identification of both channel coefficients and transmitted signals in a noise free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case to further improve error performance an optimal unitary ufcp code is designed by appropriately and uniquely factorizing a pair of energy efficient cross quadrature amplitude modulation qam constellations to maximize the coding gain subject to a transmission bit rate constraint after a deep investigation of the fractional coding gain function a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the qam constellations in the denominator of the objective as well as carefully design a constellation triple forming two ufcps with one collaborating with the other two so as to make the accumulated minimum euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time to avoid as many corner points of the qam constellations with the largest energy as possible to achieve the minimum of the numerator in other words the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression computer simulations demonstrate that error performance of the optimal unitary ufcp code presented in this paper outperforms those of the differential code and the signal to noise ratio efficient training code

on the capacity of the blockwise incoherent mpsk channel the capacity of m ary phase shift keying mpsk over an additive white gaussian noise awgn channel with carrier phase unknown but constant over l symbols is investigated it is shown that capacity achieving channel inputs are uniformly distributed and independent mpsk symbols capacity over a range of signal to noise ratio snr and l is presented for binary phase shift keying bpsk and quaternary phase shift keying qpsk upper and lower easy to compute bounds on capacity are derived it is proven that for large l the coherent capacity is approached an analytic asymptotic expression for low l spl middot snr is derived exhibiting the expected quadratic dependence on the snr

blind detection of pam and qam in fading channels this correspondence considers block detection for blind wireless digital transmission at high signal to noise ratio snr block detection errors are primarily due to the received sequence having multiple possible decoded sequences with the same likelihood we derive analytic expressions for the probability of detection ambiguity written in terms of a dedekind zeta function in the zero noise case with large constellations expressions are also provided for finite constellations which can be evaluated efficiently independent of the block length simulations demonstrate that the analytically derived error floors exist at high snr

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

iterative decision feedback differential demodulation of bit interleaved coded mdpsk for flat rayleigh fading channels a simple receiver structure previously proposed by the authors for convolutional coded m ary differential phase shift keying transmission over flat rayleigh fading channels without channel state information is analyzed in detail we present a thorough discussion of the iterative decoding procedure which is referred to as iterative decision feedback differential demodulation iterative df dm the convergence behavior of iterative df dm is theoretically examined the analysis supports the observation that the iterative decoding scheme works well for target bit error rates which are usually of interest furthermore the associated cut off rate for error free decision feedback is studied judging from this performance parameter remarkable gains in power efficiency compared to conventional differential demodulation are indicated while the computational complexity of the decoding remains low the results from information theory are in good agreement with the given simulation results

a decoding of block codes the a algorithm is applied to maximum likelihood soft decision decoding of binary linear block codes this paper gives a tutorial on the a algorithm compares the decoding complexity with that of exhaustive search and viterbi decoding algorithms and presents performance curves obtained for several codes

decision feedback differential detection of differentially encoded 16apsk signals multiple symbol differential detection dd with reference signal estimation based on the feedback of past detected symbols is presented for differentially encoded 16 level amplitude phase shift keying 16dapsk a suboptimal decision is derived the approximate analysis of the bit error rate ber performance taking into account the decision error propagation effect is presented in an additive white gaussian noise awgn channel and the ber performance is compared with those of 16dpsk and 16 quadrature amplitude modulation 16qam

maximum likelihood differential detection of uncoded and trellis coded amplitude phase modulation over awgn and fading channels spl minus metrics and performance this paper derives metrics for maximum likelihood differential detection of uncoded and trellis coded mpsk and qam transmitted over rayleigh and rician fading channels receiver structures based on these metrics are proposed and their error probability performance analyzed and or simulated the results represent a generalization of the notion of multiple symbol differential detection previously introduced by the authors for mpsk over an awgn to the fading channel and other modulations for the coded cases ideal interleaving deinterleaving is assumed and furthermore the presence or absence of channel state information an interesting side result is that for a constant envelope modulation transmitted over a fading channel with unknown but rapidly varying phase error the other extreme to the slowly varying phase error case normally assumed for differential detection under certain practical assumptions it is shown that the optimum receiver is of the limiter discriminator type