on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

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

nd convolutional codes i performance analysis a noncoherent coded system which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection is presented in this two part paper where part i focuses on the performance analysis of the system and part ii deals with the structural properties of the underlying convolutional codes these convolutional codes are referred to as nd convolutional codes it is shown that nd convolutional codes provide a general framework for various noncoherent coding systems including differential systems two models of the carrier phase are examined and the relationships between them is established for the first one the carrier phase remains constant for l channels signals whereas for the second one it unvaries throughout the transmission period the regular structure of nd codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities as well as a simple expression for the generalized cutoff rate the exponential rate of the error probability which is the single parameter governing the error performance at large signal to noise ratios is identified via large deviations techniques this parameter leads to the interesting conclusion that increasing l does not necessarily monotonically improve the error performance of the noncoherent system the same conclusion is reached by examining upper bounds and computer simulation results of several interesting examples these examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes some of which are tabulated in part ii of the paper is required

global behavior of positive solutions of nonlinear three point boundary value problems we investigate the structure of the positive solution set for nonlinear three point boundary value problems of the form u h t f u 0 u 0 0 u 1 lambdau eta where eta epsilon 0 1 is given lambda epsilon 0 1 n is a parameter f epsilon c 0 infinity 0 infinity satisfies f s 0 for s 0 and h epsilon c 0 1 0 infinity is not identically zero on any subinterval of 0 1 our main results demonstrate the existence of continua of positive solutions of the above problem c 2004 elsevier ltd all rights reserved

phase quantized block noncoherent communication analog to digital conversion adc is a key bottleneck in scaling dsp centric receiver architectures to multigigabit s speeds recent information theoretic results obtained under ideal channel conditions perfect synchronization no dispersion indicate that low precision adc 1 4 bits could be a suitable choice for designing such high speed systems in this work we study the impact of employing low precision adc in a carrier asynchronous system specifically we consider transmission over the block noncoherent additive white gaussian noise channel and investigate the achievable performance under low precision output quantization we focus attention on an architecture in which the receiver quantizes only the phase of the received signal this has the advantage of being implementable without automatic gain control using multiple 1 bit adcs preceded by analog multipliers for standard uniform phase shift keying psk modulation we study the structure of the transition density of the phase quantized block noncoherent channel several results based on the symmetry inherent in the channel model are provided to characterize this transition density low complexity procedures for computing the channel information rate and for block demodulation are obtained using these results numerical computations are performed to compare the performance of quantized and unquantized systems for different quantization precisions and different block lengths with qpsk modulation it is observed for example that for snr larger than 2 3 db 8 bin phase quantization of the received signal recovers about 80 85 of the mutual information attained with unquantized observations while 12 bin phase quantization recovers more than 90 of the unquantized mutual information dithering the constellation is shown to improve the performance in the face of drastic quantization

eigenvalue problems for nonlinear differential equations on a measure chain abstract values of are determined for which there exist positive solutions of the second order differential equation on a measure chain u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive valued and both lim x 0 f x x and lim x f x x exist

subspace arrangements over finite fields cohomological and enumerative aspects abstract the enumeration of points on or off the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function we discuss the basic relations between these two points of view counting points is also related to the l adic cohomology of the arrangement as a variety we describe the eigenvalues of the frobenius map acting on this cohomology which corresponds to a finer decomposition of the zeta function the l adic cohomology groups and their decomposition into eigenspaces are shown to be fully determined by combinatorial data finally it is shown that the zeta function is determined by the topology of the corresponding complex variety in some important cases

nodal solutions to nonlinear eigenvalue problems on time scales abstract using global bifurcation theory we obtain the existence of solutions with specified numbers of simple generalized zeros for the nonlinear eigenvalue problem on time scales t u t q t u t r f u t t t u 0 u 1 0 where r 0 is a given constant in addition we argue that our existence theorem is a generalization of a previous result which shows the existence of at least one positive solution for the above problem

equivariant poincare polynomials and counting points over finite fields abstract suppose a finite group acts as a group of automorphisms of a smooth complex algebraic variety which is defined over a number field we show how in certain circumstances an equivariant comparison theorem in l adic cohomology may be used to convert the computation of the graded character of the induced action on cohomology into questions about numbers of rational points of varieties over finite fields this is carried through in three applications first for the symmetric group acting on the moduli space of n points on a genus zero curve second for a unitary reflection group acting on the complement of its reflecting hyperplanes and third for the symmetric group action on the space of configurations of points in any smooth variety which satisfies certain strong purity conditions

curves of positive solutions of boundary value problems on time scales abstract let t r be a time scale with a inf t b sup t we consider the nonlinear boundary value problem 2 p t u t q t u t f t u t on t 4 u a u b 0 where r 0 and f t r r satisfies the conditions f t 0 t t r f t f t t t r we prove a strong maximum principle for the linear operator defined by the left hand side of 1 and use this to show that for every solution u of 1 2 u is positive on t a b in addition we show that there exists max 0 possibly max such that if 0 max then 1 2 has a unique solution u while if max then 1 2 has no solution the value of max is characterised as the principal eigenvalue of an associated weighted eigenvalue problem in this regard we prove a general existence result for such eigenvalues for problems with general nonnegative weights

on the capacity of the wiener phase noise channel bounds and capacity achieving distributions in this paper the capacity of the additive white gaussian noise awgn channel affected by time varying wiener phase noise is investigated tight upper and lower bounds on the capacity of this channel are developed the upper bound is obtained by using the duality approach and by considering a specific distribution over the output of the channel in order to lower bound the capacity first a family of capacity achieving input distributions is found by solving a functional optimization of the channel mutual information then lower bounds on the capacity are obtained by drawing samples from the proposed distributions through monte carlo simulations the proposed capacity achieving input distributions are circularly symmetric non gaussian and the input amplitudes are correlated over time the evaluated capacity bounds are tight for a wide range of signal to noise ratio snr values and thus they can be used to quantify the capacity specifically the bounds follow the well known awgn capacity curve at low snr while at high snr they coincide with the high snr capacity result available in the literature for the phase noise channel

the rational cohomology of overline mathcal m _4 we present two approaches to the study of the cohomology of moduli spaces of curves together they allow us to compute the rational cohomology of the moduli space m over bar 4 of stable comple

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

the cohomology of the regular semisimple variety abstract we use the equivariant cohomology of hyperplane complements and their toral counterparts to give formulae for the poincare polynomials of the varieties of regular semisimple elements of a reductive complex lie group or lie algebra as a result we obtain vanishing theorems for certain of the betti numbers similar methods usingl adic cohomology may be used to compute numbers of rational points of the varieties over the finite field f q in the classical cases one obtains both for the poincare polynomials and for the numbers of rational points polynomials which exhibit certain regularity conditions as the dimension increases this regularity may be interpreted in terms of functional equations satisfied by certain power series or in terms of the representation theory of the weyl group

symbol insertion a low complexity joint peak power reduction and forward error correction for single carrier systems in this paper we present a new modulation code named symbol insertion si that simultaneously achieves both peak to average power ratio papr reduction and forward error correction for pulse shaped single carrier systems in a low complexity manner based on the fact that papr highly depends on the successive phase patterns of discrete complex symbols the proposed code controls phase shifts by inserting a redundant symbol between consecutive information bearing symbols at the receiver by viewing the inserted symbols as parities we exploit them for error correction we show that when the si is used as an inner code of serially concatenated codes its error rate performance is close to those of conventional capacity approaching codes the proposed system thus becomes favorable if the amount of papr reduction is taken into account furthermore the si with a rotationally invariant insertion scheme can accommodate itself to noncoherent detection

homology stability for classical regular semisimple varieties we use techniques from homotopy theory in particular the connection between configuration spaces and iterated loop spaces to give geometric explanations of stability results for the cohomology of the varieties of regular semisimple elements in the simple complex lie algebras of classical type a b or c as well as in the group gl n bbb c we show that the cohomology spaces of stable versions of these varieties have an algebraic stucture which identifies them as free poisson algebras with suitable degree shifts using this we are able to give explicit formulae for the corresponding poincare series which lead to power series identities by comparison with earlier work the cases of type b and c involve ideas from equivariant homotopy theory our results may be interpreted in terms of the actions of a weyl group on its coinvariant algebra i e the coordinate ring of the affine space on which it acts modulo the invariants of positive degree this space coincides with the cohomology ring of the flag variety of the associated lie group and on the cohomology of its associated complex discriminant variety

nodal solutions for nonlinear eigenvalue problems we are concerned with determining values of for which there exist nodal solutions of the boundary value problems u ra t f u 0 0 t 1 u o u 1 0 the proof of our main result is based upon bifurcation techniques

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

the cohomology of the space of magnetic monopoles denote byx q the reduced space ofsu 2 monopoles of chargeq in 3 in this paper the cohomology ofx q the cohomology with compact supports ofx q and the image of the latter in the former are all calculated as representations of q which acts onx 2 this provides a non trivial lower bound for thel 2 cohomology ofx q which is compatible with some conjectures of sen it is also shown that granted some assumptions about the metric onx q itsl 2 cohomology does not exceed this bound in the situation referred to in the paper as the coprime case

joint carrier phase estimation and turbo decoding using bit carrier phase app decoder in this paper we present an algorithm for joint carrier phase estimation and turbo decoding for the case of rapidly varying carrier phase during the transmitted block the proposed algorithm shows improved performance over previously proposed communication schemes both coherent and noncoherent for channels with additive white gaussian noise and high carrier phase noise the novel algorithm utilizes a modified two dimensional bit carrier phase a posteriori probability bcapp decoder containing additional states representing the received carrier phase the bcapp decoder calculates two extrinsic metrics one representing the bit soft value and the other representing the received carrier phase probability density function approximation a modified structure of the turbo code iterations is suggested implementing separate propagation of the two metrics between the bcapp decoders one additional attractive property of the suggested algorithm is its robustness against phase noise model mismatch

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

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

rational points and cohomology of discriminant varieties abstract let g be a finite unitary reflection group acting in a complex vector space v c n the discriminant varietyxg of g is defined as the space of regular orbits of g on v classical examples include the varieties of complex polynomials of degree n with distinct resp non zero distinct roots the normaliser g of g in gl v acts on xg in this work we determine the action of g g on the cohomology of xg in the classical cases this amounts to computing the cohomology of xg with certain local coefficient systems our methods are to compute equivariant weight polynomials by means of explicit counting of the rational points of certain varieties over finite fields and then to exploit the weight purity of the relevant varieties we obtain some power series identities as a byproduct

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

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

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

representations on the cohomology of hypersurfaces and mirror symmetry abstract we study the representation of a finite group acting on the cohomology of a non degenerate invariant hypersurface of a projective toric variety we deduce an explicit description of the representation when the toric variety has at worst quotient singularities as an application we conjecture a representation theoretic version of batyrev and borisov s mirror symmetry between pairs of calabi yau hypersurfaces and prove it when the hypersurfaces have dimension at most 3 an interesting consequence is the existence of pairs of calabi yau orbifolds whose hodge diamonds are mirror with respect to the usual hodge structure on singular cohomology

on the information rate and repeat accumulate code design for phase noise channels we investigate the information rate of channels affected by phase noise aiming at predicting the ultimate performance limits in this scenario moreover a closed form upper bound is also derived for phase shift keying psk modulations finally we consider the design of nonsystematic irregular repeat accumulate ra codes for this channel trying to give new insights on the codes to be employed for such an application

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

turbo decoding of concatenated channel coding and trellis shaping for peak power controlled single carrier systems trellis shaping ts has found its application in the peak power control of band limited single carrier signals our recent work has demonstrated that a well designed ts can control the symbol transitions such that the output signal has almost constant envelope which significantly alleviates the linearity requirement of power amplifiers compared to transmission without constellation shaping however the ts involves signal constellation expansion exclusively for peak power control therefore unlike trellis coded modulation tcm that increases the minimum euclidean distances med the ts decreases the med thus incurring the increase in signal to noise power ratio snr required for achieving a certain error rate in this letter in order to overcome this drawback we propose a serial concatenation of coding and shaping together with an effective decoding algorithm that utilizes the memory effect i e error correcting capability of the shaped symbols the achievable performance of the proposed system is analyzed in terms of the average mutual information the simulation results demonstrate that the iterative decoding of the proposed concatenated system with outer convolutional codes and inner trellis shaping offers a significant performance gain

probability of error in frequency hop spread spectrum multiple access communication systems with noncoherent reception expressions are developed for the probability of error for asynchronous frequency hop spread spectrum multiple access networks using markov hopping patterns and binary frequency shift keying bfsk with one symbol transmitted per hop the expressions are exact when there is one interfering user and orthogonal bfsk is used they provide excellent approximations when there are more than one interfering user it is also shown that the error probability when markov hopping patterns are used is a good approximation to the error probability when memoryless hopping patterns are used by computing the channel capacity and the associated throughput a simple hard decision receiver is shown to perform much better than a receiver using perfect side information to erase the symbols transmitted on hops that were hit when all the users have the same power and one binary symbol is transmitted per hop

on the constrained capacity of block differential modulation and detection in this paper we consider block differential modulation bdm to tackle the phase slip problem in digital communication systems when the received signal phase can drift the synchronizer can suddenly choose a wrong reference phase e g adding multiples of 2 m in case of m ary phase shift keying phase slips are detrimental for any coherent system since they cause long error bursts till an opposite phase slip occurs bdm is a generalization of differential modulation dm neither of them relies on the absolute carrier phase however bdm differentially encodes information between small blocks of symbols and exploits couples of adjacent blocks to decode this allows simple and practical demapping without sacrificing capacity we show that for low and moderate phase slip probabilities bdm approaches the constrained capacity of coherent transmission in particular at high spectral efficiencies we provide closed form results for the constrained capacity in absence of phase slips for phase shift keying and quadrature amplitude modulation and we evaluate numerically the constrained capacity through an efficient monte carlo method when phase slips occur besides we provide simple upper and lower bounds

phase noise effects on turbo trellis coded over m ary coherent channels the effect of the phase noise on the performance of bandwidth efficient coded modulation is studied to this end the average mutual information ami for specific constellations such as 8 phase shift keying and 16 quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white gaussian noise channel the ami not only quantifies the effect of the phase noise from an information theoretic viewpoint but also serves as an estimate for a permissible amount of the phase noise for a given signal to noise ratio the bit error rate ber performance of a near optimal turbo trellis coded modulation scheme is then investigated over such a channel for this purpose an optimal branch metric which best fits the channel characteristics is derived furthermore simple branch metrics referred to as suboptimal simplified and gaussian metrics are derived which may offer the tradeoff between ber performance and computational complexity numerical analysis shows that a near optimal coded modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis coded modulation scheme

optimal alphabets and binary labelings for bicm at low snr optimal binary labelings input distributions and input alphabets are analyzed for the so called bit interleaved coded modulation bicm capacity paying special attention to the low signal to noise ratio snr regime for 8 ary pulse amplitude modulation pam and for 0 75 bit symbol the folded binary code results in a higher capacity than the binary reflected gray code brgc and the natural binary code nbc the 1 db gap between the additive white gaussian noise awgn capacity and the bicm capacity with the brgc can be almost completely removed if the input symbol distribution is properly selected first order asymptotics of the bicm capacity for arbitrary input alphabets and distributions dimensions mean variance and binary labeling are developed these asymptotics are used to define first order optimal foo constellations for bicm i e constellations that make bicm achieve the shannon limit 1 59 db it is shown that the eb n0 required for reliable transmission at asymptotically low rates in bicm can be as high as infinity that for uniform input distributions and 8 pam there are only 72 classes of binary labelings with a different first order asymptotic behavior and that this number is reduced to only 26 for 8 ary phase shift keying psk a general answer to the question of foo constellations for bicm is also given using the hadamard transform it is found that for uniform input distributions a constellation for bicm is foo if and only if it is a linear projection of a hypercube a constellation based on pam or quadrature amplitude modulation input alphabets is foo if and only if they are labeled by the nbc if the constellation is based on psk input alphabets instead it can never be foo if the input alphabet has more than four points regardless of the labeling

linear precoders for bit interleaved coded modulation on awgn channels analysis and design criteria this paper investigates linear precoding for bit interleaved coded modulation bicm on additive white gaussian noise awgn channels concatenating a linear precoder as an inner encoder with an outer convolutional encoder produces a powerful code with a limited decoding complexity linear precoders are examined and optimized for two scenarios using i a noniterative decoding strategy and ii an iterative decoding strategy under a perfect feedback assumption the precoder design is based on an information theoretical approach on the one hand and a pair wise error probability pep analysis on the other hand both approaches render convenient precoder design rules for a binary phase shift keying bpsk signal set the optimal precoders that result from these rules are also derived numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach

global bifurcation on time scales abstract we consider the structure of the solution set of a nonlinear sturm liouville boundary value problem defined on a general time scale using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization and we show that certain nodal properties of the solutions are preserved along these continua these results extend the well known results of rabinowitz for the case of sturm liouville ordinary differential equations

coding for the discretely phase ambiguous additive white gaussian channel communication over the additive white gaussian channel subject to a discrete phase ambiguity at the receiver is considered when this phase ambiguity is considered as a discretely distributed random variable the channel is termed the acoherent additive white gaussian aawg channel it is shown that the optimum decoder for the aawg channel is not practically implementable and a suboptimum decoder that is asymptotically optimum at high signal to noise ratio is developed the low signal to noise ratio performance of the suboptimum decoder is also examined by considering the structural possibilities for this decoder it is shown that one implementation leads to rotationally invariant codes other implementations based on a rotationally disjoint property lead to a variety of solutions that offer a general framework for communication over this channel some of these solutions use a parallel receiver configuration various solutions are compared in terms of implementation and performance

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

cohomology of moduli spaces of curves of genus three via point counts in this article we consider the moduli space of smooth n pointed non hyperelliptic curves of genus 3 in the pursuit of cohomological information about this space we make s n equivariant counts of

cohomology of coxeter arrangements and solomon s descent algebra the authors would like to acknowledge support from the dfg priority programme spp1489 algorithmic and experimental methods in algebra geometry and number theory part of the research for this paper was carried out while the authors were staying at the mathematical research institute oberwolfach supported by the research in pairs programme the second author wishes to acknowledge support from science foundation ireland

nd convolutional codes ii structural analysis for pt i see ibid vol 43 no 2 p 558 75 1997 the structural properties of a noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection is presented in this second part of a two part paper where the performance analysis was provided in part i these convolutional codes are referred to as nd convolutional codes and they provide a general framework for various noncoherent coding systems including differential systems for several practical models of the carrier phase the exponential rate in which the error probability decays to zero derived in part i of the paper is used here to obtain the free equivalent distance of nd codes which is the single parameter dominating the error performance at large signal to noise ratios the free equivalent distance is upper bounded by the free nd distance which constitutes a more convenient and practical parameter to work with and it is the basis for a computer search for optimal nd codes the resultant codes of the computer search are compared to codes which are optimal for coherent detection and it is verified that the latter codes are not necessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd distance the ambiguity problem inherent to noncoherent systems is also treated in this paper in the general framework of nd catastrophic codes and necessary and sufficient conditions for catastrophic error propagation are identified

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

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

cohomology actions and centralisers in unitary reflection groups in an earlier work the second author proved a general formula for the equivariant poincare polynomial of a linear transformation g which normalises a unitary reflection group g acting on the cohomology of the corresponding hyperplane complement this formula involves a certain function called a z function below on the centraliser cg g which was proved to exist only in certain cases for example when g is a reflection or is g regular or when the centraliser is cyclic in this work we prove the existence of z functions in full generality applications include reduction and product formulae for the equivariant poincare polynomials the method is to study the poset l cg g of subspaces which are fixed points of elements of cg g we show that this poset has euler characteristic 1 which is the key property required for the definition of a z function the fact about the euler characteristic in turn follows from the join atom property of l cg g which asserts that if x1 xk is any set of elements of l cg g which are maximal set theoretically then their setwise intersection bigcap i 1 kx i lies in l cg g 2000 mathematical subject classification primary 14r20 55r80 secondary 20c33 20g40

multiplicity results for second order two point boundary value problems with superlinear or sublinear nonlinearities we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t epsilon 0 1 u 0 u 1 0 where a epsilon c 0 1 0 infinity and f r r is continuous and satisfies f s s 0 for s not equal 0 we establish existence and multiplicity results for nodal solutions to the problems if either f 0 0 f infinity infinity or f 0 infinity f 0 0 where f s s approaches f 0 and f infinity as s approaches 0 and infinity respectively we use bifurcation techniques to prove our main results c 2004 elsevier inc all rights reserved