the ζ determinant and the additivity of the η invariant on the smooth self adjoint grassmannian in this paper we discuss the existence of the determinant of a dirac operator on a compact manifold with boundary we show that the determinant is well defined in the case of the operator with a domain determined by a boundary condition from the smooth self adjoint grassmannian discussed in the papers 5 13 29 we prove a generalization of a pasting formula for the invariant see 34 the results of the paper are used in the recent proof of the projective equality of the determinant and quillen determinant on see 30 31

the stretched golay and other codes for high snr finite delay quantization of the gaussian source at 1 2 bit per sample error correcting codes are considered as codebooks for high performance vector quantization vq of the iid gaussian source at fractional bit rate a family of good rate one half codes is introduced the stretched golay codes the performance of these codes is compared to other good block codes trellis coded quantization and other techniques the stretched golay codes are shown to outperform previously published results for block lengths 32 40 56 and 64 the good performance together with fast decoding make these techniques attractive for applications such as low bit rate coding of speech

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

adiabatic limits of the η invariants the odd dimensional atiyah patodi singer problem we study the invariant of boundary value problems of atiyah patodi singer type we prove the formula for the spectral flow of the families overs1 assuming a product structure in a collar neighbourhood of the boundary we show that the invariant behaves the same way as on a closed manifold we also study the adiabatic limit of the spectral invariants in nice cases we are able to split them into a contribution from the interior one from the cylinder and an error term then we show that the error term disappears with the increasing length of the cylinder

scattering by cavity backed antennas on a circular cylinder conformal arrays are popular antennas for aircraft spacecraft and land vehicle platforms due to their inherent low weight drag and observables however to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer in fact it has been common practice to use limited measurements and planar approximations in designing such nonplanar antennas we extend the finite element boundary integral method to scattering by cavity backed structures in an infinite metallic cylinder in particular we discuss the formulation specifics such as weight functions dyadic green s function implementation details and particular difficulties inherent to cylindrical structures special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements scattering results are presented and validated as much as possible

differential trellis decoding of convolutional codes this paper investigates the principle of metric differences for trellis decoding of convolutional codes based on this differential method a new algorithm referred to as differential trellis decoding dtd is proposed dtd offers an alternative to the conventional add compare select acs method for implementing the viterbi algorithm

the leech lattice and the golay code bounded distance decoding and multilevel constructions multilevel constructions of the binary golay code and the leech lattice are described both constructions are based upon the projection of the golay code and the leech lattice onto the 6 3 4 hexacode over gf 4 however unlike the previously reported constructions the new multilevel constructions make the three levels independent by way of using a different set of coset representatives for one of the quaternary coordinates based upon the multilevel structure of the golay code and the leech lattice efficient bounded distance decoding algorithms are devised the bounded distance decoder for the binary golay code requires at most 431 operations as compared to 651 operations for the best known maximum likelihood decoder efficient bounded distance decoding of the leech lattice is achieved by means of partitioning it into four cosets of q sub 24 beyond the conventional partition into two h sub 24 cosets the complexity of the resulting decoder is only 953 real operations on the average and 1007 operations in the worst case as compared to about 3600 operations for the best known in maximum likelihood decoder it is shown that the proposed algorithms decode correctly at least up to the guaranteed error correction radius of the maximum likelihood decoder thus the loss in coding gain is due primarily to an increase in the effective error coefficient which is calculated exactly for both algorithms furthermore the performance of the leech lattice decoder on the awgn channel is evaluated experimentally by means of a comprehensive computer simulation the results show a loss in coding gain of less than 0 1 db relative to the maximum likelihood decoder for ber ranging from 10 sup 1 to 10 sup 7

maximum likelihood soft decoding of binary block codes and decoders for the golay codes maximum likelihood soft decision decoding of linear block codes is addressed a binary multiple check generalization of the wagner rule is presented and two methods for its implementation one of which resembles the suboptimal forney chase algorithms are described besides efficient soft decoding of small codes the generalized rule enables utilization of subspaces of a wide variety thereby yielding maximum likelihood decoders with substantially reduced computational complexity for some larger binary codes more sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the 24 12 golay code yielding a computational gain factor of about 2 with respect to previous methods a ternary single check version of the wagner rule is applied for efficient soft decoding of the 12 6 ternary golay code

spectral boundary conditions for generalizations of laplace and dirac operators spectral boundary conditions for laplace type operators on a compact manifold x with boundary are partly dirichlet partly oblique neumann conditions where the partitioning is provided by a pseudodifferential projection they have an interest in string and brane theory relying on pseudodifferential methods we give sufficient conditions for the existence of the associated resolvent and heat operator and show asymptotic expansions of their traces in powers and power log terms allowing a smearing function the leading log coefficient is identified as a non commutative residue which vanishes when 1 the study has new consequences for well posed spectral boundary problems for first order dirac like elliptic operators generalizing the atiyah patodi singer problem it is found e g that the zeta function is always regular at zero in the selfadjoint case there is a stability of the zeta function value and the eta function regularity at zero under perturbations of the boundary projection of order dim x

modeling conformal antennas on metallic prolate spheroid surfaces using a hybrid finite element method in this paper the hybrid finite element boundary integral fe bi method appropriate for modeling conformal antennas on doubly curved surfaces is developed the fe bi method is extended to model doubly curved convex surfaces by means of a specially formulated asymptotic dyadic green s function the fe bi method will then be used to examine the effect of curvature variation on the resonant input impedance of a cavity backed conformal slot antenna and a conformal patch antenna recessed in a perfectly conducting electrically large prolate spheroid surface the prolate spheroid shape provides a canonical representation of a doubly curved mounting surface the numerical results for conformal slot and patch antennas on the prolate spheroid are compared as a function of curvature and orientation

constrained designs for maximum likelihood soft decoding of rm 2 m and the extended golay codes we present algorithms for maximum likelihood soft decoding of the second order reed muller codes rm 2 m and the extended 24 12 8 golay code the decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered such representation enables application of certain elimination rules a structure called constrained design is established to support the elimination procedures remarkably efficient algorithms are obtainable by this approach the method of elimination is applicable also in combination with existing coset decoding schemes

gauge theories on manifolds with boundary the boundary value problem for laplace type operators acting on smooth sections of a vector bundle over a compact riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied the condition of strong ellipticity of this boundary value problem is formulated the resolvent kernel and the heat kernel in the leading approximation are explicitly constructed as a result the previous work in the literature on heat kernel asymptotics is shown to be a particular case of a more general structure for a bosonic gauge theory on a compact riemannian manifold with smooth boundary the problem of obtaining a gauge field operator of laplace type is studied jointly with local and gauge invariant boundary conditions which should lead to a strongly elliptic boundary value problem the scheme is extended to fermionic gauge theories by means of local and gauge invariant projectors after deriving a general condition for the validity of strong ellipticity for gauge theories it is proved that for euclidean yang mills theory and rarita schwinger fields all the above conditions can be satisfied for euclidean quantum gravity however this property no longer holds i e the corresponding boundary value problem is not strongly elliptic some non standard local formulae for the leading asymptotics of the heat kernel diagonal are also obtained it is shown that due to the lack of strong ellipticity the heat kernel diagonal is non integrable near the boundary

bounds on the dimension of codes and subcodes with prescribed contraction index abstract let c be a linear code over gf q spanned by the rows of a matrix g of rank k a nonnegative integer is said to be the contraction index of c if a maximal set of pairwise linearly independent columns of g has k elements we derive several upper and lower bounds on the dimension of a proper subcode of c with a prescribed contraction index v q of length n minimum hamming distance d and contraction index for certain values of n and d the latter bound is shown to be tight for all q and this substantially generalizes the results obtained by delsarte and by duc for 1

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

on maximum likelihood soft decoding of some binary self dual codes efficient algorithms are derived for maximum likelihood ml soft decision decoding of some binary self dual codes a family of easily decodable self dual codes is derived by modifying a known f sub 24 which has a weight distribution resembling that of the 24 12 8 golay code g sub 24 the ml decoding of f sub 24 is accomplished by only 227 real additions compared to 651 required for g sub 24 yet the error rates of the two decoders are similar for moderate noise conditions

weakly parametric pseudodifferential operators and atiyah patodi singer boundary problems this paper introduces a class of pseudodifferential operators depending on a parameter in a particular way the main application is a complete expansion of the trace of the resolvent of a dirac type operator with nonlocal boundary conditions of the kind introduced by atiyah patodi and singer aps this extends the partial expansion in g2 to a complete one and extends the complete expansion in gs 1 to the case where the dirac operator does not have a product structure near the boundary a secondary application is to obtain a complete expansion of the resolvent of a bdo on a compact manifold essentially reproving a result of agranovich agr the resolvent expansion yields immediately an expansion of the trace of the heat kernel and determines the singularities of the zeta function moreover a pseudodifferential factor can be allowed a major motive for these expansions is to obtain index formulas for elliptic operators there are many such applications in the physics and geometry literature the index formula comes from one particular term in the expansion but each term is a spectral invariant and they have been used for other purposes as well as for the index in particular branson and gilkey have a number of papers e g bg and gi analyzing these invariants and drawing geometric consequences interest in the asymptotic behavior of the resolvent goes back to carleman c more recently agmon agm developed it extensively for analytic applications he introduced the fundamental idea of treating the resolvent parameter essentially as another cotangent variable this idea was developed in s1 to analyze the singularities of the zeta function of an elliptic odo on a compact manifold and in 3 to analyze the resolvent of a differential operator with differential boundary conditions the technique works smoothly for differential operators producing so called local invariants integrals over the underlying

hybrid finite element boundary integral method for cavities recessed in an elliptic cylinder the highly versatile finite element boundary integral method is presented for accurate modeling of fields within cavities recessed in a perfectly conducting infinite elliptic cylinder properties of flush mounted cavities and antennas are explored and compared with prior developments this formulation represents a significant advancement over prior techniques since surface curvature variation either across a single element or across an array of elements is now accurately included into the antenna model an advantage of this approach is the ability to model cavities with curvature varying from planar to the constant curvature of a circular cylinder computed eigenvalues for planar rectangular and cylindrical rectangular closed cavities are compared with theoretical values eigenvalues are presented for elliptic rectangular cavities furthermore the input impedance of a conformal cavity backed patch antenna mounted on an elliptic cylinder is presented and compared with a similar antenna on a circular cylinder

coset codes viewed as terminated convolutional codes coset codes are considered as terminated convolutional codes based on this approach three new general results are presented first it is shown that the iterative squaring construction can equivalently be defined from a convolutional code whose trellis terminates this convolutional code determines a simple encoder for the coset code considered and the state and branch labelings of the associated trellis diagram become straightforward also from the generator matrix of the code in its convolutional code form much information about the trade off between the state connectivity and complexity at each section and the parallel structure of the trellis is directly available based on this generator matrix it is shown that the parallel branches in the trellis diagram of the convolutional code represent the same coset code c sub 1 of smaller dimension and shorter length utilizing this fact a two stage optimum trellis decoding method is devised the first stage decodes c sub 1 while the second stage decodes the associated convolutional code using the branch metrics delivered by stage 1 finally a bidirectional decoding of each received block starting at both ends is presented if about the same number of computations is required this approach remains very attractive from a practical point of view as it roughly doubles the decoding speed this fact is particularly interesting whenever the second half of the trellis is the mirror image of the first half since the same decoder can be implemented for both parts

poles of zeta and eta functions for perturbations of the atiyah patodi singer problem the zeta and eta functions of a differential operator of dirac type on a compact n dimensional manifold provided with a well posed pseudodifferential boundary condition have been shown in g99 to be meromorphic on with simple or double poles on the real axis extending results from g99 we show how perturbations of the boundary condition of order j affect the poles in particular they preserve a possible regularity of zeta at 0 and a possible simple pole of eta at 0 when j n this applies to perturbations of spectral boundary conditions also when the structure is non product and the problem is non selfadjoint

accurate asymptotic solution for the surface field due to apertures in a conducting cylinder asymptotic solutions for the surface field due to a magnetic point source on a cylinder can simplify the computational task in the analysis of mutual coupling e g in conformal arrays although several asymptotic solutions are at present available their accuracy is limited the aim here is to obtain a new approximate solution with improved accuracy an asymptotic solution of the exact modal solution for the field on a cylinder which contains terms up to k 0 t 2 where t is the distance from the source is derived approximate terms up to k 0 t 3 are included from the solution for a source on a plane conductor and an earlier asymptotic solution the new approximate solution consists of the exact solution for a plane conductor modulated by a fock function plus a contribution associated with the cylinder which vanishes in the limit of infinite radius typically for cylinders of radius greater than one and half wavelengths it agrees to within 0 5 db in magnitude and 1 deg in phase of the modal solution results for dominant mode mutual and self admittances of rectangular apertures on a cylinder obtained from this solution are presented a formula is also given for calculating self admittances from an asymptotic solution there is excellent agreement between admittances computed from the asymptotic solution and the modal solution one exception is the self susceptance of an axial slot where the error is larger than expected although the error is low enough to be acceptable in most practical cases

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed