Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure

Explicit Constructions of Quasi-Uniform Codes from Groups

We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian groups. Potentials applications comprise the design of almost affine codes and non-linear network codes

How to Compute Modulo Prime-Power Sums

The problem of computing modulo prime-power sums is investigated in distributed source coding as well as computation over Multiple-Access Channel (MAC). We build upon group codes and present a new class of codes called Quasi Group Codes (QGC). A QGC is a subset of a group code. These codes are not closed under the group addition. We investigate some properties of QGC's, and provide a packing and a covering bound. Next, we use these bounds to derived achievable rates for distributed source coding as well as computation over MAC. We show that strict improvements over the previously known schemes can be obtained using QGC's

Optimal prefix codes for pairs of geometrically-distributed random variables

Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the redundancy penalty of symbol-by-symbol encoding, while preserving the simplicity of the encoding and decoding procedures typical of Golomb codes and their variants. It is shown that optimal codes for these so-called two-dimensional geometric distributions are \emph{singular}, in the sense that a prefix code that is optimal for one value of the parameter $q$ cannot be optimal for any other value of $q$. This is in sharp contrast to the one-dimensional case, where codes are optimal for positive-length intervals of the parameter $q$. Thus, in the two-dimensional case, it is infeasible to give a compact characterization of optimal codes for all values of the parameter $q$, as was done in the one-dimensional case. Instead, optimal codes are characterized for a discrete sequence of values of $q$ that provide good coverage of the unit interval. Specifically, optimal prefix codes are described for $q=2^{-1/k}$ ($k\ge 1$), covering the range $q\ge 1/2$, and $q=2^{-k}$ ($k>1$), covering the range $q<1/2$. The described codes produce the expected reduction in redundancy with respect to the one-dimensional case, while maintaining low complexity coding operations.Comment: To appear in IEEE Transactions on Information Theor

Quasi-TEM modes in rectangular waveguides: a study based on the properties of PMC and hard surfaces

Hard surfaces or magnetic surfaces can be used to propagate quasi-TEM modes inside closed waveguides. The interesting feature of these modes is an almost uniform field distribution inside the waveguide. But the mechanisms governing how these surfaces act, how they can be characterized, and further how the modes propagate are not detailed in the literature. In this paper, we try to answer these questions. We give some basic rules that govern the propagation of the quasi-TEM modes, and show that many of their characteristics (i.e. their dispersion curves) can be deduced from the simple analysis of the reflection properties of the involved surfaces