Contributions to the Simplex Code Conjecture |
Common terms and phrases
arbitrary assume Balakrishnan ball density conjecture center of mass Chapter Communications Theory configuration constraint contain the origin convex hull convex region correct decoding define denote dimensions energy Farber function corresponding Gaussian noise geometric global optimality hyper hypersphere of radius implies induction inequality integral Landau and Slepian Lemma linearized version maximize the intersection maximizes the mean mean width minimizes monotonically decreasing function n-dimensional n-dimensions n+1 n+1 noise function optimum P₂ polytope probability of error problem projected prove r)dr r+Ar R₁ regular simplex maximizes Shannon signal set signal-to-noise ratios simplex code conjecture simplex conjecture simplicial cone simplified proof single hyperplane solid angle sphere spherical cap spherical simplex subspace subtended surface symmetric tetrahedron U.S. Air Force U.S. Navy unit hypersphere V₁ vectors vertices volume W₁ x)dx zero