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A code is implicitly constructed' from a lattice and its Dirichlet regions and, for Gaussian noise, the worst error probability of any code point is upperbounded in closed form by a chi-square distribution. The bound shows that fairly efficient codes can be obtained, particularly, at high signal-to-noise ratio (SNR) the bound approaches asymptotically the error bound of an optimal code. The derivation is by a promising new method in which the Minkowski-H!awka theorem of the geometry of numbers is used in place of the we!l-known random coding arguments.
Date of Publication: Jul 1975