Cristiano Torezzan

Spherical codes on torus layers

A new class of spherical codes is constructed by selecting a finite subset of flat tori that foliate the unit sphere S2L−1 ⊂ ℝ2L and constructing a structured codebook on each torus in the finite subset. The codebook on each torus is the image of a lattice restricted to a specific hyperbox in ℝL. Group structure and homogeneity, useful for efficient decoding, are inherited from the underlying lattice codebook. Upper and lower bounds on performance are derived and a systematic search algorithm is presented for constructing optimal codebooks. The torus layer spherical codes presented here exhibit good performance when compared to the well known apple-peeling, wrapped and laminated codes.

Optimum commutative group codes

A method for finding an optimum

Curves on torus layers and coding for continuous alphabet sources

n

Curves on Flat Tori and Analog Source-Channel Codes

n-dimensional commutative group code of a given order

Spherical codes for the Gaussian wiretap channel with continuous input alphabets

M

A low complexity coding and decoding strategy for the quadratic Gaussian CEO problem

M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.