Abstract
Lattices in \(\mathbb {R}^{n}\) with sublattices which have an orthogonal basis are associated with spherical codes in \(\mathbb {R}^{2n}\) generated by a finite commutative group of orthogonal matrices. They also can be used to construct homogeneous spherical curves for transmitting a continuous alphabet source over an AWGN channel. In both cases, the performance of the decoding process is related to the packing density of the lattices (see ( 2.13)). In the continuous case, the packing density of these curves relies on the search for projection lattices with good packing density. We present here a survey on this topic mainly based on [18, 31, 96, 105].
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