1 research outputs found
Encoding and Indexing of Lattice Codes
Encoding and indexing of lattice codes is generalized from self-similar
lattice codes to a broader class of lattices. If coding lattice
and shaping lattice satisfy
, then
is a quotient group that can be
used to form a (nested) lattice code . Conway and Sloane's method
of encoding and indexing does not apply when the lattices are not self-similar.
Results are provided for two classes of lattices. (1) If
and both have generator matrices in triangular form,
then encoding is always possible. (2) When and
are described by full generator matrices, if a solution
to a linear diophantine equation exists, then encoding is possible. In
addition, special cases where is a cyclic code are also
considered. A condition for the existence of a group homomorphism between the
information and is given. The results are applicable to a variety
of coding lattices, including Construction A, Construction D and LDLCs. The
, and convolutional code lattices are shown to be good choices for
the shaping lattice. Thus, a lattice code can be designed by
selecting and separately,
avoiding competing design requirements of self-similar lattice codes