Coset Decomposition in Lattices Yields
Sample-Block Number Systems
- J. O. Coleman
- The representation of a scalar by a sequence of digits
weighted by powers of some radix is here generalized
to vectors. The radix becomes a matrix, and its
powers are applied to digits that are vectors taken
from a lattice. Familiar notions of overflow and
truncation error apply, and the familiar
two's-complement approach to representing vectors on
the ``wrong side'' of zero generalizes cleanly.
Blocking 1D samples into vectors before conversion to
these vector number systems can yield advantages in
computational efficiency related to the packing
efficiency of lattice points, much as data
communication is improved by error-correcting block
codes, a closely related topic.
- DOWNLOADABLE PREPRINT:
- Presentated to the
2002 IEEE International Symposium on Circuits and Systems (ISCAS 2002), Scottsdale AZ,
USA, May 26-29, 2002.
- DATE OF ENTRY: