Author

Walid Kassem

Date of Award

1981

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical and Computer Engineering

Supervisor

Dr. J. Anderson

Co-Supervisor

Dr. R. de Buda

Abstract

Lattices are used to construct a class of equal-energy codes for the Gaussian channel and the resultant error probability tends to zero for large n at all rates below channel capacity. The error probability is explicitly bounded for any given lattice code and then further further bounded for a general code using the Minkowski-Hlawka theorem of the geometry of numbers. Similar bounds are applied also to maximum-energy codes, to show that such lattice codes are near-optimal.

Finally, the error bounds are applied to explicit codes defined for all n=2ᵐ. These codes are shown to have a low Pℯ at rates higher than any previously attained.