781 research outputs found
Cantor polynomials for semigroup sectors
A packing function on a set Omega in R^n is a one-to-one correspondence
between the set of lattice points in Omega and the set N_0 of nonnegative
integers. It is proved that if r and s are relatively prime positive integers
such that r divides s-1, then there exist two distinct quadratic packing
polynomials on the sector {(x,y) \in \R^2 : 0 \leq y \leq rx/s}. For the
rational numbers 1/s, these are the unique quadratic packing polynomials.
Moreover, quadratic quasi-polynomial packing functions are constructed for all
rational sectors.Comment: 12 page
Algebraic number theory and code design for Rayleigh fading channels
Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available.
The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible
to a large audience
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