Defining canonical-signed-digit number systems as arithmetic codes

The canonical-signed-digit (CSD) number system is widely used to represent filter coefficients for filter implementation using efficient addition/subtraction networks for the multiplication of 2´s complement input signals. Higher radix CSD has been proposed for dramatic reduction of terms that must be combined. In this paper, we redefine CSD and radix-4 CSD as arithmetic codes. By defining these number representations using the well-known theory of arithmetic coding, we provide the opportunity to transfer techniques from one field to another.