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.