Error Correction in Adders using Systematic Subcodes

It is presently known that (single) error correction in adders can be obtained by use of biresidue codes, which use two separate checkers with respect to two different check bases of the form 2
^c
-1. It is shown here that a class of systematic subcodes derived from the nonsystematic AN codes can provide error correction using only one checker. However, the check base A of these codes is not of the form 2
^c
-1 and therefore involves a somewhat complex addition structure involving two or more end-around-carries (EAC's). Here we present a generalized theory for the construction of a systematic subcode for a given AN code in such a way that error control properties of the AN code are preserved in this new code. The ``systematic weight'' and ``systematic distance'' functions in this new code depend not only on its number representation system but also on its addition structure. Finally, to illustrate this theory, a simple error-correcting adder organization using a systematic subcode of 29 N code is sketched in some detail.