  The binary adder is a two-user multiple access channel whose inputs are
binary and whose output is the real sum of the inputs. While the Shannon
capacity region of this channel is well known, little is known regarding its
zero-error capacity region, and a large gap remains between the best inner and
outer bounds. In this paper, we provide an improved outer bound for this
problem. To that end, we introduce a soft variation of the Saur-Perles-Shelah
Lemma, that is then used in conjunction with an outer bound for the Shannon
capacity region with an additional common message.
