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

A VC-dimension-based Outer Bound on the Zero-Error Capacity of the Binary Adder Channel