Single user tracing superimposed codes

We investigate the zero-error capacity region of r-out of T user multiple access OR channel. A family ℱ subsets of [n]={1, . . . ,n} is an r-single-user-tracing superimposed code (r-SUT) if there exists such a single-user-tracing function φ: 2^[n]→ℱ that for all ℱ⊆ℱ with |ℱ´|≤r, φ(∪_A∈ℱ_´A)∈ℱ´. In this paper we introduce the concept of these codes and investigate bounds on their rate. We also consider disjointly r-superimposed codes.