Single-user tracing and disjointly superimposed codes

The zero-error capacity region of r-out-of-T user multiple-access OR channel is investigated. A family F of 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 1 ≤ |F´| ≤ r, φ(∪_A∈F´A) ∈ F´. In this correspondence, we introduce the concept of these codes and give bounds on their rate. We also consider disjointly r-superimposed codes.