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 /spl phi/:2/sup [n]/ /spl rarr/ F that for all F' /spl sube/ F with 1 /spl les/ |F'| /spl les/ r, /spl phi/(/spl cup//sub A/spl isin/F/'A) /spl isin/ F'. In this correspondence, we introduce the concept of these codes and give bounds on their rate. We also consider disjointly r-superimposed codes.