Tracing many users with almost no rate penalty

Noga Alon, Vera Asodi

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


For integers n, r ≥ 2 and 1 ≤ k ≤ r, a family F of subsets of [n] = {1,⋯,n} is called k-out-of-r multiple-user tracing if, given the union of any ℓ ≤ r sets from the family, one can identify at least (min(k, ℓ) of them. This is a generalization of superimposed families (k = r) and of single-user tracing families (k = 1). The study of such families is motivated by problems in molecular biology and communication. In this correspondence, we study the maximum possible cardinality of such families, denoted by h(n, r, k), and show that there exist absolute constants c1, c2, c3, c4 < 0 such that min(c1/r, c3/k2) ≤ log h(n, r, k)/n ≤ min (c2/r, c4 log k/k2). In particular, for all k ≤ √r, log h(n, r, k)/n = θ(1/r). This improves an estimate of Laczay and Ruszinkó.

Original languageEnglish (US)
Pages (from-to)437-439
Number of pages3
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Multiple-user tracing codes
  • Probabilistic construction of codes
  • Superimposed codes


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