<p><b>Abstract</b>—Fault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset <tmath>$C$</tmath> of points in an undirected graph <tmath>$G=(V,E)$</tmath> is called an identifying code if the sets <tmath>$B(v) \cap C$</tmath> consisting of all elements of <tmath>$C$</tmath> within distance one from the vertex <tmath>$v$</tmath> are different. We also require that the sets <tmath>$B(v) \cap C$</tmath> are all nonempty. We take <tmath>$G$</tmath> to be the infinite square lattice with diagonals and show that the density of the smallest identifying code is at least 2/9 and at most 4/17.</p>