Multiple Object Identification Coding

Abstract

In the case of ordinary identification coding, a code is devised to identify a single object among $N$ objects. But, in this paper, we consider a coding problem to identify $K$ objects at once among $N$ objects in the both cases that $K$ objects are ranked or not ranked. By combining Moulin–Koetter scheme with the $\varepsilon $ -almost strongly universal class of hash functions used in Kurosawa–Yoshida scheme, an efficient and explicit coding scheme is proposed for $K$ -multiple-object identification ( $K$ -MOID) coding. Furthermore, it is shown that the $K$ -MOID capacity $ C_{\text {$K$-MOID}}$ , which is the maximum achievable coding rate in the $K$ -MOID coding, is equal to the ordinary channel capacity, and the proposed scheme can attain $ C_{\text {$K$-MOID}}$ .