On optimal error exponents in noiseless channel identification

Recently Yamamoto and Ueda proposed multiple object identification (MOID) codes to identify multiple objects via a channel at once, which is an extension of identification (ID) codes. They gave the explicit construction of MOID codes and derived the achievable triplet of coding rate R, the error exponents E
₁
and E
₂
of type I and type II decoding error probabilities. However, they did not treat the converse problem of the coding theorem. In this paper, we consider the coding rate of multiple objects R
_k
in addition to R, E
₁
, and E
₂
, and derive a condition that (R, R
_k
, E
₁
, E
₂
) must satisfy for any MOID codes of noiseless channels.