Deterministic identification over K-input multiple-access channels with average input cost constraints is considered. The capacity region for deterministic identification is determined for an average-error criterion, where arbitrarily large codes are achievable. For a maximal-error criterion, upper and lower bounds on the capacity region are derived. The bounds coincide if all average partial point-to-point channels are injective under the input constraint, i.e. all inputs at one terminal are mapped to distinct output distributions, if averaged over the inputs at all other terminals. The achievability is proved by treating the MAC as an arbitrarily varying channel with average state constraints. For injective average channels, the capacity region is a hyperrectangle. The modulo-2 and modulo-3 binary adder MAC are presented as examples of channels which are injective under suitable input constraints. The binary multiplier MAC is presented as an example of a non-injective channel, where the achievable identification rate region still includes the Shannon capacity region.

翻译：考虑具有平均输入代价约束的K输入多址接入信道上的确定性识别问题。在平均错误准则下，确定了确定性识别的容量区域，其中可实现任意大的码本。针对最大错误准则，推导了容量区域的上下界。若所有平均部分点对点信道在输入约束下均为单射，即当对所有其他终端的输入进行平均时，一个终端的所有输入映射到不同的输出分布，则上下界重合。通过将多址接入信道视为具有平均状态约束的任意变化信道，证明了可达性。对于单射平均信道，容量区域为超矩形。以模2与模3二进制加法多址接入信道为例，说明其在适当输入约束下具有单射性；以二进制乘法多址接入信道为例，说明其非单射性，但其可达的识别速率区域仍包含香农容量区域。