Modern communication systems impose strict demands on data rate, reliability, and power efficiency. In this context, emerging communication paradigms such as identification via channels have become an important topic in post-Shannon information theory, offering the potential for substantially higher identification rates than in conventional channel coding.Deterministic identification is particularly interesting for specialized communication scenarios because it provides a balance between implementation complexity and the communication gains due to higher identification rates. It is therefore a promising communication scheme for future communication systems, including molecular communication systems. Additive Gaussian channels, particularly the additive white Gaussian channel, are among the most important channel models for analyzing the performance of communication systems in information and communication theory. This importance stems from both their mathematical tractability and their ubiquitous appearance in practical applications. To date the deterministic identification capacity for additive Gaussian channels remains unknown even for the simplest case of the additive white Gaussian channel. In this paper, we establish tight bounds on the deterministic identification capacity of additive Gaussian channels by introducing a new perspective on deterministic identification. To this end, we apply results from lattice theory to obtain new capacity results.

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