The paper establishes the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC).
The key contributions are:
A refined version of Hayashi's theorem is proposed to prove the achievability part. This involves using the capacity-achieving output distribution as an auxiliary distribution instead of the actual output distribution induced by the uniform input distribution.
A finer quantization method is developed to prove the converse part. The input alphabet is partitioned into small sectors instead of hypercubes, which provides a more accurate approximation.
The results show that the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity, with the only difference being that the maximum number of messages in RID scales double exponentially in the blocklength.
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arxiv.org
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