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We analyze message identification via Gaussian channels with noiseless feedback, which is part of the Post Shannon theory. The consideration of communication systems beyond the Shannon's approach is useful in order to increase the efficiency of information transmission for certain applications. We consider the Gaussian channel with feedback. If the noise variance is positive, we propose a coding scheme that generates infinite common randomness between the sender and the receiver and show that any rate for identification via the Gaussian channel with noiseless feedback can be achieved. The remarkable result is that this applies to both rate definitions 1 n log M (as Shannon defined it for the transmission) and 1 n log log M (as defined by Ahlswede and Dueck for identification). We can even show that our result holds regardless of the selected scaling for the rate.

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Identification is a communication paradigm that promises some exponential advantages over transmission for applications that do not actually require all messages to be reliably transmitted, but where only few selected messages are important. Notably, the identification capacity theorems prove the identification is capable of exponentially larger rates than what can be transmitted, which we demonstrate with little compromise with respect to latency for certain ranges of parameters. However, there exist more trade-offs that are not captured by these capacity theorems, like, notably, the delay introduced by computations at the encoder and decoder. Here, we implement one of the known identification codes using software-defined radios and show that unless care is taken, these factors can compromise the advantage given by the exponentially large identification rates. Still, there are further advantages provided by identification that require future test in practical implementations.