In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the block length.
In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the block length.
The authors have introduced the new notion of resolvability of a channel, as the dual of the capacity, which is defined as the minimum complexity per input letter needed to generate an input process whose output distribution via the channel arbitrarily accurately approximates any prescribed achievable output distribution. The resolvability thus introduced has revealed a deep relationship between the minimum achievable rate for source coding, the channel capacity, the identification capacity and the problem of random number generation. However, the validity of the proof of the converse for the resolvability formula established by Han and Verdu (see IEEE Trans. on Inform. Theory, vol.39, no.3, p.379, 1993) hinged heavily on the assumption that the input alphabet of the channel is finite. Our main purpose in this paper is to show that we can relax this restriction and to show that the resolvability formula of Han and Verdu continues to hold also for a wide class of channels with continuous input alphabet, including as a special case, additive white Gaussian noise (AWGN) channels with power constraint.>
Identification capacity is developed without randomization at neither the encoder nor the decoder. In particular, full characterization is established for the deterministic identification (DI) capacity for the Gaussian channel and for the general discrete memoryless channel (DMC) with and without constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness given at the encoder, resulting in a double exponential number of messages. In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates can be significantly higher than those of transmission. Ahlswede and Dueck further stated a capacity result for the deterministic setting of a DMC, but did not provide an explicit proof. In this paper, a detailed proof is given for both the Gaussian channel and the general DMC. The DI capacity of a Gaussian channel is infinite regardless of the noise.
Given a general channel, we first formulate the idetification capacity problem as well as the resolvability problem with input cost constraint in as the general form as possible, along with relevant fundamental theorems. Next, we establish some mild sufficient condition for the key lemma linking the identification capacity with the resolvability to hold for the continuous input alphabet case with input cost constraint. Under this mild condition, it is shown that we can reach the {\em continuous}-input fundamental theorem of the same form as that for the fundamental theorem with {\em finite} input alphabet. Finally, as important examples of this continuous-input fundamental theorem, we show that the identification capacity as well as the resolvability coincides with the channel capacity for stationary additive white (and also non-white) Gaussian noise channels.
Two kinds of channels are considered: (1) discrete-time channel with additive noise, and (2) Poisson and white Gaussian (i.e., continuous-time) channels. For the type (1) channel there are given some sufficient conditions when the Shannon and identification capacities coincide. It is shown that the identification capacity of Poisson and Gaussian channels without bandwidth constraint is infinite. Conversely, for a white Gaussian channel with bandwidth constraint, the identification capacity coincides with the Shannon capacity.
Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity CID can strictly exceed the ordinary (exponential) transmission capacity C.
In this paper, we prove that the entanglement-assisted transmission capacity CE is a strong converse bound for this task: CID≤CE. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization CID=CE of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which CID<CE. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity CID.
This work establishes that the physical layer can be used to perform information-theoretic authentication in additive white Gaussian noise (AWGN) channels, as long as the adversary is not omniscient. The model considered consists of an encoder, decoder, and adversary, where the adversary knows the message given to the encoder, has a non-causal noisy observation of the encoder’s transmission and may use unlimited transmission power, while the decoder observes a noisy version of the sum of the encoder and adversary’s outputs. A method to modify a generic existing channel code to enable authentication is presented. This method relies on injecting message-dependent noise into the transmission and accepting the transmission as authentic only if the correct noise levels for the decoded message are observed. One drawback to this method is that the encoder must still transmit a low-power signal in the case where there is no message to send. It is shown that this modification costs an asymptotically negligible amount of the coding rate, while still enabling authentication as long as the adversary’s observation is not noiseless. Also notable is that this modification is not (asymptotically) a function of the statistical characterization of the adversary’s channel and no secret key is required. We believe these features will pave the way for a robust practical implementation. Using these results, the channel-authenticated capacity is calculated and shown to be equal to the non-adversarial channel capacity. As our results will show, information-theoretic authentication in AWGN channels is possible without the need for the legitimate party to have a model-based advantage over the adversary. While this modular scheme is designed for use in the given channel model, it is applicable to a wide range of settings.