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IEEE International Symposium on Information Theory (ISIT)

Multi-terminal Strong Coordination Over Noisy Channels with Secrecy Constraints

Viswanathan Ramachandran, Tobias J. Oechtering, Mikael Skoglund

Published Jul 7, 2024• 4 citations
Publisher

Abstract

We investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel (MAC-WT). In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver on observing the channel output must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. Furthermore, we demand that an external eavesdropper learns essentially nothing about the sources and the simulated output sequence by observing its corresponding MAC-WT output. This is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder. The shared randomness rate tuples which permit such channel simulation with strong secrecy are of interest. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are independent and the legitimate receiver's channel is composed of deterministic links.

DOI
10.1109/isit57864.2024.10619089

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We investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel (MAC-WT). In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver on observing the channel output must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. Furthermore, we demand that an external eavesdropper learns essentially nothing about the sources and the simulated output sequence by observing its corresponding MAC-WT output. This is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder. The shared randomness rate tuples which permit such channel simulation with strong secrecy are of interest. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are independent and the legitimate receiver's channel is composed of deterministic links.
A fundamental problem in decentralized networked systems is to coordinate actions of different agents so that they reach a state of agreement. In such applications, it is additionally desirable that the actions at various nodes may not be anticipated by malicious eavesdroppers. Motivated by this, we investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel. In this setup, independent and identically distributed copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver observing the channel output and side information correlated with the sources must produce approximately i.i.d. copies of an output variable jointly distributed with the sources. Furthermore, we demand that an external eavesdropper learns essentially nothin g about the sources and the simulated output sequence by observing its own MAC-WT output. This setting is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder, that is unavailable to the eavesdropper. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are conditionally independent given the decoder side information and the legitimate channel is composed of deterministic links. Further, we also analyze a more general scenario with possible encoder cooperation, where one of the encoders can non-causally crib from the other encoders input, for which an achievable rate region is proposed. We then explicitly compute the rate regions for an example both with and without cribbing between the encoders, and demonstrate that cribbing strictly improves upon the achievable rate region.
We develop an outer bound for the secrecy capacity region of a class of multiple access wiretap channels (MAC-WT). In this class, which we call the weak eavesdropper class, each user's link to the legitimate receiver is stronger than its link to the eavesdropper. Our outer bound partially matches the achievable region in an n-letter form. In addition, a looser version of our outer bound provides close approximations to the capacity region of the Gaussian MAC-WT channel. In particular, we prove that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual rates for all weak eavesdropper Gaussian MAC-WT, and within 0.5 bits/channel use in all directions for certain weak eavesdropper Gaussian MAC-WT channels.
In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confidential message against any sequence of channel states experienced by the eavesdropper. This yields the conclusion that secure communication is possible regardless of the location or channel states of (potentially infinite number of) eavesdroppers. Additionally, it is observed that, the present setting renders the secrecy capacity problems for multi-terminal wiretap-type channels more tractable as compared the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access wiretap channel (MIMO MAC-WT) and the Gaussian MIMO broadcast wiretap channel (MIMO BC-WT) where the transmitter(s) and the intended receiver(s) have the same number of antennas.
The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. We present a new hybrid inner bound on the secrecy capacity region of this feedback model, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other (decode each other's transmitted message from the feedback), but also to generate two secret keys respectively shared between the legitimate receiver and the two transmitters. We show that this hybrid inner bound is strictly larger than the already existing decode-and-forward (DF) inner bound. Moreover, we provide a sato-type outer bound on the secrecy capacity region of the MAC-WT with noiseless feedback. The results of this paper are further explained via a Gaussian example.
We derive a rate region which is achievable by the Wiretap MAC with Common Message under the strong secrecy criterion. We follow Devetak's approach to establishing strong secrecy. Using the concentration of the normed sum of bounded i.i.d. random variables around its mean, it is possible to show the existence of a code where the channel outputs at the eavesdropper are almost independent of the messages. The encoders may use a certain amount of common randomness. We give the example of a channel where the availability of common randomness is necessary for secret transmission.
In this paper, we study the two transmitter multiple-access channel (MAC) with noncausal side information at one (single-sided) or both (two-sided) of the encoders in the presence of an external wiretapper (WT) and under individual and collective secrecy constraints. Our work consists of four parts. First, we consider the discrete memoryless (DM-MAC-WT) case of the model and derive inner and outer bounds on the secrecy capacity region under both of the secrecy constraints. Second, the results are extended to the Gaussian memoryless case [Gaussian multiple-access channel WT (GMAC-WT)] in detail and are used to illustrate numerically that the secrecy rate region is enlarged by increasing the power of the interference signal which is known noncausally at the encoder. Third, we analyze the strong interference regime as an important regime in GMAC with side information and show that under collective secrecy constraint, we can achieve the secrecy capacity region of the single-sided channel asymptotically for a special case in which the signal and noise powers satisfy specific constraints. To the best of our knowledge, this capacity region is the first one obtained for GMAC-WT. Finally, we show that our results include previous works as its special cases for both the single-sided and two-sided channel models.