Periodic Reporting for period 1 - CYBERNETS (Cybernetic Communication Networks: Fundamental Limits and Engineering Challenges)
Reporting period: 2015-06-01 to 2017-05-31
Information transmission in G-ICs with noisy channel-output feedback (G-IC-NOF) was studied from two perspectives: centralized and decentralized networks. From the perspective of centralized networks, the main results beyond the state of the art are the fundamental limits of the G-IC-NOF, e.g. an approximation to the capacity region. Another contribution is an approximation of the Nash equilibrium region of the G-IC-NOF.
Simultaneous data and energy transmission in fully distributed CCNs with feedback was studied focusing on two canonical channels: The G-IC with perfect channel-output feedback (G-IC-POF) and the G-MAC with perfect channel output feedback (G-MAC-POF). In both cases, the main results beyond the state of the art are the information-energy capacity regions.
Data injection attacks to the state-estimation system of electricity grids was studied aiming to identify their fundamental limits. The main results beyond the state of the art are some characterizations of the trade-offs between the maximum distortion that an attack can introduce and the probability of being detected by the network operator in both centralized and decentralized standpoints. Stealth attacks that minimize the amount of information that the operator obtains from the grid and the probability of attack detection were also studied.
The results obtained in this project reached a wide audience worldwide given the number of tutorials and invited talks carried out during the project duration. A graduate-level course was taught in Ecole Normale Supérieur (ENS) de Lyon that was made available to the students of ENS de Lyon and students of INSA de Lyon. The webpage of the project also shows all publications, applets and videos that are product of this project (cybernets.inria.fr).
Result 1: The capacity region of the linear deterministic interference channel with noisy channel-output feedback (LD-IC-NOF) is fully characterized. A capacity-achieving scheme is obtained using a random coding argument and three well- known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing outer bounds as well as a set of new outer bounds that are obtained by using genie-aided models of the original LD-IC- NOF. Using the insights gained from the analysis of the LD-IC- NOF, an achievability region and a converse region for the two- user Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are presented. Finally, the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within 4.4 bits.
Result 2: The fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) with and without feedback are fully characterized. More specifically, all the achievable information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. Furthermore, the fundamental limits on the individual and sum-rates given a minimum energy rate ensured at an energy harvester are also characterized. In the case without feedback, an achievability scheme based on power-splitting and successive interference cancellation is shown to be optimal. Alternatively, in the case with feedback (G-MAC-F), a simple yet optimal achievability scheme based on power-splitting and Ozarow’s capacity achieving scheme is presented. Finally, the energy transmission enhancement induced by the use of feedback is quantified. Feedback can at most double the energy transmission rate at high SNRs when the information transmission sum-rate is kept fixed at the sum-capacity of the G-MAC, but it has no effect at very low SNRs.
Result 3: Multiple attacker data injection attack construction in electricity grids with minimum-mean-square-error state estimation is studied for centralized and decentralized scenarios. A performance analysis of the trade-off between the maximum distortion that an attack can introduce and the probability of the attack being detected by the network operator is considered. In this setting, optimal centralized attack construction strategies are studied. The decentralized case is examined in a game- theoretic setting. A novel utility function is proposed to model this trade-off and it is shown that the resulting game is a potential game. The existence and cardinality of the corresponding set of Nash Equilibria (NEs) of the game is analyzed. Interestingly, the attackers can exploit the correlation among the state variables to facilitate the attack construction. It is shown that attackers can agree on a data injection vector construction that achieves the best trade-off between distortion and detection probability by sharing only a limited number of bits offlline. For the particular case of two attackers, numerical results based on IEEE test systems are presented.