A Theoretically Novel Trade-off for Sparse Secret-key Generation

Abstract

We in this paper theoretically go over a ratedistortion based sparse dictionary learning problem. We show that the Degrees-of-Freedom (DoF) interested to be calculated − satnding for the minimal set that guarantees our rate-distortion trade-off − are basically accessible through a Langevin equation. We indeed explore that the relative time evolution of DoF, i.e., the transition jumps is the essential issue for a relaxation over the relative optimisation problem. We subsequently prove the aforementioned relaxation through the Graphon principle w.r.t. a stochastic Chordal Schramm-Loewner evolution etc via a minimisation over a distortion between the relative realisation times of two given graphs 𝒢 1 and 𝒢 2 as Min 𝒢 1 ,𝒢 2 D 𝑡 𝒢 1 , 𝒢 , 𝑡 𝒢 2 , 𝒢 . We also extend our scenario to the eavesdropping case. We finally prove the efficiency of our proposed scheme via simulations.