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

Abstract

We in this paper theoretically go over a rate-distortion 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 \textit{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 \textit{Graphon} principle w.r.t. a stochastic \textit{Chordal Schramm-Loewner} evolution etc {via a minimisation over a distortion between the relative realisation times of two given graphs $\mathscr{G}_1$ and $\mathscr{G}_2$ as $ \mathop{{\rm \mathbb{M}in}}\limits_{ \mathscr{G}_1, \mathscr{G}_2} {\rm \; } \mathcal{D} \Big( t\big( \mathscr{G}_1 , \mathscr{G} \big) , t\big( \mathscr{G}_2 , \mathscr{G} \big) \Big)$}. We also extend our scenario to the eavesdropping case. We finally prove the efficiency of our proposed scheme via simulations.