A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective

Adaptive controllers and signal processors play a key role in dealing with parameter uncertainties. This paper proposes an adaptive and new information theoretic algorithm for secure and optimal source-coding. We optimise the volume of the achievable rate-distortion-equivocation region by the private Helen's rate (HR), defining a stochastic mean-field game (MFG). The aforementioned stochasticity deals with the additional uncoded side-information (SI) at the encoder-decoder, or even possibly-decoded SI at the eavesdropper (Eve). The stochastic partial derivative equations (SPDEs), namely the Hamilton-JacobiBellman (HJB) and the Fokker-Planck-Kolmogorov (FPK) are presented, being solved by a discretised Lagrangian. We explore the Information-flow over the resultant Riemann-Sphere and our proposed SMFG's stability from a many-body-theoretic perspective. We also show that while the equivocation (uncertainty) rate is Δ ≤ min{H(X), R
_h
}, I(Y; Z|W) which is upper-bounded to min{I(X; Y), I(Y; Z|W)}, versus I(X; Z|W) theoretically converges to the information-Bottleneck-bound H(X). Simulation results also show an out-performance of our scheme over the existing work, proving the SMFG's stability and an adequate distance to Pareto-Optimal sets. Our generic solution covers a comprehensive field of studies determining smooth non-linearity.