Information-Theoretic Health Monitoring for NAND Flash Memory via Jensen-Shannon Divergence Contraction

We introduce an information-theoretic framework for monitoring NAND flash memory health based on Jensen-Shannon divergence (JSD) contraction coefficients. Flash cell degradation due to program/erase cycling is modeled as a Z-channel with time-dependent error probability ε(t). Using the exact formula η_JSD(Z_ε) = 1 - ε, we define a health metric H(t) = 1 - 2·BER(t) that provides a theoretically grounded measure of information preservation capacity. We validate this framework against empirical data from Mielke, Cai, and Choi et al., demonstrating accurate end-of-life predictions consistent with industry specifications (3K-5K P/E cycles for 3x-nm MLC NAND). The super-tensorization property η_JSD(Z_ε^⊗n) = 1 - ε^n reveals that page-level information is preserved exponentially well even with degraded single-bit reliability. This work represents the first application of strong data processing inequality (SDPI) contraction coefficients to storage system reliability.