Channel Capacity Formulations for Non-Volatile Memories With Unreachable Levels

This paper investigates the channel capacity of unreachable memory cells (UMCs), where a cell is deemed -unreachable if it cannot store values beyond a specific state, . Memories with these impairments are modeled as discrete memoryless channels (DMCs), similar to those used in information theory and communications. We derive Shannon-type capacity equations for memories with unreachable levels and substitution errors. These novel equations generalize classical Shannon capacity to systems with UMCs. We also compare ideal memories (without imperfections or errors) with normal memories affected by random errors only, as well as defective and erroneous memories. Our findings corroborate previous studies, particularly regarding random distributions of defective cells. Our results highlight the impact of increasing faulty cells and substitution errors, demonstrating the necessity of greater redundancy to maintain system performance.