Codes for Memory Cells with Unreachable Levels

This paper focuses on the problem of unreachable memory cells (UMCs). A cell is considered s-unreachable if it cannot store values for higher levels > s. We first provide codes for UMCs and prove that the same parameters as in the coding schemes in recent work on partially stuck memory cells (PSMCs) can be used for UMCs. In the second part, we present a various code construction built upon poly-alphabetic codes, allowing different alphabets to be used in each coordinate. We improve upon previous works for some code parameters while considering certain patterns of unreachable cell distributions. The latter construction gives UMC codes that reach the Singleton-like bound derived for polyalphabetic codes, and our Gilbert– Varshamov-like-bound built on polyalphabetic codes outperforms GV-like bound on partially stuck-at code constructions.