2022/05/13 by Haider Al Kim, Kim, Haider Al, Kai Jie Chan +1
Computer Science · #Advanced Data Storage Technologies #Algorithms and Data Compression #Cellular Automata and Applications #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2205.06781
openalex publication_date 2022/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work deals with error correction for non-volatile memories that are partially defective at some levels. Such memory cells can only store incomplete information since some of their levels cannot be utilized entirely due to, e.g., wearout. On top of that, this paper corrects random errors t≥ 1 that could happen among u partially defective cells while preserving their constraints. First, we show that the probability of violating the partially defective cells' restriction due to random errors is not trivial. Next, we update the models in [1] such that the coefficients of the output encoded vector plus the error vector at the partially defective positions are non-zero. Lastly, we state a simple proposition (Proposition 3) for masking the partial defects using a code with a minimum distance d such that d≥ 2(u+t)+1. "Masking" means selecting a word whose entries correspond to writable levels in the (partially) defective positions. A comparison shows that masking u cells by this proposition for a particular BCH code is as effective as using the complicated coding scheme proven in [1, Theorem 1].