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This work deals with error correction for non-volatile memories that arepartially defective at some levels. Such memory cells can only store incompleteinformation since some of their levels cannot be utilized entirely due to,e.g., wearout. On top of that, this paper corrects random errors $t\geq 1$ thatcould happen among $u$ partially defective cells while preserving theirconstraints. First, we show that the probability of violating the partiallydefective cells' restriction due to random errors is not trivial. Next, weupdate the models in [1] such that the coefficients of the output encodedvector plus the error vector at the partially defective positions are non-zero.Lastly, we state a simple proposition (Proposition 3) for masking the partialdefects using a code with a minimum distance $d$ such that $d\geq 2(u+t)+1$."Masking" means selecting a word whose entries correspond to writable levels inthe (partially) defective positions. A comparison shows that masking $u$ cellsby this proposition for a particular BCH code is as effective as using thecomplicated coding scheme proven in [1, Theorem 1].

Codes for Preventing Zeros at Partially Defective Memory Positions