论文标题
预防零处的零位置的代码
Codes for Preventing Zeros at Partially Defective Memory Positions
论文作者
论文摘要
这项工作涉及在某些级别部分有缺陷的非易失性记忆的错误校正。此类内存单元只能存储不完整的信息，因为它们的某些级别不能完全使用，例如磨损。最重要的是，本文纠正了随机错误$ t \ geq 1 $，这些错误在保留其约束的同时可能会在$ u $中发生部分故障。首先，我们表明，由于随机误差而违反部分有缺陷的细胞限制的可能性并不微不足道。接下来，我们更新[1]中的模型，以使输出编码向量的系数加上部分缺陷位置处的误差向量为非零。最后，我们陈述了一个简单的命题（命题3），用于使用具有最小距离$ d $的代码掩盖部分缺陷，以便$ d \ geq 2（u+t）+1 $。 “掩盖”是指选择一个单词，其条目对应于（部分）有缺陷的位置中的可写级别。一个比较表明，该命题对特定BCH代码掩盖$ U $单元与使用[1，定理1]中证明的复杂编码方案一样有效。
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 $t\geq 1$ 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 $d\geq 2(u+t)+1$. "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].
