Coding and bounds for partially defective memory cells

Haider Al Kim, Sven Puchinger, Ludo Tolhuizen, Antonia Wachter-Zeh

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper considers coding for so-called partially stuck (defect) memory cells. Such memory cells can only store partial information as some of their levels cannot be used fully due to, e.g., wearout. First, we present new constructions that are able to mask u partially stuck cells while correcting at the same time t random errors. The process of “masking” determines a word whose entries coincide with writable levels at the (partially) stuck cells. For u> 1 and alphabet size q> 2 , our new constructions improve upon the required redundancy of known constructions for t= 0 , and require less redundancy for masking partially stuck cells than former works required for masking fully stuck cells (which cannot store any information). Second, we show that treating some of the partially stuck cells as erroneous cells can decrease the required redundancy for some parameters. Lastly, we derive Singleton-like, sphere-packing-like, and Gilbert–Varshamov-like bounds. Numerical comparisons state that our constructions match the Gilbert–Varshamov-like bounds for several code parameters, e.g., BCH codes that contain all-one word by our first construction.

Original languageEnglish
Pages (from-to)4019-4058
Number of pages40
JournalDesigns, Codes, and Cryptography
Issue number12
StatePublished - Dec 2023


  • (Partially) Stuck cells
  • Defective memory
  • Error-correcting codes
  • Flash memories
  • Gilbert-Varshamov bound
  • Non-volatile memories


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