Detection of Limited Magnitude Errors in Emerging Multilevel Cell Memories by One-Bit Parity (OBP) or Two-Bit Parity (TBP) Articles uri icon



publication date

  • December 2021

start page

  • 1792

end page

  • 1802


  • 4


  • 9

International Standard Serial Number (ISSN)

  • 2168-6750


  • Emerging memory technologies rely on Multilevel Cells (MLC) to achieve high density; the use of multiple levels per cell allows storage of multiple bits, but it also reduces the margins and makes it error prone. Error control codes (including error correction and detection codes) can be used to protect MLC memories from errors; however, most existing coding schemes have been designed for traditional binary memories (so storing a single bit). In MLC memories, errors cause a change from a level to an adjacent level or to the next one (depending on the employed technology), so they are often referred to as limited magnitude errors. For a binary coding of levels to bits, these limited magnitude errors can corrupt several bits making traditional coding schemes inefficient. In this paper, error detection of MLC memories is considered when a binary encoding of levels to bits is used and two new schemes are proposed: One-Bit Parity (OBP) and Two-Bit Parity (TBP). The first scheme targets errors of magnitude-1 for detection using a single parity bit that checks only one bit per cell. The second scheme detects both magnitude-1 and -2 errors using only two parity bits. Both schemes are compared to existing alternatives, namely Gray coding combined with a single parity bit (GP) for OBP and Interleaved Parity (IP) for TBP. The results show that OBP reduces the encoding and error detection circuitry complexity and delay, while TBP additionally reduces the number of parity bits for some configurations. Therefore, OBP and TBP can be efficient alternatives for detection of limited magnitude errors in MLC memories that use a binary encoding of levels to bits.


  • Computer Science
  • Electronics
  • Telecommunications


  • multilevel cell memories; error control codes; limited magnitude errors