Constrained rank modulation schemes

Rank modulation schemes for non-volatile memories (NVMs) represent information by the relative rankings of cell charge levels. This approach has several benefits; in particular, the scheme resolves the “write-asymmetry” limitation that NVMs suffer from. However, cell writing is still affected by a common NVM problem: inter-cell coupling, which can result in inadvertently increasing the charge level of neighboring cells. This is a potential source of error in the rank modulation scheme. In this paper, we explore the idea of constrained coding over permutations. These constraints minimize the impact of inter-cell coupling while still allowing the use of the rank modulation scheme. We study various constraints and their resulting rates, capacities, and other properties, and introduce an explicit constrained rank modulation code construction.