On The Generalization of Error - Correcting WOM

WOM (Write Once Memory) codes are codes for efficiently storing and updating data in a memory whose state transition is irreversible. Storage media that can be classified as WOM includes flash memories, optical disks and punch cards. Error-correcting WOM codes can correct errors besides its regular data updating capability. They are increasingly important for electronic memories using MLCs (multi-level cells), where the stored data are prone to errors. In this paper, we study error-correcting WOM codes that generalize the classic models. In particular, we study codes for jointly storing and updating multiple variables instead of one variable in WOMs with multi-level cells. The error-correcting codes we study here are also a natural extension of the recently proposedfoating codes [7]. We analyze the performance of the generalized errorcorrecting WOM codes and present several bounds. The number of valid states for a code is an important measure of its complexity. We present three optimal codes for storing two binary variables in n q-ary cells, where n = 1, 2, 3, respectively. We prove that among all the codes with the minimum number of valid states, the three codes maximize the total number of times the variables can be updated.