Universal Rewriting in Constrained Memories

A constrained memory is a storage device whose elements change their states under some constraints. A typical example is flash memories, in which cell levels are easy to increase but hard to decrease. In a general rewriting model, the stored data changes with some pattern determined by the application. In a constrained memory, an appropriate representation is needed for the stored data to enable efficient rewriting. In this paper, we define the general rewriting problem using a graph model. This model generalizes many known rewriting models such as floating codes, WOM codes, buffer codes, etc. We present a novel rewriting scheme for the flash-memory model and prove it is asymptotically optimal in a wide range of scenarios. We further study randomization and probability distributions to data rewriting and study the expected performance. We present a randomized code for all rewriting sequences and a deterministic code for rewriting following any i.i.d. distribution. Both codes are shown to be optimal asymptotically.