Abstract
In this work, we propose and study a new class of non-binary rewriting codes, called write l-step-up memories (WPM) codes. From an information-theoretic point of view, this coding scheme is a generalization of non-binary write-once memories (WOM) codes. From a practical point of view, this coding scheme can be used not only to increase the lifetime of flash memories but also mitigate their over-shooting problem. We first provide an exact formula for the capacity region and the maximum sum-rate of WPM codes. Lastly, we present several explicit constructions of high-rate WPM codes with efficient encoding/decoding algorithms.