Floating Codes for Joint Information Storage in Write Asymmetric Memories

Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories and other non-volatile memories based on floating-gate cells have become a very important family of such memories. We model them by the write asymmetric memory (WAM), a memory where each cell is in one of q states - state 0, 1, middotmiddotmiddot, q - 1 - and can only transit from a lower state to a higher state. Data stored in a WAM can be rewritten by shifting the cells to higher states. Since the state transition is irreversible, the number of times of rewriting is limited. When multiple variables are stored in a WAM, we study codes, which we call floating codes, that maximize the total number of times the variables can be written and rewritten. In this paper, we present several families of floating codes that either are optimal, or approach optimality as the codes get longer. We also present bounds to the performance of general floating codes. The results show that floating codes can integrate the rewriting capabilities of different variables to a surprisingly high degree.