Floating Codes for Joint Information Storage in Write Asymmetric Memories

Abstract

Abstract-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, ***, 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.

Data Representation for Flash Memories

“…It matches the number of rewrites guaranteed by the floating codes of Example 4 (and their generalization in [16]). So these codes are optimal.…”

“…It is interesting to see if there exist codes that allow data to be rewritten many times without block erasure. The flash memory model we use in this section is the Write Asymmetric Memory (WAM) model [16].…”

“…The joint coding of these data variables are useful for increasing the number of rewrites supported by coding. The rewriting codes in this setting have been named Floating Codes [16].…”

“…The floating codes in the above example are generalized in [16] for any value of n and q (but still with k = ℓ = 2), and are shown to guarantee…”

“…We now prove that this is optimal. First, we show an upper bound to t, the number of guaranteed rewrites, for floating codes [16].…”