d-imbalance WOM codes for reduced inter-cell interference in multi-level NVMs

Abstract

Abstract-In recent years, due to the spread of multi-level nonvolatile memories (NVM), q-ary write-once memories (WOM) codes have been extensively studied. By using WOM codes, it is possible to rewrite NVMs t times before erasing the cells. The use of WOM codes enables to improve the performance of the storage device, however, it may also increase errors caused by inter-cell interference (ICI). This work presents WOM codes that restrict the imbalance between code symbols throughout the write sequence, hence decreasing ICI. We first specify the imbalance model as a bound d on the difference between codeword levels. Then a 2-cell code construction for general q and input size is proposed. An upper bound on the write count is also derived, showing the optimality of the proposed construction. In addition to direct WOM constructions, we derive closed-form optimal write regions for codes constructed with continuous lattices.On the coding side, the proposed codes are shown to be competitive with known codes not adhering to the bounded imbalance constraint. On the memory side, we show how the codes can be deployed within flash wordlines, and quantify their BER advantage using accepted ICI models.

Construction of Fixed Rate Non-Binary WOM Codes Based on Integer Programming

“…6: output fail and quit. 7: end if 8: y := min{x ∈ ω(d) | g(x) = m} 9: if s y then 10: s ′ := y 11: else 12:…”

“…In other words, if the cells satisfy the d imbalance constraint, then the level difference between a pair of adjacent cells is limited to d. It is known that a large level difference of adjacent cells tends to induce ICI. The d imbalance constraint is thus helpful to reduce ICI [12]. Figure. 6 presents state transition graphs for 4 level flash memories of two cells (n = 2) with the d imbalance constraint (d = 1, 2).…”

“…This example shows universality of the proposed construction, i.e., it can be applied to any state transition graph. Table V shows the comparison between upper bound presented in [12] and the worst numbers of writes of the Worst numbers of writes t * of proposed WOM codes for q level flash memories with n = 3 cells. 4 8 4 8 5 7 -7 17 6 5 13 5 13 7 5 13 5 13 8 5 13 5 13…”

“…Bhatia et al [10] showed a construction of non-binary WOM codes that relies on the lattice continuous approximation. Cassuto and Yaakobi [7] proposed a construction of fixed rate non-binary WOM codes using lattice tiling.Recently, fixed rate WOM code for reducing Inter-Cell Interference (ICI) is proposed by Hemo and Cassuto [12]. It is known that ICI causes drift of the threshold voltage of a flash cell according to the voltages of adjacent flash cells [12].…”

“…Cassuto and Yaakobi [7] proposed a construction of fixed rate non-binary WOM codes using lattice tiling.Recently, fixed rate WOM code for reducing Inter-Cell Interference (ICI) is proposed by Hemo and Cassuto [12]. It is known that ICI causes drift of the threshold voltage of a flash cell according to the voltages of adjacent flash cells [12]. The drift of threshold voltage degrades the reliability of the flash cell and it should be avoided.…”