Geometric WOM codes and coding strategies for multilevel flash memories

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

“…Indeed, it was shown [22] that by using WOM codes in multi-level NVMs, it is possible to reduce write amplification, and thus increase the lifetime of the device. This justifies the recent extensive study of q-ary WOM codes [3], [9], [11], [12], [18] that generalize the original binary WOM model [24] to multi-level flash. In light of this promise, the main issue holding back WOM codes from deployment seems to be concerns related to intercell interference (ICI) [8].…”

“…Proof: In order to find the maximal sum-rate of C d-imb (2, q, 2, (Z 1 , Z 2 )) with imbalance parameter d, we now need to adjust the optimization problem of ( 12) to the d-imbalance model, and to find the values of Z 1 and Z 2 that maximize Z 1 • Z 2 . By a similar argument to the one proved in [4], the minimization in (12) implies that the optimal sum-rate boundary must satisfy the identical-area condition of Lemma 9. Then among the β d (x) curves of Lemma 9 parametrized by Z 2 , the corresponding value of Z 1 is determined by Lemma 10.…”

“…where x sup is the maximal value of the support of β (x). The solution of (12) gives the hyperbola boundary β (x) of Theorem 7. After deriving the continuous boundaries between the writes, the WOM code is constructed by discretization and a label assignment algorithm.…”