On the Capacity of the Flash Memory Channel with Feedback

In this paper, the binary channel that changes the 101 input pattern to a 111 with probability ε, and leaves the other input patterns unchanged, is considered as a model for inter-cell interference (ICI) in NAND flash memories. The capacity with feedback of this channel is cast as a dynamic programming (DP) problem, and is numerically evaluated using the value iteration procedure. An analytical upper bound on the feedback capacity is derived using the "Q-graph"-based technique of Sabag et al. [1], and the bound is shown to be numerically close in value to the feedback capacity arrived at from the DP problem. For the special case of the channel where ε is equal to 1 (which we call the deterministic flash memory channel), the capacities with and without feedback (which are identical) are shown to be roughly 0.8114, which, in turn, is the capacity of the constrained system that forbids the 101 input pattern.