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On the capacity of sticky storage devices

When required to make a transition to a new state, a memory cell may, with a probability dependent on the state, refuse to do so (i.e., “stick”). Assuming that error correcting codes can be used at each write-read cycle, one seeks the maximum error-free (in the Shannon sense), long-term average capacity per cell and cycle. This problem is solved here for binary cells with either unilateral or symmetric stickiness. The methods used apply to more general cases as well. In the Appendix, some essential inequalities of dynamic programming are demonstrated.