Invertible Zero-Error Dispersers and Defective Memory with Stuck-At Errors

Kuznetsov and Tsybakov [11] considered the problem of storing information in a memory where some cells are ‘stuck’ at certain values. More precisely, For 0 < r,p < 1 we want to store a string z ∈ {0,1} rn in an n-bit memory x = (x 1,…,x n ) in which a subset S ⊆ [n] of size pn are stuck at certain values u 1,…,u pn and cannot be modified. The encoding procedure receives S, u 1,…,u pn and z and can modify the cells outside of S. The decoding procedure should be able to recover z given x (without having to know S or u 1,…,u pn ). This problem is related to, and harder than, the Write-Once-Memory (WOM) problem.