Abstract-This paper studies a new model of stuck-at memory cells which is motivated by the defect model of multi-level cells in non-volatile memories such as flash memories and phase change memories. If a cell can store the levels 0, 1, . . . , q − 1, we say that it is partially stuck-at s if it can only store values which are at least s, where 1 ≤ s ≤ q − 1. In this paper, we consider the case s = 1. A lower bound on the redundancy of a code which masks u partially stuck-at cells is 