Time–Space Constrained Codes for Phase-Change Memories

Phase-change memory (PCM) is a promising nonvolatile solid-state memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells (i.e., changing cell levels), to balance the heat both in time and in space. In this paper, we study the time-space constraint for PCM, which was originally proposed by Jiang and coworkers. A code is called an (α, β, p)- constrained code if for any α consecutive rewrites and for any segment of β contiguous cells, the total rewrite cost of the β cells over those α rewrites is at most p. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang and coworkers. Then, we generalize their construction for (α ≥ 1, β = 1, p = 1)-constrained codes and show another construction for (α = 1, β ≥ 1, p ≥ 1)-constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of α, β, and p.