1Rewriting Flash Memories and Dirty-Paper Coding

Abstract—This paper considers that write-once memory (WOM) codes can be seen as a type of dirty-paper code. The current state of the memory, which is known to the encoder, plays the role of the known interference of dirty-paper coding. Erez, Shamai and Zamir showed that lattice strategies can achieve the capacity of the known-interference channel. In this paper, lattices are used to design a WOM code. Encoding is performed modulo a shaping lattice with respect to a lattice fundamental region to obtain a codeword, to be added to the current state of the memory. The fundamental region is designed to accommodate the limitations of the flash memory system, particularly, that values can only increase. The criterion for evaluation is average number of writes. In order to improve the average number of writes, “coset select ” bits are introduced, to maximize the average number of writes. For an eight-dimensional lattice, numerical results for practical parameter choices show a promising trend. I