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In this paper, we propose a construction of non-binary WOM(Write-Once-Memory) codes for WOM storages such as flash memories. The WOMcodes discussed in this paper are fixed rate WOM codes where messages in afixed alphabet of size $M$ can be sequentially written in the WOM storage atleast $t^*$-times. In this paper, a WOM storage is modeled by a statetransition graph. The proposed construction has the following two features.First, it includes a systematic method to determine the encoding regions in thestate transition graph. Second, the proposed construction includes a labelingmethod for states by using integer programming. Several novel WOM codes for $q$level flash memories with 2 cells are constructed by the proposed construction.They achieve the worst numbers of writes $t^*$ that meet the known upper boundin many cases. In addition, we constructed fixed rate non-binary WOM codes withthe capability to reduce ICI (inter cell interference) of flash cells. One ofthe advantages of the proposed construction is its flexibility. It can beapplied to various storage devices, to various dimensions (i.e, number ofcells), and various kind of additional constraints.

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

Construction of Fixed Rate Non-Binary WOM Codes based on Integer Programming