Non-binary WOM-codes for multilevel flash memories

A Write-Once Memory (WOM)-code is a coding scheme that allows information to be written in a memory block multiple times, but in a way that the stored values are not decreased across writes. This work studies non-binary WOM-codes with applications to flash memory. We present two constructions of non-binary WOM-codes that leverage existing high sum-rate WOM-codes defined over smaller alphabets. In many instances, these constructions provide the highest known sum-rates of the non-binary WOM-codes. In addition, we introduce a new class of codes, called level distance WOM-codes, which mitigate the difficulty of programming a flash memory cell by eliminating all small-magnitude level increases. We show how to construct such codes and state an upper bound on their sum-rate.