WOM codes with uninformed encoder

Abstract

Write-once memory (WOM) is a storage device consisting of q-ary cells that can only increase their value. A WOM code is a coding scheme which allows one to write multiple times to the WOM without decreasing the levels of the cells. In the conventional model of WOM, it is assumed that the encoder can read the memory state before encoding, while the decoder reads only the memory state after encoding, but not before that. However, there are three more models in this setup. We follow an earlier work by Wolf et al. who studied the capacity results of all possible four models in which the encoder/decoder is or is not informed with the previous state of the memory before encoding, respectively. The two challenging models we study here assume that the encoder is uninformed with the memory state (that is, the encoder cannot read the memory prior to encoding). We show that if the decoder is also uninformed with the memory state before encoding, then codes in the Z channel provide constructions for the binary case, and codes correcting non-binary asymmetric errors are used for non-binary codes. In case the decoder is informed with the previous state, then erasure-correcting codes are invoked in the binary case, and codes in the Manhattan distance are used for the non-binary case.