Michal Horovitz – WOM codes with uninformed encoder


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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.
I will 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/decoding respectively. I will focus on the two challenging models where the encoder is uninformed with the memory state (that is, the encoder cannot read the memory prior to encoding). I will present a connection between the Z-channel and the model where the decoder is uninformed, and similarly, between the erasure-channel and the case where the decoder is informed with the previous state.