Polar write once memory codes

A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding complexities scale as O(N log N) where N is the blocklength. For N sufficiently large, the error probability decreases sub-exponentially in N. Some simulation results with finite length codes are presented.