Capacity achieving multiwrite WOM codes

In this paper we give an explicit construction of a capacity achieving family of binary t-write WOM codes for any number of writes t, that have a polynomial time encoding and decoding algorithms. The block length of our construction is N=(t/\epsilon)^{O(t/(\delta\epsilon))} when \epsilon is the gap to capacity and encoding and decoding run in time N^{1+\delta}. This is the first deterministic construction achieving these parameters. Our techniques also apply to larger alphabets.