Capacity achieving two-write WOM codes

In this paper we give several new constructions of WOM codes. The novelty in our constructions is the use of the so called Wozencraft ensemble of linear codes. Specifically, we obtain the following results. We give an explicit construction of a two-write Write-Once-Memory (WOM for short) code that approaches capacity, over the binary alphabet. More formally, for every ε > 0, 0 < p < 1 and n = (1/ε) ^O(1/pε) we give a construction of a two-write WOM code of length n and capacity H(p) + 1 - p - ε. Since the capacity of a two-write WOM code is max _p (H(p)+1-p), we get a code that is ε-close to capacity. Furthermore, encoding and decoding can be done in time O(n ²•poly(logn)) and time O(n•poly(logn)), respectively, and in logarithmic space. We highlight a connection to linear seeded extractors for bit-fixing sources. In particular we show that obtaining such an extractor with seed length O(logn) can lead to improved parameters for 2-write WOM codes.