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 \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give a
construction of a two-write WOM code of length n and capacity
H(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p
(H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore,
encoding and decoding can be done in time O(n^2.poly(log n)) and time
O(n.poly(log n)), respectively, and in logarithmic space.
We obtain a new encoding scheme for 3-write WOM codes over the binary
alphabet. Our scheme achieves rate 1.809-\epsilon, when the block length is
exp(1/\epsilon). This gives a better rate than what could be achieved using
previous techniques.
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(log
n) can lead to improved parameters for 2-write WOM codes. We then give an
application of existing constructions of extractors to the problem of designing
encoding schemes for memory with defects.Comment: 19 page
