TY - GEN

T1 - Capacity achieving two-write WOM codes

AU - Shpilka, Amir

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860811265&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-29344-3_53

DO - 10.1007/978-3-642-29344-3_53

M3 - פרסום בספר כנס

AN - SCOPUS:84860811265

SN - 9783642293436

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 631

EP - 642

BT - LATIN 2012

Y2 - 16 April 2012 through 20 April 2012

ER -