Capacity achieving two-write WOM codes

Amir Shpilka*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationLATIN 2012
Subtitle of host publicationTheoretical Informatics - 10th Latin American Symposium, Proceedings
Pages631-642
Number of pages12
DOIs
StatePublished - 2012
Externally publishedYes
Event10th Latin American Symposiumon Theoretical Informatics, LATIN 2012 - Arequipa, Peru
Duration: 16 Apr 201220 Apr 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7256 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
Country/TerritoryPeru
CityArequipa
Period16/04/1220/04/12

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