Capacity achieving multiwrite WOM codes

TL;DR

This paper presents a deterministic, capacity-achieving construction of multiwrite WOM codes with efficient encoding and decoding algorithms, applicable to binary and larger alphabets, for any number of writes.

Contribution

It introduces the first explicit, deterministic construction of capacity-achieving multiwrite WOM codes with polynomial-time algorithms for any number of writes.

Findings

Achieves capacity for any number of writes t

Provides polynomial-time encoding and decoding algorithms

Extends techniques to larger alphabets

Abstract

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.