Polar write once memory codes

TL;DR

This paper introduces a polar coding scheme for write once memory (WOM) that achieves capacity with scalable complexity, extends to generalized WOMs, and includes finite-length simulation results.

Contribution

It presents a novel polar coding scheme for WOMs that attains capacity and generalizes to complex WOM models using nonbinary polar codes.

Findings

Achieves capacity region of noiseless WOMs

Encoding and decoding complexity scales as O(N log N)

Finite-length simulations demonstrate practical performance

Abstract

A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding complexities scale as O(N log N) where N is the blocklength. For N sufficiently large, the error probability decreases sub-exponentially in N. The results can be generalized from binary to generalized WOMs, described by an arbitrary directed acyclic graph, using nonbinary polar codes. In the derivation we also obtain results on the typical distortion of polar codes for lossy source coding. Some simulation results with finite length codes are presented.