Linear Programming Decoding of Binary Linear Codes for Symbol-Pair Read Channels

TL;DR

This paper introduces a linear programming decoding algorithm for binary linear codes tailored for symbol-pair read channels, providing ML certification and error correction guarantees based on a new fractional pair distance metric.

Contribution

It presents a novel LP decoding method for symbol-pair channels, proving ML certification and establishing a new fractional pair distance for error correction bounds.

Findings

LP decoder has ML certificate property

Decodes up to loor d_{fp}/2 - 1 pair errors

Introduces fractional pair distance as a new metric

Abstract

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read resolution. The proposed decoding algorithm is based on a linear programming (LP). It is proved that the proposed LP decoder has the maximum-likelihood (ML) certificate property, i.e., the output of the decoder is guaranteed to be the ML codeword when it is integral. We also introduce the fractional pair distance $d_{fp}$ of a code which is a lower bound on the pair distance. It is proved that the proposed LP decoder will correct up to $\lceil d_{fp}/2\rceil-1$ pair errors.