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

Abstract

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbolpair read channel has recently been introduced by Cassuto and Blaum to model channels whose write resolution is higher than its 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 f p of a code which is a lower bound on the pair distance. It is proved that the proposed LP decoder will correct up to ⌈d f p /2⌉ − 1 pair errors.