An approach to the performance of SPC product codes on the erasure channel

Sara D.  Cardell; Joan-Josep  Climent

doi:10.3934/amc.2016.10.11

Article Contents

2016, Volume 10, Issue 1: 11-28. Doi: 10.3934/amc.2016.10.11

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An approach to the performance of SPC product codes on the erasure channel

Sara D. Cardell^1, and
Joan-Josep Climent^2,

1.
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas (UNICAMP), R. Sérgio Buarque de Holanda, 651, Cidade Universitária, Campinas - SP, 13083-859
2.
Departament de Matemàtiques, Universitat d'Alacant, Ap. Correus 99, E-03080, Alacant

Received: October 31, 2014

Revised: August 31, 2015

Published: January 2016

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Abstract

Product codes can be used to correct errors or recover erasures. In this work we consider the simplest form of a product code, this is, the single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. The code is actually capable of recovering a higher number of erasure patterns. We count the number of uncorrectable erasure patterns of size $n \times n $ with $t$ erasures, for $t=8$, $2n-3$, $2n-2$ and $ 2n-1$, using the relation between erasure patterns and bipartite graphs.

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Mathematics Subject Classification: Primary: 14G50; Secondary: 97K30.

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