Open AccessEnhanced Upper Bound for Erasure Recovery in SPC Product Codes
Author(s) -
Muqaibel Ali
Publication year - 2009
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.09.0109.0131
Subject(s) - erasure , algorithm , decoding methods , online codes , computer science , upper and lower bounds , focus (optics) , tornado code , erasure code , product (mathematics) , mathematics , block code , concatenated error correction code , mathematical analysis , physics , geometry , optics , programming language
Single parity check (SPC) product codes are simple yet powerful codes that are used to correct errors and/or recover erasures. The focus of this paper is to evaluate the performance of such codes under erasure scenarios and to develop a closed‐form tight upper bound for the post‐decoding erasure rate. Closed‐form exact expressions are derived for up to seven erasures. Previously published closed‐form bounds assumed that all unrecoverable patterns should contain four erasures in a square. Additional non‐square patterns are accounted for in the proposed expressions. The derived expressions are verified using exhaustive search. Eight or more erasures are accounted for by using a bound. The developed expressions improve the evaluation of the recoverability of SPC product codes without the need for simulation or search algorithms, whether exhaustive or novel.