Further results on majority-logic decoding of product codes (Corresp.)

Abstract

In this correspondence additional results on majority-logic decoding of product codes are presented. If one of the component codes is decodable using Rudolph's nonorthogonal algorithm, and the other using Reed-Massey's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> -step orthogonalization, then the resulting product code is majority-logic decodable in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</tex> steps, where nonorthogonal checks are used in the first step and orthogonal checks in the remaining steps. If the component codes are both decodable using Rudolph's algorithm, the product code is majority-logic decodable using the same procedure.