Design of non binary LDPC codes using their binary image: algebraic properties

Abstract

In this paper, we develop algebraic properties of regular (2, t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> , N) non binary LDPC codes designed using their binary image. First, we characterize the algebraic properties of optimized rows of the parity check matrix H associated with a code, and then we study the algebraic properties of cycles and stopping sets associated with the underlaying Tanner graph