Binary LDPC Codes Constructed Based on Symplectic Spaces over Finite Fields

Shangdi Chen1, Junying Liang1
1College of Science, Civil Aviation University of China, Tianjin, 300300, China

Abstract

This paper mainly presents a construction of LDPC codes based on symplectic spaces. By two subspaces of type (m, r) to produce a subspace of type (m + 1,r) or (m + 1,r + 1) in \(\mathbb{F}^{2v}\) , we use all subspaces of type (m,r) to mark rows and all subspaces of type (m + 1, r) and (m + 1, r + 1) to mark columns of check matrix H. A construction of LDPC codes has been given based on symplectic spaces. As a special case, we use all subspaces of type (1,0) to mark rows and all subspaces of type (2,0) and (2,1) to mark columns of check matrix \(H_1\), in \(\mathbb{F}^4_q\), the cycles of length 6 of \(H_1\), is further discussed.

Keywords: LDPC codes; symplectic spaces; totally isotropic subspaces; non-isotropic subspaces