An Unnoticed Strong Connection Between Algebraic-Based and Protograph-Based LDPC Codes, Part II: Nonbinary Case and Code Construction

This paper is the second part of a series of two papers on the investigation of the connection between two methods for constructing LDPC codes, namely the superposition and the protograph-based methods. In the first part, by taking the graph point of view, we established a strong connection between these two construction methods and showed that, in the binary case, the protograph-based construction of LDPC codes is a special case of the superposition construction of LDPC codes. Several special types of superposition construction of binary algebraic quasi-cyclic (QC) LDPC codes were presented. In this second part, we continue the investigation of the connection between the superposition and the protograph-based methods for constructing nonbinary LDPC codes, especially non-binary QC-LDPC codes. Several special superposition methods for constructing nonbinary QC-LDPC codes are presented. The constructed codes can be regarded as algebraic-protograph QC-LDPC codes. These codes not only have rich algebraic structures, but also perform well.