The Construction of Low-Density Parity-Check Codes Based on Protograph

Low-Density Parity-Check (LDPC) codes have low linear decoding complexity, which is a kind of good codes with excellent performance. Therefore, LDPC codes have great research value. This article is based on vector space over finite field as a theoretical tool by the inclusive relation of vector subspaces to construct protograph, and then constructs the LDPC codes with larger girth based on protograph by the modified progressive edge growth(M-PEG) algorithm, and utilize the related knowledge, such as Anzahl theorem in vector space, determines the code length, code rate and code word number of the LDPC codes. Moreover, the LDPC codes constructed are compared with the existing codes, and the constructed codes are better than some existing ones.