Constructions Of LDPC Codes Based On Rectangular Lattices

Low Density Parity Check Codes(LDPC)have the excellent performance in approaching the Shannon limit.They based on sparse parity check matrix and have lower decoding complexity.The research on LDPC codes is one of the most popular research in the field of channel coding,and LDPC codes are widely used in many fields.Improving the performance of LDPC code is also of great significance for its application,which is one of the research focuses.This paper starts from linear block codes,explains the definition and the Tanner model for LDPC codes.The structural features of the parity check matrix and the factors affecting the performance of LDPC codes are summarized.Three factors affecting LDPC code performance are analyzed,and the necessity of eliminating the short loop to improve the performance of LDPC code is illustrated.Vasic et al.have proposed a algorithm for removing 4-cycle and 6-cycle in the check matrix based on rectangular lattices.This algorithm is avilable only when the column weight is three,and the LDPC codes consrtucted by this algorithm have girths no more than eight.Then we analyzed the correspondence between nodes and lines in the rectangular lattices and find the conditions for the existence of polygons in the rectangular lattices.After we find out slopes that satisfy these conditions,LDPC codes with specific girth can be constructed.Using this algorithm,we constructed three kinds of LDPC codes,the first one has a large column weight with girth 8,the second one has column weight of 3 with girth 10,and the last one has column weight of 3 with girth 12.Then we compared the performance between the codes we constrected and the codes constructed by other algorithm,the results of performance comparison show that the LDPC codes constructed by our improved algorithm have better performance.