Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề Research Article High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs | Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2007 Article ID 48158 5 pages doi 2007 48158 Research Article High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs Gabofetswe Malema and Michael Liebelt School of Electrical and Electronic Engineering The University of Adelaide North Terrace Adelaide 5005 SA Australia Received 12 November 2005 Revised 2 September 2006 Accepted 25 October 2006 Recommended by Wolfgang Gerstacker LDPC codes of column weight of two are constructed from minimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into matrix form produces an adjacency matrix with column weight of two and girth double that of the graph. The number of 1 s in each row row weight is equal to the degree of the corresponding vertex. By constructing graphs with different vertex degrees we can vary the rate of corresponding LDPC code matrices. Cage graphs are used as examples of distance graphs to design codes with different girths and rates. Performance of obtained codes depends on girth and structure of the corresponding distance graphs. Copyright 2007 G. Malema and M. Liebelt. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. INTRODUCTION Low-density parity-check LDPC codes have been shown to have very good error correcting capability performing close to the Shannon limit 1 . It was also shown in 2 that LDPC codes with column weight j 3 have a minimum distance that grows linearly with code length N for given j and row-weight k and that minimum distance for codes with j 2 grows logarithmically with N. However column-weight-two codes have shown potential in partial response channels 3 4 . They also .
