Polygon Semi regular Low Density Parity Check Codes: Graphs Designs and Codes

I proposed a new algorithm for the allocation of g- values to the binary vectors. An infinite family of simple graphs in generated by placing copies of polygons in parallel such that degree of each vertex is three. We call them polygon graphs. Since polygon graphs are bipartite therefore they can be used as Tanner graphs to generate low density parity check codes. An incidence structure defined on these polygon graphs in named as polygon semi design. Rows of incidence matrix are reduced by deleting rows from the bottom one by one. These matrices serve as parity check matrices to define low density parity check codes for various dimensions. Size of the stopping sets in the associated Tanner graphs of LDPC codes determine the performance of codes over binary erasure channel. The generated polygon semi regular LDPC codes are simulated and their performance is presented by BER. plots. There exists polygon semi regular LDPC codes e.g. (25,4,17), (49,6,19) etc. The LDPC codes of girth 6 presented by Vera Pless has parameters (25,4,10), (49,6,14). This shows a significant improvement in terms of minimum distance.