Constructing LDPC codes by error minimization progressive edge growth

A novel approach to constructing Tanner graphs using progressive edge growth (PEG) is introduced. It yields LDPC codes providing minimized block error probability in Binary Erasure Channels (BEC). The constructed codes exhibit superior performance over codes generated by previously known algorithms, both for BEC and AWGN channels. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated codes is derived. This allows analytical prediction of the codes' error floor performance. Finally, the method is generalized for generating simple in implementation LDPC codes based on lifted graphs.