A Euclidean Geometry Based Algebraic Construction Technique for Girth-8 Gallager LDPC Codes

A construction technique is proposed for low-density parity-check (LDPC) codes based on finite Euclidean geometries EG(m,2
^s
). These codes are shown to be regular Gallager codes with Tanner graphs of girth eight. The minimum distance of these codes is shown to be lower-bounded by 2
^m
. The codes are also amenable to an efficient partly parallel decoder implementation, which may be used in conjunction with the turbo decoding message passing (TDMP) algorithm for LDPC decoding. Finally, simulation results show that these codes have very good error-correcting performance