On the stopping distance of finite geometry LDPC codes

In this letter, the stopping sets and stopping distance of finite geometry LDPC (FG-LDPC) codes are studied. It is known that FG-LDPC codes are majority-logic decodable and a lower bound on the minimum distance can be thus obtained. It is shown in this letter that this lower bound on the minimum distance of FG-LDPC codes is also a lower bound on the stopping distance of FG-LDPC codes, which implies that FG-LDPC codes have considerably large stopping distance. This may explain in one respect why some FG-LDPC codes perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs.