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This paper addresses the problem of irregular LDPC code design with good minimum pseudo-distance properties. In particular, for Binary Erasure Channels (BEC), the problem is to design irregular LDPC codes such that the size of their minimum stopping set (stopping distance) is maximized. The stopping distance determines the performance of LDPC codes under iterative decoding in the error-floor region. The problem of finding the stopping distance of the LDPC code graph is shown to be NP-hard, i.e., no efficient algorithm for explicit identification and removal of small stopping sets exists (except for very short length LDPC codes).
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