On the design of irregular gldpc codes with low error floor over the BEC

The design of GLDPC codes for the binary erasure channel with low error floor under iterative decoding is investigated. Both bounded distance and maximum a posteriori decoding at the check nodes are considered. For both check node decoding algorithms a key parameter is identified, discriminating between an exponentially small and exponentially large expected number of small size stopping sets. A code design technique is proposed based on this theoretical investigation.