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The proposed work is based on the fact that the complete set of bit nodes for an LDPC code may not always be required at the receiving side for successful decoding. A corresponding strategy is therefore built up. In contrast to common practice, the total number of iterations available is shared among different sets. The first set runs the decoding algorithm with all its bit nodes. Successive sets (in case of decoding failure) runs each with a different selection of "erased" bit nodes, leading to an overall non-monotonic behavior. The end result is a system capable of effectively dealing with the problem of cycles and trapping sets without even being aware of their existence. Reported results show an important coding gain over conventional systems.