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Abstract: We describe a family of instanton-based optimization methods developedrecently for the analysis of the error floors of low-density parity-checkLDPC codes.
Instantons are the most probable configurations of the channelnoise which result in decoding failures.
We show that the general idea and therespective optimization technique are applicable broadly to a variety ofchannels, discrete or continuous, and variety of sub-optimal decoders.Specifically, we consider: iterative belief propagation BP decoders, Gallagertype decoders, and linear programming LP decoders performing over theadditive white Gaussian noise channel AWGNC and the binary symmetric channelBSC.The instanton analysis suggests that the underlying topological structures ofthe most probable instanton of the same code but different channels anddecoders are related to each other.
Armed with this understanding of thegraphical structure of the instanton and its relation to the decoding failures,we suggest a method to construct codes whose Tanner graphs are free of thesestructures, and thus have less significant error floors.



Author: Shashi Kiran Chilappagari, Michael Chertkov, Mikhail G.
Stepanov, Bane Vasic


Source: https://arxiv.org/



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