Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes - Computer Science > Information TheoryReport as inadecuate




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Abstract: We introduce the notion of the stopping redundancy hierarchy of a linearblock code as a measure of the trade-off between performance and complexity ofiterative decoding for the binary erasure channel. We derive lower and upperbounds for the stopping redundancy hierarchy via Lovasz-s Local Lemma andBonferroni-type inequalities, and specialize them for codes with cyclicparity-check matrices. Based on the observed properties of parity-checkmatrices with good stopping redundancy characteristics, we develop a noveldecoding technique, termed automorphism group decoding, that combines iterativemessage passing and permutation decoding. We also present bounds on thesmallest number of permutations of an automorphism group decoder needed tocorrect any set of erasures up to a prescribed size. Simulation resultsdemonstrate that for a large number of algebraic codes, the performance of thenew decoding method is close to that of maximum likelihood decoding.



Author: Thorsten Hehn, Olgica Milenkovic, Stefan Laendner, Johannes B. Huber

Source: https://arxiv.org/







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