Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
arXiv:0708.0905 · doi:10.1109/TIT.2008.2006456
Abstract
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and Bonferroni-type inequalities, and specialize them for codes with cyclic parity-check matrices. Based on the observed properties of parity-check matrices with good stopping redundancy characteristics, we develop a novel decoding technique, termed automorphism group decoding, that combines iterative message passing and permutation decoding. We also present bounds on the smallest number of permutations of an automorphism group decoder needed to correct any set of erasures up to a prescribed size. Simulation results demonstrate that for a large number of algebraic codes, the performance of the new decoding method is close to that of maximum likelihood decoding.
40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on Information Theory
References in corpus (2)
Cited by in corpus (11)
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- Stopping Set Distributions of Some Linear Codes
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- Bit Level Soft Decision Decoding of Triple Parity Reed Solomon Codes through Automorphism Groups
- New Two-Stage Automorphism Group Decoders for Cyclic Codes in the Erasure Channel