Permutation decoding and the stopping redundancy hierarchy of cyclic and extended cyclic codes

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

Research output: Contribution to journalArticlepeer-review


We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the tradeoff between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovász's Local Lemma (LLL) 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 (ML) decoding.

Original languageEnglish (US)
Pages (from-to)5308-5331
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - 2008


  • Automorphism group
  • Binary erasure channel
  • Bose-Chaudhudri-Hocquenghem (BCH) codes
  • Cyclic codes
  • Hamming codes
  • Permutation decoding
  • Stopping redundancy hierarchy
  • Stopping sets

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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