Generating parity check equations for bounded-distance iterative erasure decoding
<|reference_start|>Generating parity check equations for bounded-distance iterative erasure decoding: A generic $(r,m)$-erasure correcting set is a collection of vectors in $\bF_2^r$ which can be used to generate, for each binary linear code of codimension $r$, a collection of parity check equations that enables iterative decoding of all correctable erasure patterns of size at most $m$.   That is to say, the only stopping sets of size at most $m$ for the generated parity check equations are the erasure patterns for which there is more than one manner to fill in theerasures to obtain a codeword.   We give an explicit construction of generic $(r,m)$-erasure correcting sets of cardinality $\sum_{i=0}^{m-1} {r-1\choose i}$. Using a random-coding-like argument, we show that for fixed $m$, the minimum size of a generic $(r,m)$-erasure correcting set is linear in $r$.   Keywords: iterative decoding, binary erasure channel, stopping set<|reference_end|>
@article{hollmann2006generating,
    title={Generating parity check equations for bounded-distance iterative erasure
  decoding},
    author={Henk D.L. Hollmann and Ludo M.G.M. Tolhuizen},
    journal={arXiv preprint arXiv:cs/0606026},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0606026},
    primaryClass={cs.IT math.IT}
}