Generating parity check equations for bounded-distance iterative erasure decoding
| dc.creator | Hollmann, Henk D. L. | |
| dc.creator | Tolhuizen, Ludo M. G. M. | |
| dc.date | 2006-06-06 | |
| dc.date.accessioned | 2026-07-07T08:16:35Z | |
| dc.date.available | 2026-07-07T08:16:35Z | |
| dc.description | 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 | |
| dc.description | Accepted for publication in Proc Int Symposium on Information Theory 2006, ISIT 06 | |
| dc.identifier | https://arxiv.org/abs/cs/0606026 | |
| dc.identifier | http://arxiv.org/abs/cs/0606026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133828 | |
| dc.subject | Information Theory | |
| dc.title | Generating parity check equations for bounded-distance iterative erasure decoding | |
| dc.type | text |