---
res:
bibo_abstract:
- Motivated by the significant performance gains which polar codes experience under
successive cancellation list decoding, their scaling exponent is studied as a
function of the list size. In particular, the error probability is fixed, and
the tradeoff between the block length and back-off from capacity is analyzed.
A lower bound is provided on the error probability under MAP decoding with list
size L for any binary-input memoryless output-symmetric channel and for any class
of linear codes such that their minimum distance is unbounded as the block length
grows large. Then, it is shown that under MAP decoding, although the introduction
of a list can significantly improve the involved constants, the scaling exponent
itself, i.e., the speed at which capacity is approached, stays unaffected for
any finite list size. In particular, this result applies to polar codes, since
their minimum distance tends to infinity as the block length increases. A similar
result is proved for genie-aided successive cancellation decoding when transmission
takes place over the binary erasure channel, namely, the scaling exponent remains
constant for any fixed number of helps from the genie. Note that since genie-aided
successive cancellation decoding might be strictly worse than successive cancellation
list decoding, the problem of establishing the scaling exponent of the latter
remains open.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Marco
foaf_name: Mondelli, Marco
foaf_surname: Mondelli
foaf_workInfoHomepage: http://www.librecat.org/personId=27EB676C-8706-11E9-9510-7717E6697425
orcid: 0000-0002-3242-7020
- foaf_Person:
foaf_givenName: Hamed
foaf_name: Hassani, Hamed
foaf_surname: Hassani
- foaf_Person:
foaf_givenName: Rudiger
foaf_name: Urbanke, Rudiger
foaf_surname: Urbanke
bibo_doi: 10.1109/tit.2015.2453315
bibo_issue: '9'
bibo_volume: 61
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: IEEE@
dct_title: Scaling exponent of list decoders with applications to polar codes@
...