---
res:
bibo_abstract:
- 'The question whether RM codes are capacity-achieving is a long-standing open
problem in coding theory that was recently answered in the affirmative for transmission
over erasure channels [1], [2]. Remarkably, the proof does not rely on specific
properties of RM codes, apart from their symmetry. Indeed, the main technical
result consists in showing that any sequence of linear codes, with doubly-transitive
permutation groups, achieves capacity on the memoryless erasure channel under
bit-MAP decoding. Thus, a natural question is what happens under block-MAP decoding.
In [1], [2], by exploiting further symmetries of the code, the bit-MAP threshold
was shown to be sharp enough so that the block erasure probability also converges
to 0. However, this technique relies heavily on the fact that the transmission
is over an erasure channel. We present an alternative approach to strengthen results
regarding the bit-MAP threshold to block-MAP thresholds. This approach is based
on a careful analysis of the weight distribution of RM codes. In particular, the
flavor of the main result is the following: assume that the bit-MAP error probability
decays as N -δ , for some δ > 0. Then, the block-MAP error probability also converges
to 0. This technique applies to transmission over any binary memoryless symmetric
channel. Thus, it can be thought of as a first step in extending the proof that
RM codes are capacity-achieving to the general case.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Shrinivas
foaf_name: Kudekar, Shrinivas
foaf_surname: Kudekar
- foaf_Person:
foaf_givenName: Santhosh
foaf_name: Kumar, Santhosh
foaf_surname: Kumar
- 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: Henry D.
foaf_name: Pfister, Henry D.
foaf_surname: Pfister
- foaf_Person:
foaf_givenName: Rudiger
foaf_name: Urbankez, Rudiger
foaf_surname: Urbankez
bibo_doi: 10.1109/isit.2016.7541600
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: IEEE@
dct_title: Comparing the bit-MAP and block-MAP decoding thresholds of Reed-Muller
codes on BMS channels@
...