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An improved bound on the list error probability and list distance properties

Bocharova, Irina LU ; Kudryashov, Boris LU ; Johannesson, Rolf LU and Loncar, Maja LU (2008) In IEEE Transactions on Information Theory 54(1). p.13-32
Abstract
List decoding of binary block codes for the additive white

Gaussian noise channel is considered. The output of a list decoder is a list of the $L$ most likely codewords, that is, the L signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst-case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix... (More)
List decoding of binary block codes for the additive white

Gaussian noise channel is considered. The output of a list decoder is a list of the $L$ most likely codewords, that is, the L signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst-case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples. (Less)
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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
list error probability, List configuration matrix, tangential union bound, list decoding, list distance
in
IEEE Transactions on Information Theory
volume
54
issue
1
pages
13 - 32
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000252256900002
  • scopus:38349153251
ISSN
0018-9448
DOI
10.1109/TIT.2007.911176
language
English
LU publication?
yes
id
e03ee458-c655-46a4-a764-ab8fcccd7179 (old id 959920)
date added to LUP
2016-04-01 13:13:21
date last changed
2022-01-27 18:02:04
@article{e03ee458-c655-46a4-a764-ab8fcccd7179,
  abstract     = {{List decoding of binary block codes for the additive white<br/><br>
Gaussian noise channel is considered. The output of a list decoder is a list of the $L$ most likely codewords, that is, the L signal points closest to the received signal in the Euclidean-metric sense. A decoding error occurs when the transmitted codeword is not on this list. It is shown that the list error probability is fully described by the so-called list configuration matrix, which is the Gram matrix obtained from the signal vectors forming the list. The worst-case list configuration matrix determines the minimum list distance of the code, which is a generalization of the minimum distance to the case of list decoding. Some properties of the list configuration matrix are studied and their connections to the list distance are established. These results are further exploited to obtain a new upper bound on the list error probability, which is tighter than the previously known bounds. This bound is derived by combining the techniques for obtaining the tangential union bound with an improved bound on the error probability for a given list. The results are illustrated by examples.}},
  author       = {{Bocharova, Irina and Kudryashov, Boris and Johannesson, Rolf and Loncar, Maja}},
  issn         = {{0018-9448}},
  keywords     = {{list error probability; List configuration matrix; tangential union bound; list decoding; list distance}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{13--32}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Information Theory}},
  title        = {{An improved bound on the list error probability and list distance properties}},
  url          = {{https://lup.lub.lu.se/search/files/3237919/959921.pdf}},
  doi          = {{10.1109/TIT.2007.911176}},
  volume       = {{54}},
  year         = {{2008}},
}