The construction of periodically time-variant convolutional codes using binary linear block codes

Naonori Ogasahara, Manabu Kobayashi, Shigeichi Hirasawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In 1996 Rosenthal and York proposed (time-invariant) BCH convolutional codes [4] in which the parity check matrix of a BCH code is used in the construction of the convolutional code. The lower bound on the minimum free distance of a BCH convolutional code is guaranteed by the BCH limit. In this paper we propose a periodically time-variant convolutional code that can be constructed not only using the BCH parity check matrix but using the check matrix of any binary linear block code and show that the lower bound on the minimum free distance is guaranteed by the minimum free distance of the binary linear block code. In addition, taking 12 binary linear block codes as examples, we perform comparisons of the proposed codes with BCH convolutional codes using three evaluation criteria (minimum free distance, number of delay elements, coding rate) and show that there exist proposed codes that are superior to existing ones.

Original languageEnglish
Pages (from-to)31-40
Number of pages10
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume90
Issue number9
DOIs
Publication statusPublished - 2007 Sep 1
Externally publishedYes

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Convolutional codes
Block codes

Keywords

  • BCH convolutional codes
  • Binary linear block codes
  • Minimality condition
  • Periodically time-variant convolutional codes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "The construction of periodically time-variant convolutional codes using binary linear block codes",
abstract = "In 1996 Rosenthal and York proposed (time-invariant) BCH convolutional codes [4] in which the parity check matrix of a BCH code is used in the construction of the convolutional code. The lower bound on the minimum free distance of a BCH convolutional code is guaranteed by the BCH limit. In this paper we propose a periodically time-variant convolutional code that can be constructed not only using the BCH parity check matrix but using the check matrix of any binary linear block code and show that the lower bound on the minimum free distance is guaranteed by the minimum free distance of the binary linear block code. In addition, taking 12 binary linear block codes as examples, we perform comparisons of the proposed codes with BCH convolutional codes using three evaluation criteria (minimum free distance, number of delay elements, coding rate) and show that there exist proposed codes that are superior to existing ones.",
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N2 - In 1996 Rosenthal and York proposed (time-invariant) BCH convolutional codes [4] in which the parity check matrix of a BCH code is used in the construction of the convolutional code. The lower bound on the minimum free distance of a BCH convolutional code is guaranteed by the BCH limit. In this paper we propose a periodically time-variant convolutional code that can be constructed not only using the BCH parity check matrix but using the check matrix of any binary linear block code and show that the lower bound on the minimum free distance is guaranteed by the minimum free distance of the binary linear block code. In addition, taking 12 binary linear block codes as examples, we perform comparisons of the proposed codes with BCH convolutional codes using three evaluation criteria (minimum free distance, number of delay elements, coding rate) and show that there exist proposed codes that are superior to existing ones.

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