Strongly-MDS convolutional codes

Heide Gluesing-Luerssen; Joachim Rosenthal; Roxana Smarandache

doi:10.1109/TIT.2005.862100

Strongly-MDS convolutional codes

Heide Gluesing-Luerssen, Joachim Rosenthal, Roxana Smarandache

Mathematics

Research output: Contribution to journal › Article › peer-review

111 Scopus citations

Abstract

Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.

Original language	English
Pages (from-to)	584-598
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	52
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2005.862100
State	Published - Feb 2006

Bibliographical note

Funding Information:
Manuscript received March 20, 2003; revised October 14, 2005. This work was supported in part by the Nationa Science Foundation under Grants DMS-0072383 and CCR-0205310. The material in this paper was presented at the 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, June/July 2002 and at the International Symposium on the Mathematical Theory of Networks and Systems (MTNS), University of Notre Dame, Notre Dame, IN, August 2002.

Keywords

Column distances
Convolutional codes
Extended row distances
Maximum-distance separable (MDS) codes
Super-regular matrices
Unit memory codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2005.862100

Cite this

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abstract = "Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.",

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note = "Funding Information: Manuscript received March 20, 2003; revised October 14, 2005. This work was supported in part by the Nationa Science Foundation under Grants DMS-0072383 and CCR-0205310. The material in this paper was presented at the 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, June/July 2002 and at the International Symposium on the Mathematical Theory of Networks and Systems (MTNS), University of Notre Dame, Notre Dame, IN, August 2002.",

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AU - Rosenthal, Joachim

AU - Smarandache, Roxana

N1 - Funding Information: Manuscript received March 20, 2003; revised October 14, 2005. This work was supported in part by the Nationa Science Foundation under Grants DMS-0072383 and CCR-0205310. The material in this paper was presented at the 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, June/July 2002 and at the International Symposium on the Mathematical Theory of Networks and Systems (MTNS), University of Notre Dame, Notre Dame, IN, August 2002.

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N2 - Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.

AB - Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.

KW - Column distances

KW - Convolutional codes

KW - Extended row distances

KW - Maximum-distance separable (MDS) codes

KW - Super-regular matrices

KW - Unit memory codes

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Strongly-MDS convolutional codes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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