Constructing strongly-MDS convolutional codes with maximum distance profile

Diego  Napp; Roxana  Smarandache

doi:10.3934/amc.2016005

Article Contents

2016, Volume 10, Issue 2: 275-290. Doi: 10.3934/amc.2016005

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Constructing strongly-MDS convolutional codes with maximum distance profile

Diego Napp^1, and
Roxana Smarandache^2,

1.
CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro
2.
Departments of Mathematics, and of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46566

Received: December 31, 2013

Published: April 2016

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Abstract

This paper revisits strongly-MDS convolutional codes with maximum distance profile (MDP). These are (non-binary) convolutional codes that have an optimum sequence of column distances and attains the generalized Singleton bound at the earliest possible time frame. These properties make these convolutional codes applicable over the erasure channel, since they are able to correct a large number of erasures per time interval. The existence of these codes have been shown only for some specific cases. This paper shows by construction the existence of convolutional codes that are both strongly-MDS and MDP for all choices of parameters.

Keywords:

Convolutional codes,
maximum distance separable (MDS) convolutional codes,
maximum distance profile (MDP) convolutional codes,
erasure channel.

Mathematics Subject Classification: Primary: 94B10, 11T71.

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