On (Partial) unit memory codes based on Gabidulin codes

On (Partial) unit memory codes based on Gabidulin codes (Partial) unit memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so-called sum rank metric. For the sum rank metric, the free rank distance, extended row rank distance, and its slope are defined analogous to the extended row distance in the Hamming metric. Upper bounds for the free rank distance and slope of (P)UM codes in the sum rank metric are derived, and an explicit construction of (P)UM codes based on Gabidulin codes is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On (Partial) unit memory codes based on Gabidulin codes

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2011 by Pleiades Publishing, Ltd.
Subject
Engineering; Communications Engineering, Networks; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946011020049
Publisher site
See Article on Publisher Site

Abstract

(Partial) unit memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so-called sum rank metric. For the sum rank metric, the free rank distance, extended row rank distance, and its slope are defined analogous to the extended row distance in the Hamming metric. Upper bounds for the free rank distance and slope of (P)UM codes in the sum rank metric are derived, and an explicit construction of (P)UM codes based on Gabidulin codes is given.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 14, 2011

References

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