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Complete j-MDP convolutional codes


Almeida, Paulo J; Lieb, Julia (2020). Complete j-MDP convolutional codes. IEEE Transactions on Information Theory, 66(12):7348-7359.

Abstract

Maximum distance profile (MDP) convolutional codes have been proven to be very suitable for transmission over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to restart decoding after a burst of erasures. However, there is a lack of constructions of these codes over fields of small size. In this article, we introduce the notion of complete 3-MDP convolutional codes, which are a generalization of complete MDP convolutional codes, and describe their decoding properties. In particular, we present a decoding algorithm for decoding erasures within a given time delay T and show that complete T-MDP convolutional codes are optimal for this algorithm. Moreover, using a computer search with the MAPLE software, we determine the minimal binary and non-binary field size for the existence of (2, 1, 2) complete 3-MDP convolutional codes and provide corresponding constructions. We give a description of all (2, 1, 2) complete MDP convolutional codes over the smallest possible fields, namely F 13 and F 16 and we also give constructions for (2, 1, 3) complete 4-MDP convolutional codes over F 128 obtained by a randomized computer search.

Abstract

Maximum distance profile (MDP) convolutional codes have been proven to be very suitable for transmission over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to restart decoding after a burst of erasures. However, there is a lack of constructions of these codes over fields of small size. In this article, we introduce the notion of complete 3-MDP convolutional codes, which are a generalization of complete MDP convolutional codes, and describe their decoding properties. In particular, we present a decoding algorithm for decoding erasures within a given time delay T and show that complete T-MDP convolutional codes are optimal for this algorithm. Moreover, using a computer search with the MAPLE software, we determine the minimal binary and non-binary field size for the existence of (2, 1, 2) complete 3-MDP convolutional codes and provide corresponding constructions. We give a description of all (2, 1, 2) complete MDP convolutional codes over the smallest possible fields, namely F 13 and F 16 and we also give constructions for (2, 1, 3) complete 4-MDP convolutional codes over F 128 obtained by a randomized computer search.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Information Systems
Physical Sciences > Computer Science Applications
Social Sciences & Humanities > Library and Information Sciences
Uncontrolled Keywords:Library and Information Sciences, Computer Science Applications, Information Systems
Language:English
Date:1 December 2020
Deposited On:10 Nov 2021 14:29
Last Modified:25 Feb 2024 02:48
Publisher:Institute of Electrical and Electronics Engineers
ISSN:0018-9448
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1109/tit.2020.3015698