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http://hdl.handle.net/10773/15106
Title: | Maximum distance separable 2D convolutional codes |
Author: | Climent, J.-J. Napp, D. Perea, C. Pinto, Raquel |
Keywords: | 2D convolutional code Circulant Cauchy matrix Generalized Singleton bound Maximum distance separable code Superregular matrix |
Issue Date: | Feb-2016 |
Publisher: | IEEE |
Abstract: | Maximum distance separable (MDS) block codes and MDS 1D convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this paper, we generalize this concept to the class of 2D convolutional codes. For that, we introduce a natural bound on the distance of a 2D convolutional code of rate $k/n$ and degree $delta $ , which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then, we prove the existence of 2D convolutional codes of rate $k/n$ and degree $delta $ that reach such bound when $n geq k (({(lfloor ({delta }/{k}) rfloor + 2)(lfloor ({delta }/{k}) rfloor + 3)})/{2})$ if $k {nmid } delta $ , or $n geq k (({(({delta }/{k}) + 1)(({delta }/{k}) + 2)})/{2})$ if $k mid delta $ , by presenting a concrete constructive procedure. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/15106 |
DOI: | 10.1109/TIT.2015.2509075 |
ISSN: | 0018-9448 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2DCCk_2014_v07_submitted.pdf | Preprint | 447.36 kB | Adobe PDF | View/Open |
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