Optimal Construction for Decoding 2D Convolutional Codes over an Erasure Channel

Author:

Pinto Raquel1ORCID,Spreafico Marcos2ORCID,Vela Carlos1ORCID

Affiliation:

1. CIDMA—Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

2. INMA—Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande 79070-900, Brazil

Abstract

In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.

Funder

Portuguese Foundation for Science and Technology

Publisher

MDPI AG

Reference28 articles.

1. Algebraic aspects of two-dimensional convolutional codes;Fornasini;IEEE Trans. Inf. Theory,1994

2. On 2D finite support convolutional codes: An algebraic approach;Valcher;Multidim. Syst. Signal Proc.,1994

3. Maximum Distance Separable 2D Convolutional Codes;Climent;IEEE Trans. Inf. Theory,2016

4. Colonius, F., Helmke, U., Wirth, F., and Praetzel-Wolters, D. (2000). Advances in Mathematical Systems Theory, Birkhäuser.

5. Weiner, P.A. (1998). Multidimensional Convolutional Codes. [Ph.D. Thesis, University of Notre Dame].

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