Abstract
In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main result reduces the decoding problem of 2D convolutional codes to a problem of decoding a set of associated 1D convolutional codes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Almeida, P., Napp, D., Pinto, R.: A new class of superregular matrices and MDP convolutional codes. Linear Algebra Appl. 439, 2145–2157 (2013). doi:10.1016/j.laa.2013.06.013
Arai, M., Yamamoto, A., Yamaguchi, A., Fukumoto, S., Iwasaki, K.: Analysis of using convolutional codes to recover packet losses over burst erasure channels. In: Proceedings of the 2001 Pacific Rim International Symposium on Dependable Computing, Seoul, pp. 258–265. IEEE (2001). doi:10.1109/PRDC.2001.992706
Charoenlarpnopparut, C.: Applications of Grbner bases to the structural description and realization of multidimensional convolutional code. Sci. Asia 35, 95–105 (2009). doi:10.2306/scienceasia1513-1874.2009.35.095
Climent, J.J., Napp, D., Perea, C., Pinto, R.: A construction of MDS 2D convolutional codes of rate 1∕n based on superregular matrices. Linear Algebra Appl. 437, 766–780 (2012). doi:10.1016/j.laa.2012.02.032
Fornasini, E., Valcher, M.E.: Algebraic aspects of two-dimensional convolutional codes. IEEE Trans. Inf. Theory 40(4), 1068–1082 (1994). doi:10.1109/18.335967
Jangisarakul, P., Charoenlarpnopparut, C.: Algebraic decoder of multidimensional convolutional code: constructive algorithms for determining syndrome decoder and decoder matrix based on Gröbner basis. Multidimens. Syst. Signal Process. 22(1–3), 67–81 (2011)
Napp, D., Perea, C., Pinto, R.: Input-state-output representations and constructions of finite support 2D convolutional codes. Adv. Math. Commun. 4(4), 533–545 (2010). doi:10.3934/amc.2010.4.533
Tomás, V.: Complete-MDP convolutional codes over the erasure channel. Ph.D. thesis, Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, Alicante (2010)
Tomás, V., Rosenthal, J., Smarandache, R.: Reverse-maximum distance profile convolutional codes over the erasure channel. In: Edelmayer, A. (ed.) Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, pp. 2121–2127 (2010)
Tomás, V., Rosenthal, J., Smarandache, R.: Decoding of convolutional codes over the erasure channel. IEEE Trans. Inf. Theory 58(1), 90–108 (2012). doi:10.1109/TIT.2011.2171530
Weiner, P.A.: Multidimensional convolutional codes. Ph.D. thesis, Department of Mathematics, University of Notre Dame, Indiana (1998)
Acknowledgements
This work was partially supported by Spanish grant MTM2011-24858 of the Ministerio de Ciencia e Innovacin of the Gobierno de Espaa. The work of D. Napp, R. Pinto, and R. Simes was partially supported by Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundao para a Cincia e a Tecnologia”), within project UID/MAT/04106/2013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Climent, JJ., Napp, D., Pinto, R., Simões, R. (2015). Burst Erasure Correction of 2D Convolutional Codes. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-17296-5_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17295-8
Online ISBN: 978-3-319-17296-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)