88
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Series concatenation of 2D convolutional codes by means of input-state-output representations

, , &
Pages 2682-2691 | Received 21 Dec 2016, Accepted 21 Nov 2017, Published online: 25 Jan 2018

References

  • Almeida, P. , Napp, D. , & Pinto, R. (2016). Superregular matrices and applications to convolutional codes. Linear Algebra and its Applications , 499 , 1–25.
  • Benedetto, S. , Divsalar, D. , Montorsi, G. , & Pollara, F. (1998). Serial concatenation of interleaved codes: Performance analysis, design, and iterative decoding. IEEE Transactions on Information Theory , 44 (3), 909–926.
  • Berrou, C. , Glavieux, A. , & Thitimajshima, P. (1993, May). Near Shannon limit error-corrrecting coding and decoding: Turbo-codes. In Proceedings of the IEEE international conference on communications (ICC’ 93) (Vol. 2, pp. 1064–1070). Geneva, Switzerland: IEEE.
  • Climent, J.-J. , Herranz, V. , & Perea, C. (2007). A first approximation of concatenated convolutional codes from linear systems theory viewpoint. Linear Algebra and its Applications , 425 , 673–699.
  • Climent, J.-J. , Herranz, V. , & Perea, C. (2008). Linear system modelization of concatenated block and convolutional codes. Linear Algebra and its Applications , 429 , 1191–1212.
  • Climent, J.-J. , Napp, D. , Perea, C. , & Pinto, R. (2016). Maximum distance separable 2D convolutional codes. IEEE Transactions Information Theory , 62 (2), 669–680.
  • Climent, J.-J. , Napp, D. , & Pinto, R. (2012). A construction of MDS 2D convolutional codes of rate 1/n based on superregular matrices. Linear Algebra and its Applications , 437 , 766–780.
  • Climent, J. J. , Napp, D. , Pinto, R. , & Simões, R. (2015). Series concatenation of 2D convolutional codes. In E. J. Solteiro Pires & T.-P. Azevedo Perdicoúlis (Eds.), Proceedings of the IEEE 9th international workshop on multidimensional systems (nDS2015) (pp. 1–6). Vila Real, Portugal: IEEE.
  • Fornasini, E. , & Marchesini, G. (1986). Structure and properties of two-dimensional systems. In S. G. Tzafestas (Ed.), Multidimensional systems, techniques and applications (pp. 37–88). New York, NY: Marcel Dekker, Inc.
  • Fornasini, E. , & Valcher, M. E. (1994). Algebraic aspects of two-dimensional convolutional codes. IEEE Transactions on Information Theory , 40 (4), 1068–1082.
  • Forney, G. D. (1967). Concatenated codes . Cambridge, MA: M.I.T.
  • Kailath, T. (1980). Linear systems . Englewood Cliffs, NJ: Prentice-Hall.
  • Lobo, R. G. , Bitzer, D. L. , & Vouk, M. A. (2012). On locally invertible encoders and muldimensional convolutional codes. IEEE Transactions on Information Theory , 58 (3), 1774–1782.
  • MacWilliams, F. J. , & Sloane, N. J. A. (1977). The theory of error-correcting codes . Amsterdam, The Nederlands: North-Holland Mathematical Library and North Holland Publishing Co.
  • Morf, M. , Levy, B. C. , & Kung, S. Y. (1977). New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness. Proceedings of the IEEE , 65 (6), 861–872.
  • Napp, D. , Perea, C. , & Pinto, R. (2010). Input-state-output representations and constructions of finite support 2D convolutional codes. Advances in Mathematics of Communications , 4 (4), 533–545.
  • Napp, D. , Pinto, R. , & Simões, R. (2016, September). Input-state-output representations of concatenated 2d convolutional codes. In P. Garrido , F. Soares , & A. P. Moreira (Eds.), Proceedings of CONTROLO 2016 , Guimarães, Portugal, 14–16 September 2016, Vol. 402 of Lecture notes in electrical engineering (pp. 3–12). Cham, Switzerland: Springer-Verlag.
  • Ozkaya, B. (2014). Multidimensional quasi-cyclic and convolutional codes ( Unpublished doctoral dissertation). Sabanci University, Turkey.
  • Rosenthal, J. , & York, E. V. (1999). BCH convolutional codes. IEEE Transactions on Information Theory , 45 (6), 1833–1844.
  • Valcher, M. E. , & Fornasini, E. (1994). On 2D finite support convolutional codes: An algebraic approach. Multidimensional Systems and Signal Processing , 5 , 231–243.
  • Weiner, P. A. (1998). Multidimensional convolutional codes ( Unpublished doctoral dissertation). South Bend, IN: Department of Mathematics, University of Notre Dame.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.