Block Toeplitz matrices for burst-correcting convolutional codes

• Joan-Josep Climent ^[1] ; Diego Napp ^[1] ; Verónica Requena ^[1]
  1. [1] Universitat d'Alacant

     Universitat d'Alacant

     Alicante, España

     
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 114, Nº. 1, 2020, págs. 133-146
• Idioma: inglés
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• Resumen

  • In this paper we study a problem in the area of coding theory. In particular, we focus on a class of error-correcting codes called convolutional codes. We characterize convolutional codes that can correct bursts of erasures with the lowest possible delay. This characterization is given in terms of a block Toeplitz matrix with entries in a finite field that is built upon a given generator matrix of the convolutional code. This result allows us to provide a concrete construction of a generator matrix of a convolutional code with entries being only zeros or ones that can recover bursts of erasures with low delay. This construction admits a very simple decoding algorithm and, therefore, simplifies the existing schemes proposed recently in the literature.