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Block Toeplitz matrices for burst-correcting convolutional codes

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

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.

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  1. Departament de Matemàtiques, Universitat d’Alacant, Alicante, Spain

    Joan-Josep Climent, Diego Napp & Verónica Requena

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  1. Joan-Josep Climent
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  2. Diego Napp
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  3. Verónica Requena
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Correspondence to Verónica Requena.

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An earlier version of this paper was presented at the Conference “Linear Algebra, Matrix Analysis and Applications. ALAMA2018”, held in Sant Joan d’Alacant on May/June 2018.

This work was partially supported by Spanish grants AICO/2017/128 of the Generalitat Valenciana and VIGROB-287 of the Universitat d’Alacant.

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Climent, JJ., Napp, D. & Requena, V. Block Toeplitz matrices for burst-correcting convolutional codes. RACSAM 114, 38 (2020). https://doi.org/10.1007/s13398-019-00744-y

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  • DOI: https://doi.org/10.1007/s13398-019-00744-y

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