1/n Turbo codes from linear system point of view

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Title: 1/n Turbo codes from linear system point of view
Authors: Herranz, Victoria | Napp, Diego | Perea, Carmen
Research Group/s: Grupo de Álgebra y Geometría (GAG)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Convolutional codes | Linear systems | Turbo codes | Effective distance
Knowledge Area: Álgebra
Issue Date: 20-Apr-2020
Publisher: Springer Nature
Citation: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2020, 114:118. doi:10.1007/s13398-020-00850-2
Abstract: The performance of turbo codes at the error floor region is largely determined by the effective free distance, which corresponds to the minimum Hamming weight among all codeword sequences generated by input sequences of weight two. In this paper, we study turbo codes of dimension one obtained from the concatenation of two equal codes and present an upper bound on the effective free distance of a turbo code with these parameters defined over any finite field. We do that making use of the so-called (A, B, C, D) state-space representations of convolutional codes and restrict to the case where A is invertible. A particular construction, from a linear systems point of view, of a recursive systematic convolutional code of rate 1/n so that the effective free distance of the corresponding turbo code attains this upper bound is also presented.
Sponsor: D. Napp was partially supported by the the Universitat d’Alacant (Grant No. VIGROB-287) and Generalitat Valenciana (Grant No. AICO/2017/128). V. Herranz and C. Perea were supported by the Ministerio de Economa, Industria y Competitividad within project TIN2016-80565-R.
URI: http://hdl.handle.net/10045/106752
ISSN: 1578-7303 (Print) | 1579-1505 (Online)
DOI: 10.1007/s13398-020-00850-2
Language: eng
Type: info:eu-repo/semantics/article
Rights: © The Royal Academy of Sciences, Madrid 2020
Peer Review: si
Publisher version: https://doi.org/10.1007/s13398-020-00850-2
Appears in Collections:INV - GAG - Artículos de Revistas

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