Construction of LDPC convolutional codes via difference triangle sets

Autor: Joachim Rosenthal, Julia Lieb, Gianira N. Alfarano

Publikováno v: Designs, Codes, and Cryptography

In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a $(k,w)$-(weak) differen

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c097fa6b27c7542887d1c2e1200d2c3
https://doi.org/10.1007/s10623-021-00912-5

A Number Theoretic Approach to Cycles in LDPC Codes

Autor: Julia Lieb, Simran Tinani

LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such codes is trying to avoid cycles of short length in the associated Tanner graph, i.e. obtaining a possibl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::969bc9a4227b398564d027b34cbf15a7
http://arxiv.org/abs/2201.11112

Erasure decoding of convolutional codes using first-order representations

Autor: Joachim Rosenthal, Julia Lieb

Publikováno v: Mathematics of Control, Signals, and Systems

It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::212037ff1738d30309dd707e6c5406a6
https://www.zora.uzh.ch/id/eprint/205958/

On the left primeness of some polynomial matrices with applications to convolutional codes

Autor: Gianira N. Alfarano, Julia Lieb

Publikováno v: Journal of Algebra and Its Applications. 20

Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible for given rate and degree. There exists a well-known criterion to check whether a code is MDP using the generator or the parity-

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::096f95092833b528704a32473c00457a
https://doi.org/10.1142/s0219498821502078

List decoding of Convolutional Codes over integer residue rings

Autor: Diego Napp, Raquel Pinto, Julia Lieb

Publikováno v: Repositório Científico de Acesso Aberto de Portugal
Repositório Científico de Acesso Aberto de Portugal (RCAAP)
instacron:RCAAP
RUA. Repositorio Institucional de la Universidad de Alicante
Universidad de Alicante (UA)

A convolutional code Cover Zpr[D] is a Zpr[D]-submodule of Znpr[D] where Zpr[D] stands for the ring of polynomials with coefficients in Zpr. In this paper, we study the list decoding problem of these codes when the transmission is performed over an e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aac20a536f6bce478e962d1c64467f9f