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Analysis of Low-Density Parity-Check Codes over Finite Integer Rings for the Lee Channel


Bariffi, Jessica; Bartz, Hannes; Liva, Gianluigi; Rosenthal, Joachim (2022). Analysis of Low-Density Parity-Check Codes over Finite Integer Rings for the Lee Channel. In: GLOBECOM 2022 - 2022 IEEE Global Communications Conference, Rio de Janeiro, Brazil, 4 December 2022 - 8 December 2022. Institute of Electrical and Electronics Engineers, 3478-3483.

Abstract

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distributions of the two channels coincide, in the limit of large block length. Random coding union bounds on the block error probability are derived for both channels. Moreover, the performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm and it is compared to the derived bounds.

Abstract

We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distributions of the two channels coincide, in the limit of large block length. Random coding union bounds on the block error probability are derived for both channels. Moreover, the performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm and it is compared to the derived bounds.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Artificial Intelligence
Physical Sciences > Computer Networks and Communications
Physical Sciences > Hardware and Architecture
Physical Sciences > Signal Processing
Physical Sciences > Renewable Energy, Sustainability and the Environment
Physical Sciences > Safety, Risk, Reliability and Quality
Language:English
Event End Date:8 December 2022
Deposited On:11 Jan 2024 12:05
Last Modified:16 Jan 2024 13:50
Publisher:Institute of Electrical and Electronics Engineers
Series Name:IEEE Global Communications Conference
ISBN:978-1-6654-3540-6
OA Status:Closed
Publisher DOI:https://doi.org/10.1109/globecom48099.2022.10000923
Other Identification Number:IEEE Catalog Number: CFP22GLO-ART
Project Information:
  • : FunderSNSF
  • : Grant ID188430
  • : Project TitleNew Constructions of Convolutional Codes