Construction of Rate (n — 1 )/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets
| Autor: | Julia Lieb, Gianira N. Alfarano, Joachim Rosenthal |
|---|---|
| Přispěvatelé: | University of Zurich |
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Degree (graph theory) 05 social sciences 340 Law Binary number 610 Medicine & health 020206 networking & telecommunications 02 engineering and technology 1710 Information Systems Set (abstract data type) 10123 Institute of Mathematics Matrix (mathematics) 510 Mathematics 2604 Applied Mathematics Convolutional code 0502 economics and business 0202 electrical engineering electronic engineering information engineering Code (cryptography) 2614 Theoretical Computer Science Tanner graph 050203 business & management Scope (computer science) 2611 Modeling and Simulation Mathematics |
| Zdroj: | ISIT |
| DOI: | 10.1109/isit44484.2020.9174510 |
| Popis: | This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an (n - 1,w)- difference triangle set are used as supports of the columns of rate (n — 1)/n convolutional codes. If the field size is large enough, the Tanner graph associated to the sliding parity-check matrix of the code is free from 4 and 6-cycles not satisfying the full rank condition. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets. The parameters of the convolutional code are shown to be determined by the parameters of the underlying difference triangle set. In particular, the free distance of the code is related to w and the degree of the code is linked to the "scope" of the difference triangle set. Hence, the problem of finding families of difference triangle set with minimum scope is equivalent to find convolutional codes with small degree. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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