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Design of a Family of Rate-Adaptive LDPC Convolutional Codes with Short Constraint Length

  • Massimo Battaglioni
  • Edoardo Carnevali
  • Franco Chiaraluce
  • Marco Baldi
  • Giovanni Cancellieri
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Abstract

This paper studies the design of some high-rate, adaptive, low-density parity-check (LDPC) convolutional codes with short constraint length, based on interleaved parity-check polynomials. Starting from some known results regarding the selection of polynomials that yield codes free of short cycles in the associated Tanner graphs, we propose some new constructions based on Golomb rulers, along with relaxed variants that do not strictly satisfy the Golomb ruler condition, but retain similar structural properties. The result is a family of rate-adaptive code constructions with code rates of the form R=(n0−1)/n0. Conditions for the absence of length-4 cycles are derived, together with upper bounds on the free distance that are met in all considered examples.

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Cite

BibTeXRIS
BibTeX
@misc{battaglioni2026design,
  title = {{Design of a Family of Rate-Adaptive LDPC Convolutional Codes with Short Constraint Length}},
  author = {Massimo Battaglioni and Edoardo Carnevali and Franco Chiaraluce and Marco Baldi and Giovanni Cancellieri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22231},
  eprint = {2610.22231},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22231},
}
RIS
TY  - UNPB
TI  - Design of a Family of Rate-Adaptive LDPC Convolutional Codes with Short Constraint Length
AU  - Massimo Battaglioni
AU  - Edoardo Carnevali
AU  - Franco Chiaraluce
AU  - Marco Baldi
AU  - Giovanni Cancellieri
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22231
UR  - https://arxiv.org/abs/2610.22231
AB  - This paper studies the design of some high-rate, adaptive, low-density parity-check (LDPC) convolutional codes with short constraint length, based on interleaved parity-check polynomials. Starting from some known results regarding the selection of polynomials that yield codes free of short cycles in the associated Tanner graphs, we propose some new constructions based on Golomb rulers, along with relaxed variants that do not strictly satisfy the Golomb ruler condition, but retain similar structural properties. The result is a family of rate-adaptive code constructions with code rates of the form R=(n_0−1)/n_0. Conditions for the absence of length-4 cycles are derived, together with upper bounds on the free distance that are met in all considered examples.
ER  -