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Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding

Publication ,  Journal Article
Coskun, MC; Liva, G; Graell I Amat, A; Lentmaier, M; Pfister, HD
Published in: IEEE Transactions on Information Theory
February 1, 2023

A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within 0.7 dB from the random coding union bound are provided.

Duke Scholars

Published In

IEEE Transactions on Information Theory

DOI

EISSN

1557-9654

ISSN

0018-9448

Publication Date

February 1, 2023

Volume

69

Issue

2

Start / End Page

823 / 841

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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MLA
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Coskun, M. C., Liva, G., Graell I Amat, A., Lentmaier, M., & Pfister, H. D. (2023). Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding. IEEE Transactions on Information Theory, 69(2), 823–841. https://doi.org/10.1109/TIT.2022.3207802
Coskun, M. C., G. Liva, A. Graell I Amat, M. Lentmaier, and H. D. Pfister. “Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding.” IEEE Transactions on Information Theory 69, no. 2 (February 1, 2023): 823–41. https://doi.org/10.1109/TIT.2022.3207802.
Coskun MC, Liva G, Graell I Amat A, Lentmaier M, Pfister HD. Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding. IEEE Transactions on Information Theory. 2023 Feb 1;69(2):823–41.
Coskun, M. C., et al. “Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding.” IEEE Transactions on Information Theory, vol. 69, no. 2, Feb. 2023, pp. 823–41. Scopus, doi:10.1109/TIT.2022.3207802.
Coskun MC, Liva G, Graell I Amat A, Lentmaier M, Pfister HD. Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding. IEEE Transactions on Information Theory. 2023 Feb 1;69(2):823–841.

Published In

IEEE Transactions on Information Theory

DOI

EISSN

1557-9654

ISSN

0018-9448

Publication Date

February 1, 2023

Volume

69

Issue

2

Start / End Page

823 / 841

Related Subject Headings

  • Networking & Telecommunications
  • 4613 Theory of computation
  • 4006 Communications engineering
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing