Successive Cancellation Decoding of Single Parity-Check Product Codes : Analysis and Improved Decoding
(2023) In IEEE Transactions on Information Theory 69(2). p.823-841- Abstract
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,... (More)
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.
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- author
- Coskun, Mustafa Cemil ; Liva, Gianluigi ; Amat, Alexandre Graell i. ; Lentmaier, Michael LU and Pfister, Henry D.
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Codes, Encoding, Error probability, Generators, list decoding, Maximum likelihood decoding, multi-kernel polar codes, Polar codes, Product codes, product codes, Successive cancellation decoding
- in
- IEEE Transactions on Information Theory
- volume
- 69
- issue
- 2
- pages
- 1 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85139441049
- ISSN
- 0018-9448
- DOI
- 10.1109/TIT.2022.3207802
- language
- English
- LU publication?
- yes
- id
- 48b82215-1fd1-4bb4-9a82-a9aa865b39fe
- date added to LUP
- 2022-12-14 12:30:26
- date last changed
- 2023-11-02 16:08:33
@article{48b82215-1fd1-4bb4-9a82-a9aa865b39fe,
abstract = {{<p>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.</p>}},
author = {{Coskun, Mustafa Cemil and Liva, Gianluigi and Amat, Alexandre Graell i. and Lentmaier, Michael and Pfister, Henry D.}},
issn = {{0018-9448}},
keywords = {{Codes; Encoding; Error probability; Generators; list decoding; Maximum likelihood decoding; multi-kernel polar codes; Polar codes; Product codes; product codes; Successive cancellation decoding}},
language = {{eng}},
number = {{2}},
pages = {{823--841}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Information Theory}},
title = {{Successive Cancellation Decoding of Single Parity-Check Product Codes : Analysis and Improved Decoding}},
url = {{http://dx.doi.org/10.1109/TIT.2022.3207802}},
doi = {{10.1109/TIT.2022.3207802}},
volume = {{69}},
year = {{2023}},
}