Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding
| Autor: | Coşkun, Mustafa Cemil, Liva, Gianluigi, Amat, Alexandre Graell i, Lentmaier, Michael, Pfister, Henry D. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Submitted to the IEEE Transactions on Information Theory. The revised version of the first submission. Major changes: 1) No dedicated section for numerical results. Instead, simulations are provided right after the relevant section. 2) More simulation results are added, including those for the BEC. Comparisons to the state-of-art polar codes and 5G-NR LDPC codes provided |
| Databáze: | arXiv |
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