List Viterbi Decoding of PAC Codes
Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a...
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| Veröffentlicht in: | IEEE transactions on vehicular technology Jg. 70; H. 3; S. 2428 - 2435 |
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| Sprache: | Englisch |
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IEEE
01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9545, 1939-9359 |
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| Abstract | Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results show that this concatenation improves the Hamming distance properties of polar codes. Motivated by the fact that the parallel list Viterbi algorithm (LVA) sorts the candidate paths locally at each trellis node, in this work, we adapt the trellis, path metric, and the local sorter of LVA to PAC codes and show how the error correction performance moves from the poor performance of the Viterbi algorithm (VA) to the superior performance of list decoding by changing the constraint length, list size, and the sorting strategy (local sorting and global sorting) in the LVA. Also, we analyze the complexity of the local sorting of the paths in LVA relative to the global sorting in the list decoding and we show that LVA has a significantly lower sorting complexity compared with list decoding. |
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| AbstractList | Polarization-adjusted convolutional (PAC) codes are special concatenated codes in which we employ a one-to-one convolutional transform as a pre-coding step before the polar transform. In this scheme, the polar transform (as a mapper) and the successive cancellation process (as a demapper) present a synthetic vector channel to the convolutional transformation. The numerical results show that this concatenation improves the Hamming distance properties of polar codes. Motivated by the fact that the parallel list Viterbi algorithm (LVA) sorts the candidate paths locally at each trellis node, in this work, we adapt the trellis, path metric, and the local sorter of LVA to PAC codes and show how the error correction performance moves from the poor performance of the Viterbi algorithm (VA) to the superior performance of list decoding by changing the constraint length, list size, and the sorting strategy (local sorting and global sorting) in the LVA. Also, we analyze the complexity of the local sorting of the paths in LVA relative to the global sorting in the list decoding and we show that LVA has a significantly lower sorting complexity compared with list decoding. |
| Author | Viterbo, Emanuele Rowshan, Mohammad |
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| Cites_doi | 10.1109/PROC.1973.9030 10.1109/ISTC.2018.8625267 10.1109/LCOMM.2018.2803163 10.1109/TIT.2015.2453267 10.1145/1468075.1468121 10.1109/ISCAS.2014.6865312 10.1109/ACSSC.2014.7094505 10.1109/LCOMM.2019.2914047 10.1109/MILCOM.2008.4753260 10.1109/TIT.2009.2021379 10.1109/TSP.2015.2439211 10.1109/TIT.1987.1057377 10.1109/ISCAS.2015.7169066 10.1109/MVT.2019.2903343 10.1515/9781400874651 10.1109/TCOMM.1994.577040 10.1109/TVT.2021.3052550 10.1109/ISIT.2011.6033904 10.1109/TIT.1967.1054010 |
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| SubjectTerms | Algorithms Complexity Concatenated codes Convolutional codes Error correction List decoding Maximum likelihood decoding path metric sorting Picture archiving and communication systems Polar codes polarization-adjusted convolutional codes Sorting Transforms Viterbi algorithm Viterbi algorithm detectors Viterbi decoding |
| Title | List Viterbi Decoding of PAC Codes |
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