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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Bibliographic Details
Published in:IEEE transactions on vehicular technology Vol. 70; no. 3; pp. 2428 - 2435
Main Authors: Rowshan, Mohammad, Viterbo, Emanuele
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:0018-9545, 1939-9359
Online Access:Get full text
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Summary: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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ISSN:0018-9545
1939-9359
DOI:10.1109/TVT.2021.3059370