List Viterbi decoding of PAC codes

Mohammad Rowshan, Emanuele Viterbo

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)2428-2435
Number of pages8
JournalIEEE Transactions on Vehicular Technology
Volume70
Issue number3
DOIs
Publication statusPublished - Mar 2021

Keywords

  • Convolutional codes
  • list decoding
  • Maximum likelihood decoding
  • path metric sorting
  • Picture archiving and communication systems
  • Polar codes
  • polar codes
  • Polarization-adjusted convolutional codes
  • Sorting
  • Transforms
  • Viterbi algorithm
  • Viterbi decoding

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