Analysis of polarization-adjusted convolutional codes (PAC): a source-channel coding method

He Sun, Emanuele Viterbo, Rongke Liu

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Polarization-adjusted convolutional (PAC) code improves the error-correction ability of polar codes by concatenating a convolutional transform with polar transform. In this paper, we establish a source-channel coding framework to develop the theory of the optimal rate assignment for PAC codes. In the source-channel coding model, each column of the convolutional matrix corresponds to a source encoder, in which multiple bits are compressed into one polarized channel. According to the source coding theory, the distortion function of each source encoder is derived. With the Shannon coding theorem, the achievable source coding rates are characterized by the polarized channel capacity and the rate distortion function. With the achievable source coding rates, the rate assignment after convolutional transform is obtained. Simulation results show that the PAC codes achieve better rate assignment than polar codes, leading to a better exploitation of the capacity on the insufficiently polarized channels and an improved error-correction performance.

Original languageEnglish
Title of host publication2021 IEEE Globecom Workshops (GC Wkshps)
EditorsSennur Ulukus
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781665423908
ISBN (Print)9781665423915
Publication statusPublished - 2021
EventIEEE Globecom Workshops (Gc Workshops) 2021 - Online, Madrid, Spain
Duration: 7 Dec 202111 Dec 2021 (Proceedings) (Website)


ConferenceIEEE Globecom Workshops (Gc Workshops) 2021
Abbreviated titleGC Wkshps 2021
Internet address


  • compression
  • polar codes
  • Polarization-adjusted convolutional codes
  • rate distortion
  • source coding

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