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List Decoding of Arıkan's PAC Codes.

Hanwen Yao1, Arman Fazeli1, Alexander Vardy1

  • 1Department of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA.

Entropy (Basel, Switzerland)
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Summary

Polarization-adjusted convolutional (PAC) codes offer improved performance over traditional polar codes at short blocklengths. This study demonstrates that list decoding can achieve similar performance to sequential decoding in PAC codes, challenging previous assumptions.

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coding theoryconvolutional codeslist decodingpolar codessequential decoding

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Area of Science:

  • Information Theory
  • Coding Theory
  • Digital Communications

Background:

  • Polar codes achieve channel capacity but struggle with performance at short blocklengths.
  • Current state-of-the-art for short blocklengths involves CRC precoding and successive-cancellation list decoding.
  • Polarization-adjusted convolutional (PAC) codes present a new scheme with significant performance gains.

Purpose of the Study:

  • To determine if sequential decoding is essential for PAC codes' superior performance.
  • To investigate the underlying reasons for PAC codes' effectiveness.
  • To compare PAC codes with existing coding schemes like polar and Reed-Muller codes.

Main Methods:

  • Investigated PAC codes using list decoding with moderately large list sizes (L>=128).
  • Analyzed PAC code performance by comparing sequential and list decoding against maximum likelihood (ML) decoding.
  • Estimated low-weight codewords in PAC codes to approximate the union bound.
  • Explored random time-varying convolutional precoding for PAC codes.

Main Results:

  • PAC codes achieve comparable performance to sequential decoding using list decoding (L>=128).
  • Both decoding methods for PAC codes closely approximate ML decoding.
  • PAC codes demonstrate superior performance compared to polar and Reed-Muller codes.
  • Random time-varying convolutional precoding with constraint length ν=2 yields similar performance.

Conclusions:

  • Sequential decoding is not essential for PAC codes; list decoding offers comparable performance and practical advantages.
  • PAC codes exhibit remarkable performance due to their structure and efficient decoding.
  • PAC codes represent a significant advancement in coding theory for short blocklength applications.