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<p>The paper investigates the emerging field of low-complexity non-binary polar code (NB-PC) decoders. It shows that customising each kernel of an NB-PC decoder through offline analysis can significantly reduce the overall decoding complexity. The proposed decoder, referred to as the fast successive cancellation polarisation-aware (FSC-PA) scheme, achieves this by minimising the computational load of parity-check nodes that share the same level of input polarisation. Compared to the state-of-the-art extended min-sum algorithm, the FSC-PA algorithm achieves an overall reduction of 60% in field additions and 30% in real additions, while incurring only a negligible performance loss (less than 0.2 dB degradation). The proposed FSC-PA scheme is compared with the classical CRC-aided fast successive cancellation list of size <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L = 32\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo>=</mo> <mn>32</mn> </mrow> </math></EquationSource> </InlineEquation> (CA-FSCL32) with a list size of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L=32\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo>=</mo> <mn>32</mn> </mrow> </math></EquationSource> </InlineEquation>. In terms of computational complexity, FSC-PA reduces the number of additions by one order of magnitude compared to CA-FSCL32. Regarding performance, the results depend on the channel type: while CA-FSCL32 outperforms FSC-PA in the binary phase shift keying (BPSK) channel, the hierarchy is reversed with the cyclic-code shift keying (CCSK) modulation, with FSC-PA achieving a gain of up to 1.7 dB in signal-to-noise ratio (SNR). Thus, FSC-PA emerges as an effective solution for coded-CCSK modulation.</p>

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Fast polarisation-aware decoder for non-binary polar codes

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Joseph Jabour,
  • Ali Chamas Al-Ghouwayel,
  • Emmanuel Boutillon

摘要

The paper investigates the emerging field of low-complexity non-binary polar code (NB-PC) decoders. It shows that customising each kernel of an NB-PC decoder through offline analysis can significantly reduce the overall decoding complexity. The proposed decoder, referred to as the fast successive cancellation polarisation-aware (FSC-PA) scheme, achieves this by minimising the computational load of parity-check nodes that share the same level of input polarisation. Compared to the state-of-the-art extended min-sum algorithm, the FSC-PA algorithm achieves an overall reduction of 60% in field additions and 30% in real additions, while incurring only a negligible performance loss (less than 0.2 dB degradation). The proposed FSC-PA scheme is compared with the classical CRC-aided fast successive cancellation list of size \(L = 32\) L = 32 (CA-FSCL32) with a list size of \(L=32\) L = 32 . In terms of computational complexity, FSC-PA reduces the number of additions by one order of magnitude compared to CA-FSCL32. Regarding performance, the results depend on the channel type: while CA-FSCL32 outperforms FSC-PA in the binary phase shift keying (BPSK) channel, the hierarchy is reversed with the cyclic-code shift keying (CCSK) modulation, with FSC-PA achieving a gain of up to 1.7 dB in signal-to-noise ratio (SNR). Thus, FSC-PA emerges as an effective solution for coded-CCSK modulation.