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Improving the decoding performance of CA-polar codes

Jiewei Feng, Peihong Yuan, Ken R. Duffy, Muriel Médard

TL;DR

The paper addresses decoding CRC-Aided polar codes by converting CA-SCL from an incomplete to a complete decoder through a code-agnostic outer decoder, forming Complete CA-SCL (CCA-SCL).It introduces a CA-polar–specific soft-output framework (SO-SCL) and adapts it to enable blockwiseUER control, leveraging the outer CRC as an error-correction aid when CA-SCL fails.Key contributions include showing BLER gains (up to ~0.2 dB for non-systematic and up to ~1 dB for systematic CA-polar codes), and demonstrating that systematic CA-polar codes mitigate LLR conversion issues and improve outer-decoding performance.Simulations confirm the practical viability of CCA-SCL and the threshold-based UER control, highlighting the approach’s relevance to 5G NR CA-polar implementations and potential hardware efficiency via parallel outer decoders.

Abstract

We investigate the use of modern code-agnostic decoders to convert CA-SCL from an incomplete decoder to a complete one. When CA-SCL fails to identify a codeword that passes the CRC check, we apply a code-agnostic decoder that identifies a codeword that satisfies the CRC. We establish that this approach gives gains of up to 0.2 dB in block error rate for CA-Polar codes from the 5G New Radio standard. If, instead, the message had been encoded in a systematic CA-polar code, the gain improves to 0.2 ~ 1dB. Leveraging recent developments in blockwise soft output, we additionally establish that it is possible to control the undetected error rate even when using the CRC for error correction.

Improving the decoding performance of CA-polar codes

TL;DR

The paper addresses decoding CRC-Aided polar codes by converting CA-SCL from an incomplete to a complete decoder through a code-agnostic outer decoder, forming Complete CA-SCL (CCA-SCL).It introduces a CA-polar–specific soft-output framework (SO-SCL) and adapts it to enable blockwiseUER control, leveraging the outer CRC as an error-correction aid when CA-SCL fails.Key contributions include showing BLER gains (up to ~0.2 dB for non-systematic and up to ~1 dB for systematic CA-polar codes), and demonstrating that systematic CA-polar codes mitigate LLR conversion issues and improve outer-decoding performance.Simulations confirm the practical viability of CCA-SCL and the threshold-based UER control, highlighting the approach’s relevance to 5G NR CA-polar implementations and potential hardware efficiency via parallel outer decoders.

Abstract

We investigate the use of modern code-agnostic decoders to convert CA-SCL from an incomplete decoder to a complete one. When CA-SCL fails to identify a codeword that passes the CRC check, we apply a code-agnostic decoder that identifies a codeword that satisfies the CRC. We establish that this approach gives gains of up to 0.2 dB in block error rate for CA-Polar codes from the 5G New Radio standard. If, instead, the message had been encoded in a systematic CA-polar code, the gain improves to 0.2 ~ 1dB. Leveraging recent developments in blockwise soft output, we additionally establish that it is possible to control the undetected error rate even when using the CRC for error correction.

Paper Structure

This paper contains 7 sections, 2 theorems, 9 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proposed pipeline for CCA-SCL
  4. Decoding using outer decoder
  5. Managing UER with SO-SCL adapted to CA-polar
  6. Simulations
  7. Conclusion

Key Result

Lemma 1

Let $|\mathscr{L}_{\text{I},j}|$ denote the reliability of the hard decision for $X_j$ based on $\mathscr{L}_{\text{I},j}$. Similarly, let $|\mathscr{L}_{\text{O},i}|$ denote the reliability of the hard decision for $\Phi_i$ based on $\mathscr{L}_{\text{O},i}$. Denote $\mathcal{X}_i=\{s|F^{\otimes n

Figures (4)

  • Figure 1: Pipeline of the proposed CCA-SCL decoder. Blue lines represent CA-SCL. Dashed lines represent new additions.
  • Figure 2: Example comparison between channel LLR $\mathscr{L}_{\text{I},i}$ and outer LLR $\mathscr{L}_{\text{O},j}$. Code parameters are $[N,K,M]=[128,114,90]$ and $E_b/N_0=6$ dB. The blue line represents the reliabilities $|\mathscr{L}_{\text{I},i}|$ for $i=1,\cdots,N$ where the reliabilities are ordered from the least to the highest. The orange line represents the ordered reliabilities $|\mathscr{L}_{\text{O},j}|$ for $j=1,\cdots,K$. As depicted by the figure, converting the LLRs through eq. \ref{['eq_converting']} results in less reliability.
  • Figure 3: BLER performance of CA-SCL and Complete CA-SCL (CCSCL) with BPSK subject to AWGN.
  • Figure 4: Verification of SO calibration for a $[64,43,32]$ CA-polar code.

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Lemma 2
  • proof