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Soft-Output Fast Successive-Cancellation List Decoder for Polar Codes

Li Shen, Yongpeng Wu, Yin Xu, Xiaohu You, Xiqi Gao, Wenjun Zhang

TL;DR

This work tackles the high decoding latency of soft-output polar decoders by proposing SO-FSCL, a soft-output fast SCL decoder that uses node-based fast decoding for Rate0, Rate1, REP, and SPC nodes. It introduces a practical approximation to the codebook probability via $P^*_{\\mathcal{U}}(\\bm{y}^N)$, allowing APP LLRs to be computed under dynamic frozen bits. The approach achieves substantial latency reductions (at least $76\%$) over SO-SCL while preserving BER/BLER performance, and demonstrates strong results on 5G polar codes and MIMO channels. These findings indicate that SO-FSCL offers a viable, efficient route for low-latency soft-output decoding in practical polar-code deployments.

Abstract

The soft-output successive cancellation list (SOSCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder for polar codes. However, the sequential nature of SCL decoding leads to a high decoding latency for the SO-SCL decoder. In this paper, we propose a soft-output fast SCL (SO-FSCL) decoder by incorporating node-based fast decoding into the SO-SCL framework. Simulation results demonstrate that the proposed SO-FSCL decoder significantly reduces the decoding latency without loss of performance compared with the SO-SCL decoder.

Soft-Output Fast Successive-Cancellation List Decoder for Polar Codes

TL;DR

This work tackles the high decoding latency of soft-output polar decoders by proposing SO-FSCL, a soft-output fast SCL decoder that uses node-based fast decoding for Rate0, Rate1, REP, and SPC nodes. It introduces a practical approximation to the codebook probability via , allowing APP LLRs to be computed under dynamic frozen bits. The approach achieves substantial latency reductions (at least ) over SO-SCL while preserving BER/BLER performance, and demonstrates strong results on 5G polar codes and MIMO channels. These findings indicate that SO-FSCL offers a viable, efficient route for low-latency soft-output decoding in practical polar-code deployments.

Abstract

The soft-output successive cancellation list (SOSCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder for polar codes. However, the sequential nature of SCL decoding leads to a high decoding latency for the SO-SCL decoder. In this paper, we propose a soft-output fast SCL (SO-FSCL) decoder by incorporating node-based fast decoding into the SO-SCL framework. Simulation results demonstrate that the proposed SO-FSCL decoder significantly reduces the decoding latency without loss of performance compared with the SO-SCL decoder.

Paper Structure

This paper contains 17 sections, 17 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Polar Codes
  5. SC and SCL Decoding
  6. SO-SCL Decoding
  7. Proposed SO-FSCL Decoding
  8. SO-FSCL Decoder for the Four Nodes
  9. Rate0 Node
  10. REP Node
  11. Rate1 Node
  12. SPC Node
  13. Calculation of the Bit-Wise APP LLRs
  14. Compatibility with Dynamic Frozen Bits
  15. Decoding Latency Analysis
  16. ...and 2 more sections

Figures (4)

  • Figure 1: An example of the SCL decoding tree of a $(4,3)$ polar code with frozen bit $u_3=0$ and list size $L=2$. The whole tree consists of invalid subtrees rooted at $\mathcal{B} =\{(0,1,1), (1,0,1)\}$, visited leaves at $\mathcal{V}=\{(0,1,0,1), (1,0,0,1)\}$, and unvisited subtrees rooted at $\mathcal{W}=\{(0,0), (1,1), (0,1,0,0), (1,0,0,0)\}$.
  • Figure 2: Examples of the partial FSCL decoding tree for length-4 Rate0, REP, Rate1, and SPC nodes underneath a decoded path $\bm{a}^{i_s-1}$.
  • Figure 3: BER performance of various soft-output polar decoders for a $(512, 256)$ polar code.
  • Figure 4: BLER performance of various soft-output polar decoders over QPSK-input $2\times 2$ MIMO channel for different polar codes.