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arxiv: 2604.17482 · v2 · submitted 2026-04-19 · 💻 cs.IT · math.IT

Recognition: no theorem link

Node-Based Soft-Output Fast Successive Cancellation List Decoding of Polar Codes

Li Shen , Yongpeng Wu , Zhen Gao , Yin Xu , Xiaohu You , Xiqi Gao , Wenjun Zhang
Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:44 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords polar codessuccessive cancellation listsoft-output decodingfast decodingnode-based decodinglatency reductioniterative decoding
0
0 comments X

The pith

Polar code list decoders can produce accurate soft outputs while cutting latency and arithmetic operations by using node-based fast methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an extension to fast successive cancellation list decoding that also generates soft outputs for polar codes. Conventional soft-output SCL achieves good accuracy but pays for it with high latency from its step-by-step nature. By solving soft-information extraction inside the special nodes that enable fast decoding, the new algorithm preserves most of the speed advantage. Simulations confirm the soft outputs stay close in quality to full SO-SCL while outperforming other soft polar decoders when used inside iterative receivers.

Core claim

The SO-FSCL decoder incorporates node-based fast decoding into the soft-output SCL framework after resolving soft-output extraction for special nodes. It functions as an optional add-on to any FSCL decoder, letting the user select hard decisions alone or full soft outputs. Latency analysis shows decoding time steps can drop 81.8 percent with unlimited resources, additions fall 41.3 percent, and comparisons fall 46.4 percent. Bit and frame error rate curves remain nearly identical to standard SO-SCL and superior to prior soft-output polar methods, especially under iterative decoding.

What carries the argument

Node-based fast successive cancellation list decoding with explicit soft-output extraction rules for special nodes.

If this is right

  • Decoding time steps fall by 81.8 percent when unlimited parallel resources are available.
  • Arithmetic operations decrease by 41.3 percent in additions and 46.4 percent in comparisons.
  • Soft-output quality equals that of conventional SO-SCL while exceeding other soft polar decoders in iterative receiver chains.
  • Existing FSCL hardware can be reused by simply enabling or disabling the soft-output path.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same node extraction technique might be applied to other list-based decoders to trade latency for richer output information.
  • Lower comparison counts could translate directly into reduced switching activity and power in ASIC or FPGA realizations.
  • Because the method preserves the original polar code structure, it remains compatible with existing code design tools and rate-matching schemes.

Load-bearing premise

Soft values can be recovered from the fast-decoded special nodes without enough error to erase the performance match with full successive cancellation list.

What would settle it

A side-by-side simulation run at the same list size and channel conditions in which the SO-FSCL frame error rate curve visibly separates from the SO-SCL curve at moderate-to-high SNR.

Figures

Figures reproduced from arXiv: 2604.17482 by Li Shen, Wenjun Zhang, Xiaohu You, Xiqi Gao, Yin Xu, Yongpeng Wu, Zhen Gao.

Figure 1
Figure 1. Figure 1: Factor graph of polar codes with N = 8. According to the channel polarization theory [2], the K most reliable polarized subchannels out of N are used for message transmission, with their indices denoted as I ⊆ [[N]]. The remaining subchannels are indexed by F = [[N]] ∩ IC . Thus, the input vector u N for polar transform consists of u[I] and u[F], which are placed with information bits and frozen bits, resp… view at source ↗
Figure 2
Figure 2. Figure 2: An example of the SCL decoding tree of a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Examples of the partial FSCL decoding tree for length- [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Flowchart of SO-FSCL Decoding. The dashed blocks represent [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: BLER vs. approximated BLER for (512, 256) 5G polar code with different Fd values over AWGN channel, evaluated at Eb/N0 = 2.5 dB. The gray dash-dotted line represents the perfect approximation of BLER, while a greater deviation from it indicates a lower accuracy. incurs negligible loss in SO performance but also suffices to achieve compatibility with dynamic frozen bits through a look￾up table. Then, we com… view at source ↗
Figure 6
Figure 6. Figure 6: BER performance of various SO polar decoders for (512, 256) 5G [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: BLER performance of QPSK-input 4×4 MIMO iterative systems with various SO decoders for different 5G codes. The maximum number of iterative detection and decoding is set to I = 5. 4 5 6 7 8 10-4 10-3 10-2 10-1 4 5 6 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: BLER performance of QPSK-input 4 × 4 MIMO iterative systems under MAP detection and MMSE detection for different 5G polar codes. Note that for the non-iterative case (I = 1), Pyndiah’s approach share the same performance with SO-FSCL, and thus is omitted from the figure. However, since the linear estimation of the MMSE detector reduces the sensitivity of the iterative process to SO accuracy, the gain of SO… view at source ↗
Figure 9
Figure 9. Figure 9: BLER performance of (256, 121) product code and (1024, 640) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance comparison of polar product codes and other codes [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Performance comparison of polar GLDPC codes and other codes [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder of polar codes. However, the sequential decoding nature of SCL introduces high decoding latency to SO-SCL. In this paper, we incorporate node-based fast decoding into the SO-SCL framework. After addressing the challenge of soft output extraction in special node decoding, we proposed the soft-output fast SCL (SO-FSCL) decoding algorithm, along with its log-domain implementation and hardware-friendly version. The proposed SO-FSCL decoder can be regarded as an add-on extension to FSCL decoder, enabling us to autonomously choose whether to output only hard decisions like FSCL or to provide additional soft outputs. Latency and complexity analyses demonstrate that SO-FSCL can significantly reduce, for example, decoding time steps by 81.8\% (with unlimited resources), the number of additions by 41.3\%, and the number of comparisons by 46.4\%. Meanwhile, simulation results indicate that SO-FSCL delivers almost the same soft-output performance as SO-SCL, outperforming other soft-output polar decoders, especially in scenarios involving iterative decoding.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the soft-output fast successive cancellation list (SO-FSCL) decoder for polar codes by extending the node-based fast SCL (FSCL) framework to also produce soft outputs. After describing how to extract a-posteriori LLRs during special-node (rate-0, rate-1, etc.) decoding, the paper gives a log-domain implementation and a hardware-friendly variant. It claims that SO-FSCL can be used as an optional add-on to plain FSCL, that it reduces decoding time steps by 81.8 % (unlimited resources), additions by 41.3 %, and comparisons by 46.4 % relative to conventional SO-SCL, and that its soft-output error-rate performance is essentially identical to SO-SCL while outperforming other soft-output polar decoders in iterative settings.

Significance. If the complexity accounting is shown to be complete, the work would provide a practical, low-latency route to soft-output list decoding that is directly compatible with existing fast-SCL hardware. The explicit add-on design and the reported latency reductions are potentially useful for iterative receivers.

major comments (2)
  1. [§5] §5 (Latency and Complexity Analysis): the headline savings (81.8 % time steps, 41.3 % additions, 46.4 % comparisons) are obtained by comparing SO-FSCL against SO-SCL. The text must explicitly demonstrate that the extra LLR-generation operations required inside each special node for every list entry are included in the operation counts; otherwise the per-node cost scales with list size L and the stated percentage reductions cannot be guaranteed for L ≥ 8 or for codes containing many special nodes.
  2. [§6] §6 (Simulation Results): the claim that SO-FSCL delivers “almost the same soft-output performance as SO-SCL” is central to the paper’s value proposition. The section should report the exact list size, code lengths, and number of Monte-Carlo trials together with any observed FER/BER gap (or confidence intervals) so that readers can judge whether the performance loss is negligible under the same conditions used for the complexity tables.
minor comments (2)
  1. [Abstract] The abstract states the reductions “for example”; adding the precise code length, rate, and list size used for those figures would make the claim immediately verifiable.
  2. [Figures 4–6 and Algorithm 2] Figure captions and the hardware-friendly pseudocode should explicitly label which blocks are new relative to the FSCL baseline so that the incremental cost of the soft-output path is visually clear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript to improve clarity on these points.

read point-by-point responses

  1. Referee: [§5] §5 (Latency and Complexity Analysis): the headline savings (81.8 % time steps, 41.3 % additions, 46.4 % comparisons) are obtained by comparing SO-FSCL against SO-SCL. The text must explicitly demonstrate that the extra LLR-generation operations required inside each special node for every list entry are included in the operation counts; otherwise the per-node cost scales with list size L and the stated percentage reductions cannot be guaranteed for L ≥ 8 or for codes containing many special nodes.

    Authors: We thank the referee for this observation. In our complexity model for SO-FSCL, the LLR-generation operations inside each special node are performed independently for every list entry and have been included in the addition and comparison counts used to derive the reported savings. These per-list costs are part of the node-specific operation formulas that scale with L. To address the request for explicit demonstration, we will revise Section 5 to add a breakdown (including equations) showing how these operations are accounted for within the totals, confirming that the percentage reductions hold under the evaluated conditions. revision: yes

  2. Referee: [§6] §6 (Simulation Results): the claim that SO-FSCL delivers “almost the same soft-output performance as SO-SCL” is central to the paper’s value proposition. The section should report the exact list size, code lengths, and number of Monte-Carlo trials together with any observed FER/BER gap (or confidence intervals) so that readers can judge whether the performance loss is negligible under the same conditions used for the complexity tables.

    Authors: We agree that explicit reporting of these parameters strengthens the performance claims. We will revise Section 6 to state the exact list size, code lengths, and number of Monte-Carlo trials used in the simulations. We will also quantify the observed FER/BER gaps between SO-FSCL and SO-SCL (which are negligible) and include confidence intervals or variance notes to allow readers to assess the closeness of the curves under the same conditions as the complexity analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the SO-FSCL derivation.

full rationale

The paper presents SO-FSCL as an algorithmic extension to FSCL that incorporates soft-output extraction for special nodes, supported by separate latency/complexity analyses (e.g., time-step reductions) and simulation comparisons to SO-SCL. No load-bearing step reduces by construction to a self-citation, fitted parameter renamed as prediction, or self-definitional equivalence; the central claims rest on explicit modifications to the decoding tree and external empirical validation rather than internal redefinition of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work is an algorithmic engineering contribution rather than a mathematical derivation; no free parameters, new axioms, or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Standard assumptions of memoryless channels and known polar code construction used in all SCL decoding literature.
    Implicit background for any polar-code decoder performance claim.

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Reference graph

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