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arxiv: 2508.16498 · v2 · pith:7DTSKT5Onew · submitted 2025-08-22 · 💻 cs.IT · math.IT

Enhanced Successive Cancellation List Decoder for Long Polar Codes Targeting Air Interface

Jiajie Li , Sihui Shen , Warren J. Gross This is my paper

Pith reviewed 2026-05-22 12:42 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords polar codessuccessive cancellation list decodingbias-enhanced decodinggeneralized partitioned SCLmemory reductionair interfacecomputational complexity
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The pith

Bias-enhanced generalized partitioned SCL decoders match standard SCL performance with 67% less memory for long polar codes.

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

The paper develops enhanced successive cancellation list decoders for long polar codes used in air interfaces. It introduces perturbation-enhanced SCL that achieves the performance of twice the list size, then simplifies to bias-enhanced SCL. The main result is that generalized partitioned SCL with list size 8 and bias enhancement reduces memory usage by 67% compared to list size 16 while maintaining similar error correction performance. Input distribution aware decoding further cuts computational complexity by up to 5.4 times with only 0.05 dB performance loss. A theoretical analysis proves the bias shifts soft information toward valid codewords.

Core claim

The authors propose bias-enhanced (BE) generalized partitioned SCL (GPSCL) decoders with list size 8 that achieve similar decoding performance to SCL decoders with list size 16, along with a 67% reduction in memory usage. They demonstrate that an accurate bias can be generated from a reduced number of codewords, reducing overhead to n XOR gates. Input-distribution-aware decoding is applied to further reduce complexity. They also theoretically prove that the bias moves the received soft information toward valid polar codewords with high likelihood.

What carries the argument

The bias-enhanced mechanism in generalized partitioned successive cancellation list (GPSCL) decoding, which uses a simple bias addition via XOR gates to approximate the benefits of a larger decoding list.

Load-bearing premise

An accurate bias can be generated under a reduced number of codewords from the list, allowing the overhead reduction while preserving performance.

What would settle it

Measuring the bit-error-rate curves for BE GPSCL decoder with list size 8 against standard SCL with list size 16 over AWGN channel for polar code length 8192 at typical air-interface rates would test if performance remains similar.

Figures

Figures reproduced from arXiv: 2508.16498 by Jiajie Li, Sihui Shen, Warren J. Gross.

Figure 1
Figure 1. Figure 1: FERs of decoding polar codes using the perturbation- [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FERs of decoding polar codes using the PE SCL decoder w [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The average number of decoding attempts for PE and BE S [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The block diagram of the BE GPSCL decoder with the fast [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FERs of decoding polar codes using the BE GPSCL decode [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FERs of decoding polar codes using the quantized BE GP [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FERs of different ways of applying IDA decoding on the [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average list sizes (Avg. L) of the IDA decoding. TABLE V PARAMETERS FOR QUANTIZED IDA DECODING. R = 0.25 R = 0.50 R = 0.75 γ ϕ γ ϕ γ ϕ n = 4096 0.625 888 0.375 229 0.375 75 n = 8192 0.375 1123 0.375 492 0.375 168 TABLE VI MAXIMUM REDUCTIONS IN COMPUTATIONAL COMPLEXITY, WHICH IS DERIVED FROM FIG. 10 AND IS COMPARED TO THE SCL-16 DECODER. R = 0.25 R = 0.50 R = 0.75 4096 8192 4096 8192 4096 8192 BE 3.5× 3.3× … view at source ↗
Figure 9
Figure 9. Figure 9: Average list sizes (Avg. L) of the quantized IDA decoding. SCL-16 BE GPSCL-8 S = 2 T = 2 IDA BE GPSCL-8 S = 2 T = 2 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 105.00 105.50 106.00 R = 0.25 R = 0.50 R = 0.75 Eb/N0 [dB] Avg. Op. (a) n = 4096 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 105.00 105.50 106.00 106.50 R = 0.25 R = 0.50 R = 0.75 Eb/N0 [dB] (b) n = 8192 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The average number of computational complexity (Av [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FERs of decoding polar codes using the decoders with [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
read the original abstract

Polar codes are the first codes with a proven capacity-achieving capability, but their decoding faces several challenges, especially under long code lengths. In this paper, we target algorithmic improvements and analyses to enable the implementation of long polar codes (e.g., length 8K bits) by addressing key challenges in memory usage and computational complexity presented by successive cancellation list (SCL) polar decoding. Perturbation-enhanced (PE) SCL decoders with a list size of $L$ reach the decoding performance of the SCL decoder with a list size of $2L$. The proposed bias-enhanced (BE) SCL decoders, which simplify the PE SCL decoder based on insights gained by an ablation study, return similar decoding performance to PE SCL decoders. Also, proposed BE generalized partitioned SCL (GPSCL) decoders with a list size of $8$ have a $67\%$ reduction in the memory usage and similar decoding performance compared to SCL decoders with a list size of $16$, and it demonstrates that an accurate bias can be generated under a reduced number of codewords from the list and reduces the overhead from $\left(L-1\right)n$ XOR gates plus $n$ priority encoders to $n$ XOR gates, where $n$ is the code length. Furthermore, input-distribution-aware (IDA) decoding is applied to BE GPSCL decoders, which shows how an accurate bias is generated under a low-complexity decoder. Up to $5.4\times$ reduction in the computational complexity is achieved compared to SCL decoders with a list size of $16$, and negligible latency overhead is added to the decoding process. The degraded decoding performance is at most $0.05\text{ dB}$ compared to BE GPSCL decoders without IDA decoding. Lastly, we theoretically prove that the bias in the BE SCL decoder moves the received soft information toward valid polar codewords with a high likelihood, and explain the decoding performance gain.

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 / 3 minor

Summary. The manuscript proposes perturbation-enhanced (PE) SCL decoders that match the performance of standard SCL with doubled list size, then simplifies them to bias-enhanced (BE) SCL decoders via ablation study. It introduces BE generalized partitioned SCL (GPSCL) decoders for length-8192 polar codes, claiming that list size 8 yields 67% memory reduction and up to 5.4× complexity reduction versus standard SCL list size 16, with at most 0.05 dB degradation; input-distribution-aware (IDA) decoding is added for further gains. A theoretical argument is presented that the bias term steers received soft information toward valid codewords.

Significance. If substantiated, the work supplies concrete algorithmic and architectural advances that could enable practical use of long polar codes in air-interface hardware by cutting memory and gate count while preserving performance. The explicit theoretical analysis of the bias effect and the demonstration of accurate bias generation from a drastically reduced path set are strengths that go beyond pure empirical tuning.

major comments (2)
  1. [Theoretical Analysis] Theoretical proof section: the proof that bias moves soft information toward valid codewords is developed for standard BE SCL. The central GPSCL claim (67% memory reduction at L=8 with performance within 0.05 dB of L=16 SCL) rests on the same bias remaining accurate when generated from a partitioned list using only n XOR gates. No explicit extension of the proof steps to the partitioned recursion or the reduced bias unit is supplied; small accumulated bias errors over 8192 bits could undermine the claimed equivalence.
  2. [GPSCL Architecture] § on GPSCL architecture and bias unit: the overhead reduction from (L-1)n XOR gates plus n priority encoders to n XOR gates is justified by the assumption that an accurate bias can still be produced from the reduced number of codewords. This assumption is load-bearing for both the memory and complexity claims yet receives only empirical support; a formal argument or counter-example analysis for the partitioned case is required.
minor comments (3)
  1. [Simulation Results] Figure captions and axis labels for the BER curves should explicitly state the code length, rate, and channel model used; current presentation makes direct comparison to prior SCL results difficult.
  2. [Ablation Study] The ablation study that motivates the simplification from PE SCL to BE SCL is referenced but not shown in detail; including the key table or figure would strengthen the justification for the bias-only design.
  3. [Notation] Notation for the bias term and the partitioned LLR update equations should be unified across sections to avoid ambiguity when the simplified n-XOR unit is introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential impact of our work on enabling practical implementations of long polar codes. We address the two major comments point by point below and will incorporate revisions to strengthen the theoretical justification and architectural analysis.

read point-by-point responses

  1. Referee: [Theoretical Analysis] Theoretical proof section: the proof that bias moves soft information toward valid codewords is developed for standard BE SCL. The central GPSCL claim (67% memory reduction at L=8 with performance within 0.05 dB of L=16 SCL) rests on the same bias remaining accurate when generated from a partitioned list using only n XOR gates. No explicit extension of the proof steps to the partitioned recursion or the reduced bias unit is supplied; small accumulated bias errors over 8192 bits could undermine the claimed equivalence.

    Authors: We agree that the proof is developed for the standard BE SCL decoder and that an explicit extension to the GPSCL case would strengthen the manuscript. The core argument shows that the bias term adjusts path metrics to favor valid codewords by leveraging the recursive structure of polar codes. For GPSCL, the bias is still computed from the highest-likelihood paths retained after partitioning, and our simulations for length-8192 codes confirm that performance remains within 0.05 dB. In the revision we will add a short subsection that sketches the extension: because partitioning preserves the dominant paths at each recursion level and the bias unit aggregates LLRs via XOR operations on these paths, the steering effect toward valid codewords is retained with bounded error accumulation, as the early-stage path selection in polar decoding limits propagation of small inaccuracies. revision: yes

  2. Referee: [GPSCL Architecture] § on GPSCL architecture and bias unit: the overhead reduction from (L-1)n XOR gates plus n priority encoders to n XOR gates is justified by the assumption that an accurate bias can still be produced from the reduced number of codewords. This assumption is load-bearing for both the memory and complexity claims yet receives only empirical support; a formal argument or counter-example analysis for the partitioned case is required.

    Authors: The referee correctly notes that the complexity and memory claims depend on the accuracy of the bias generated from the reduced path set. The manuscript supports this via extensive simulations showing that the n-XOR bias unit produces an effective bias for L=8 GPSCL. To provide the requested formal support, the revised manuscript will include a brief analytical argument: the generalized partitioning recursively decomposes the code such that the retained paths at each stage are the most probable ones under the channel, and the simplified bias computation using only n XOR gates approximates the full-list bias sufficiently closely because polar code construction concentrates reliability in specific bit positions. We will also add a short discussion of why counter-examples (e.g., pathological path omissions) do not occur for the standard polar constructions and code lengths considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper introduces BE SCL and GPSCL decoder variants with a claimed theoretical proof that bias shifts received soft information toward valid polar codewords, plus empirical claims of 67% memory reduction at L=8 with performance within 0.05 dB of L=16 SCL. The proof is presented as an independent analysis of the bias mechanism rather than a quantity fitted from or defined by the same simulation data used to tune the bias generator. No equations reduce the performance or complexity gains to tautological redefinitions of inputs, and the reduced bias unit (n XOR gates) is justified by explicit architectural simplification rather than by construction from the target result. Self-citations are not load-bearing for the central claims, and the derivation remains externally falsifiable via simulation benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claims rest on standard properties of polar codes and SCL decoding plus the new bias construction; no free parameters are explicitly fitted in the abstract, and no new physical entities are postulated.

axioms (1)
  • domain assumption Standard successive cancellation list decoding properties for polar codes hold under the proposed perturbations and partitioning.
    Invoked when claiming that PE and BE variants reach the performance of larger-list SCL.
invented entities (1)
  • bias term in BE SCL no independent evidence
    purpose: To steer received soft information toward valid codewords and simplify the perturbation-enhanced decoder.
    Introduced as a simplification of PE SCL; the paper provides a theoretical argument but no independent falsifiable prediction outside the decoder itself.

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