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arxiv: 2604.16709 · v1 · submitted 2026-04-17 · 📡 eess.SP

A Universal Systematic Method to Generate Error Patterns on Memoryless Channels

Marwan Jalaleddine , Jiajie Li , Syed Mohsin Abbas , Warren J. Gross This is my paper

Pith reviewed 2026-05-10 07:26 UTC · model grok-4.3

classification 📡 eess.SP
keywords error pattern generationmemoryless channelsGRANDOSDPOSDmaximum-likelihood decodingAWGNRayleigh fading
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0 comments X

The pith

Error patterns generated once from a memoryless channel's PDF can be reused on any future received vector without retuning for code or SNR.

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

The paper introduces a systematic procedure that draws a finite list of error patterns directly from the probability density function of any memoryless channel. These patterns are then fed into existing decoders such as GRAND, OSD and POSD to guess the noise that affected a received signal. A sympathetic reader would care because prior pattern lists had to be rebuilt by hand for each new channel, SNR or code, which limited how easily high-performance decoding could be deployed in practice.

Core claim

The authors claim that their PDF-derived error pattern set, when substituted into GRAND, OSD or POSD, produces decoding performance that matches or exceeds the performance obtained with currently used pre-generated lists on AWGN channels, Gaussian-mixture channels, Rayleigh fading channels with perfect CSI, and Rayleigh fading channels without perfect CSI.

What carries the argument

A one-time generation step that ranks candidate error patterns by their probability under the channel PDF and retains the highest-probability subset as a reusable list.

Load-bearing premise

A finite set of error patterns derived once from the channel PDF remains effective for every future received vector and does not need re-tuning when the code or SNR changes.

What would settle it

A simulation in which the PDF-derived patterns produce a visibly higher block-error rate than code-and-SNR-specific patterns on the same channel and code at the same SNR.

Figures

Figures reproduced from arXiv: 2604.16709 by Jiajie Li, Marwan Jalaleddine, Syed Mohsin Abbas, Warren J. Gross.

Figure 1
Figure 1. Figure 1: Time needed to generate TEPs with Monte-Carlo Simulations and our proposed method as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The steps followed to generate the EW error patterns in an AWGN channel. [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of decoding performance of different sets of TEPs with GRAND, POSD and OSD on an AWGN channel. Straight lines represent 654 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Percentage of overlap of the pre-generated test error patterns (TEPs) with EW TEPs for GRAND, POSD, and OSD over an AWGN channel. [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The distribution of the PDF of the transmitted [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The LLR value as a function of the received signal. [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Decoding performance of the TEPs on custom mixture of Gaussian channels. [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Percentage of the overlap of the TEPs generated by SOTA methods with the EW error patterns with a mixture of Gaussian distribution channels. [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of decoding performance of different error patterns with GRAND, POSD and OSD on a Rayleigh fading channel with perfect knowledge 654 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of decoding performance of different error patterns with GRAND, OSD and POSD on a Rayleigh fading channel with no perfect 654 [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Percentage of overlap of the EW error patterns generated on an AWGN channel with different decoders and types of fading channels. EW error [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
read the original abstract

The high computational cost of approaching the performance of Maximum-likelihood (ML) decoding has limited its practical use for decades. Because the complexity grows exponentially with the message length, researchers have spent years developing algorithms like Ordered Statistics Decoding (OSD), Partial Ordered Statistics Decoding (POSD) and Guessing Random Additive Noise decoding (GRAND) which try to approach ML performance. OSD, POSD and GRAND work by trying to guess the error patterns affecting the received signals. However, there does not exist a systematic method to extend the error pattern guesses to novel channels. This work introduces a systematic method that uses the Probability Density Function (PDF) of a memoryless channel to generate a set of error patterns that can be applied on any future received signal on this channel. Simulation results show that our proposed method applied on GRAND, OSD and POSD generally matches or outperforms current pre-generated error patterns on additive white Gaussian noise (AWGN) channel, mixture of Gaussian distribution channels, Rayleigh fading channel with perfect knowledge of Channel State Information (CSI) and Rayleigh fading channel with no perfect knowledge of Channel State Information (NCSI).

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

3 major / 1 minor

Summary. The manuscript proposes a systematic method that derives a finite set of error patterns directly from the probability density function (PDF) of any memoryless channel; this fixed set is then asserted to be usable for every future received vector on that channel inside GRAND, OSD, and POSD decoders. Simulations on AWGN, Gaussian-mixture, and Rayleigh-fading channels (with and without CSI) are reported to show that the resulting decoders generally match or exceed the performance obtained with existing pre-generated error-pattern lists.

Significance. If the method can be shown to produce a channel-specific but code- and SNR-independent pattern list that reliably approaches ML performance, it would remove a long-standing practical barrier to deploying GRAND/OSD-style decoders on non-standard memoryless channels. The core idea of a PDF-driven, one-time pattern generation step is conceptually attractive and could be adopted by other ordered-search or guessing decoders.

major comments (3)
  1. [Abstract] Abstract: the central performance claim is stated only qualitatively (“generally matches or outperforms”) with no numerical BER/BLER values, no error-bar information, no table or figure reference, and no explicit baseline description. Because the empirical support is the sole evidence offered for the method’s utility, this absence makes the claim unverifiable from the given text.
  2. [Method] Method description (assumed Section 3 or 4): the procedure that converts the continuous channel PDF into a finite, ordered list of error patterns is not specified. In particular, the discretization rule, the stopping criterion for list size, and whether the list depends on SNR or code parameters are missing; without these steps the “universal” and “generated once” assertions cannot be evaluated.
  3. [Simulations] Simulation results (assumed Section 5): no experiments are described that test whether the same fixed pattern list remains effective when the underlying code (rate, length, minimum distance) or the operating SNR is changed. The universality claim requires precisely this invariance; its absence is load-bearing for the paper’s main contribution.
minor comments (1)
  1. [Abstract] The abstract lists four channels but does not state the exact SNR ranges, code parameters, or list sizes used; adding these details would improve reproducibility even before the quantitative tables are supplied.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback. We will revise the manuscript to address the concerns raised regarding the abstract, method description, and simulation results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central performance claim is stated only qualitatively (“generally matches or outperforms”) with no numerical BER/BLER values, no error-bar information, no table or figure reference, and no explicit baseline description. Because the empirical support is the sole evidence offered for the method’s utility, this absence makes the claim unverifiable from the given text.

    Authors: We agree with the referee that the abstract would be strengthened by including quantitative details. In the revised manuscript, we will incorporate specific BER/BLER values from our simulations, mention error bars where applicable, reference the corresponding figures and tables, and briefly describe the baseline methods used. This will allow readers to verify the performance claims directly from the abstract. revision: yes

  2. Referee: [Method] Method description (assumed Section 3 or 4): the procedure that converts the continuous channel PDF into a finite, ordered list of error patterns is not specified. In particular, the discretization rule, the stopping criterion for list size, and whether the list depends on SNR or code parameters are missing; without these steps the “universal” and “generated once” assertions cannot be evaluated.

    Authors: The conversion procedure is outlined in Section 3, where the PDF is discretized over a finite error space to compute pattern probabilities, which are then sorted in decreasing order. The list size is determined by a cumulative probability threshold to ensure coverage of likely errors. This process is independent of SNR and code parameters, relying only on the channel PDF. We will enhance the description with explicit steps, including the discretization method and stopping criterion, and provide pseudocode for clarity in the revised version. revision: yes

  3. Referee: [Simulations] Simulation results (assumed Section 5): no experiments are described that test whether the same fixed pattern list remains effective when the underlying code (rate, length, minimum distance) or the operating SNR is changed. The universality claim requires precisely this invariance; its absence is load-bearing for the paper’s main contribution.

    Authors: Our current simulations focus on demonstrating the method across diverse channel models, but we recognize the value of explicitly testing the list's invariance. The method's design ensures the error patterns are generated solely from the channel PDF, making them independent of code parameters and SNR. To provide empirical validation, we will add new simulation results in the revised manuscript that apply the same fixed list to different code lengths, rates, minimum distances, and across varying SNRs for the same channel. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation from channel PDF is independent

full rationale

The paper introduces a systematic generation of a finite error-pattern set directly from the memoryless channel PDF, then applies that fixed set to GRAND/OSD/POSD without re-derivation. No equations, fitted parameters, or self-citations are shown that would make the reported performance or universality reduce to the inputs by construction. The method is presented as a one-time PDF-based procedure whose effectiveness is validated externally via simulation on specific channels; the central claim does not tautologically rest on renaming its own outputs or on load-bearing self-citations. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the channel PDF alone is sufficient to produce a high-quality finite error-pattern list without additional fitted parameters or channel-specific heuristics.

axioms (1)
  • domain assumption A finite set of error patterns derived from the channel PDF will contain the most probable errors for any received vector on that channel.
    Invoked when the method is said to generate patterns that can be applied to any future received signal.

pith-pipeline@v0.9.0 · 5500 in / 1283 out tokens · 30883 ms · 2026-05-10T07:26:42.600980+00:00 · methodology

discussion (0)

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