Pith. sign in

REVIEW 3 major objections 5 minor 60 references

The paper claims METTLE is the first erasure code that simultaneously achieves high coding efficiency, low coding complexity, and low decoding latency.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 02:35 UTC pith:HLLJTLST

load-bearing objection A clever streaming-code construction whose central efficiency claim currently rests on a nonstandard failure metric and omitted density evolution. the 3 major comments →

arxiv 2602.10020 v2 pith:HLLJTLST submitted 2026-02-10 cs.IT math.IT

METTLE: Efficient Streaming Erasure Code with Peeling Decodability

Qianru Yu , Tianji Yang , Jingfan Meng , Jun Xu (Jim) This is my paper
classification cs.IT math.IT MSC 94B3568P30
keywords streaming erasure codespeeling decoderspatial couplingmulti-edge typelow-density generator-matrix codesforward error correctionlatency-efficiency trade-offburst erasure channels
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims to solve a long-standing open problem: designing one erasure code that is highly coding-efficient, cheap to encode and decode, and natively streaming with low decoding latency. It proposes METTLE, which adapts a spatially coupled hashing data structure into a blockless code whose decoder peels packets from left to right as they arrive. If the claim holds, METTLE decodes 47.7 to 84.6 times faster than the RaptorQ benchmark while staying within a few percent of its coding efficiency, and keeps average decoding latency between 37 and 199 packets across ten channel models. The paper reports this as the first code to meet all three requirements at once.

Core claim

METTLE is a spatially coupled, multi-edge type LDGM code: each source packet is XORed into a small number of bins within a time-coupling window of width w=600, and the first edge of every packet is deterministic, landing on a unique bin so that no two leading edges collide. The remaining edges follow exponentially decaying binomial distributions (parameters 1/2, 1/4, 1/8), which the paper says make the left boundary sparsely populated and easy to peel. Because each packet is represented by a leading edge that can be released immediately, the decoder peels progressively from left to right, giving average latencies of tens to a couple hundred packets. The paper reports overhead ratios of 5.5%

What carries the argument

The central mechanism is a hashing-generated Tanner graph with three ingredients: time coupling (each packet is treated as a ball thrown into l bins inside a sliding window instead of a whole block), a touch-less leading edge (TLE, the first edge is deterministic and injective, so it never collides with another packet's first edge), and multi-edge type (MET, the remaining edges are drawn from binomial distributions with halving means). The TLE guarantees immediate release and left-to-right peeling; the MET distribution shapes the graph so that the left 'coast' is sparse enough to start the peeling wave; and a tail-compression technique halves the spatial-coupling termination loss from (1+c)w

Load-bearing premise

The central claim depends on the peeling decoder actually succeeding with probability at least 0.999 at the reported overhead ratios on all ten channels; the paper supports this with 1000-run Monte Carlo simulations, while the density-evolution equations that would analytically validate the chosen edge distributions are explicitly omitted (Part I Section II.C.2; Part II Section 3.4).

What would settle it

Run the documented construction with the same parameters (l=4, w=600, binomial parameters 1/2, 1/4, 1/8, tail compression) on a BEC(0.1) channel with 10^5 source packets and measure failure probability at overhead 0.25; if more than 0.1% of runs fail, or if an independent density-evolution recursion predicts a threshold above 0.1 erasure rate at that overhead, the reported operating point does not hold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • METTLE delivers average decoding latency of 37 to 199 packets across ten channels, enabling interactive applications that cannot tolerate block-level delay.
  • METTLE is 47.7 to 84.6 times faster to decode than RaptorQ at comparable latency, and the gap grows superlinearly as RaptorQ's block size increases.
  • Coding overhead stays within a few percent of RaptorQ on most tested channels, and METTLE beats RaptorQ on the most bursty channels, while far outperforming LT codes.
  • METTLE can adjust its overhead ratio on the fly and has a systematic variant at no efficiency cost, making it suitable for one-to-many streaming and feedback-limited links.

Where Pith is reading between the lines

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

  • If the simulated thresholds survive independent scrutiny, METTLE-type schemes could replace Reed-Solomon-based streaming codes in interactive video, cloud gaming, and telesurgery, because low latency no longer forces a small block size.
  • The touch-less leading edge idea is the most transferable piece: making one edge deterministic and collision-free could be applied to other peeling-based data structures to impose ordered decodability without sacrificing randomness.
  • The paper explicitly omits the density-evolution equations that would analytically justify the parameter choices (Part I Section II.C.2; Part II Section 3.4), so the reported thresholds currently rest on Monte Carlo evidence; an independent asymptotic analysis would determine whether they are true thresholds or finite-size artifacts.
  • At 10% erasure, the per-symbol error floor of about 10^-4 (epsilon^l with l=4) means isolated undecodable packets remain, so applications targeting strict all-symbol recovery would need retransmission or looser success criteria.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes METTLE, a streaming erasure code constructed as a spatially/temporally coupled multi-edge-type LDGM code with a deterministic 'touchless leading edge' (TLE). It claims to be the first code to simultaneously provide (1) high coding efficiency, (2) low coding complexity, and (3) low decoding latency. Part I reports overhead ratios needed to reach a 10^-3 failure probability on five BEC and five Gilbert-Elliott channels, average decoding latencies of 37–199 packets, and decoding speeds 47.7–84.6× faster than RaptorQ configured with a small source block. Part II provides the conceptual derivation from IBLT and Walzer's scheme, describes the MET and TLE modifications, and presents a separate Monte Carlo evaluation. The central evidence is simulation-based; the density-evolution analysis that justifies the key parameter choices is mentioned but not written down.

Significance. If the claims are validated, the paper would describe a practically valuable design: O(1) per-symbol encoding/decoding, decoding latency of tens to hundreds of packets independent of source-block size, overhead competitive with RaptorQ at small source blocks, and resilience to bursty GE channels. The hashing-based implicit Tanner graph, the systematic variant, and continuous rate adaptation are also attractive systems properties. The simulation study covers a broad set of channels and the scheme is described in enough detail to be reimplemented. However, the validation currently rests on two load-bearing gaps: the success metric excludes an error-floor class of undecodable symbols, and the density-evolution analysis used to tune the MET distribution and window size w=600 is omitted. These gaps prevent the accepted 'first erasure code to meet all three requirements' claim from being supported as stated.

major comments (3)
  1. [Part I §III.C, §III.E; Part II §4.1] The failure definitions are inconsistent and the error floor undermines Table IV under the standard all-symbols-recovery criterion. §III.E states that a ball is undecodable when all l=4 bins containing it are erased (probability ε^4) and that such isolated balls are not counted as decoding failures. For n=10^5, the expected number is nε^4 (≈0.016 at ε=0.02, ≈4.1 at ε=0.08, ≈10 at ε=0.1), and the probability of at least one such loss is ≈1−exp(−nε^4), already ~1.6×10^-2 at ε=0.02. This floor is independent of c, so no overhead in Table IV can meet the stated 10^-3 failure probability if 'success' means recovering all source packets, which is the criterion used in Part II §4.1 and in the RaptorQ comparison. The abstract's central claim is therefore not supported under the standard definition.
  2. [Part I §II.C.2; Part II §3.4] The paper justifies the key parameters—w=600, the MET Binomial(1/2,1/4,1/8) edge distributions, and the tail-compression factor—by 'numerical DE computations, verified by simulations,' but the density-evolution equations are omitted in both parts. Because the same simulation pipeline was used both to select these parameters and to report the overhead thresholds, the Table IV efficiency numbers are not independently derivable from the manuscript, and the risk of in-sample tuning cannot be assessed. The DE recursion, the threshold computation, and the parameter-search procedure should be included, or a public implementation/solver should be referenced.
  3. [Part I §III.C; Part II §4.1] The Monte Carlo evidence is insufficient to establish the claimed 10^-3 failure thresholds. Part II states that each data point uses 1000 independent runs; at that sample size, observing zero failures gives a one-sided 95% upper bound of about 3.7×10^-3, so a failure probability of 10^-3 cannot be distinguished from one several times larger. The paper reports overhead values as thresholds without confidence intervals, and Part I does not state the number of runs. The efficiency comparison to RaptorQ should be accompanied by either many more runs near the threshold or explicit confidence intervals.
minor comments (5)
  1. [Part I Table II vs Part II Table 3] The reported average latency for BEC(0.01) differs (61 packets in Part I, 57 in Part II). Clarify whether this is due to updated overhead accounting, tail compression, or different simulation settings.
  2. [Part I Introduction vs Part II Section 1.2] Part I says LT coding efficiency matches METTLE only at k≈500,000, while Part II says the equivalent LT block size is 4×10^4. Reconcile or explain the different conditions.
  3. [References] Reference [16] is a website ('Selected publications') rather than a citable archival paper; it is used for the tail-compression technique and the systematic variant. These details should be self-contained or cited to a stable technical report.
  4. [Part I §III.B and §III.C] The text says 'the same parameter settings are used across all three evaluations,' but the overhead ratio c varies by channel in Table IV; clarify that the structural parameters (l, w, MET distributions) are fixed while c is channel-dependent.
  5. [Part II Table 1] The row for Videoconferencing-heavy reads '0.05 0.5 7.81%' and appears to be missing the ϵ_g and ϵ_b entries that are present in Part I Table I; fix the table formatting.

Circularity Check

1 steps flagged

METTLE's reported 10^-3 failure probability and efficiency comparison are self-definitional: the failure event is defined to exclude the irreducible LDGM error floor, which by the paper's own calculation already exceeds the target at all tested erasure rates.

specific steps
  1. self definitional [Part I §III.C (Coding efficiency comparison) and §III.E (Error-floor events); Part II §4.1]
    "A METTLE decoding failure refers to the situation that the number of erasures is large enough to cause the leftward peeling process to stall somewhere along a “mega-codeword” of size N = 10^5(1+c) packets ... except for an isolated few that may “hit the error floor” ... For obvious reasons ... we do not count such isolated undecodable balls as decoding failures."

    The target “decoding failure probability of 10^-3” that defines METTLE's reported overhead ratios (Table IV) is defined to exclude error-floor events. But §III.E states that a ball is undecodable when all l=4 bins containing it are erased, with probability ε^4, and that this “cannot be reduced by increasing c”; at ε=0.1 there are on average 10 permanently lost balls per 10^5-block. Hence the standard all-symbol failure probability is 1−exp(−nε^4), which is >10^-3 for every ε≥0.02 and ~1 at ε=0.1, independent of c. Thus the claimed 10^-3 target is reached only because the failure definition excludes exactly the failures overhead cannot cure. Part II §4.1 uses the opposite all-symbols criterion (“A run counts as successful only if all n=10^5 source packets are successfully decoded”), confirm

full rationale

The non-circular core of the paper is the METTLE construction itself: time-coupling of Walzer's spatially coupled IBLT, the TLE deterministic first edge, and the multi-edge binomial distributions are real design elements, and the peeling decoder's low complexity and streaming latency are supported by direct simulation rather than by a self-citation chain. The self-citations ([1], [16]) are not load-bearing for the central construction: the tail compression is also described and tested in Part II, and the systematic-variant claim is peripheral. The omitted density-evolution equations are an evidentiary gap, not a circular reduction, and the tuning of w=600 and the MET parameters by the same simulation pipeline is a validation concern rather than a demonstrated equation-level circularity. The demonstrated circularity is the self-definitional success metric: the paper's headline efficiency numbers and the “first erasure code to meet all three requirements” claim depend on a failure definition that excludes the error-floor losses which, by the paper's own analysis, dominate the all-symbol failure probability at every channel setting used. This makes the central efficiency claim partially circular by construction, though the underlying code still has independent structural content.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central performance claims rest on simulation with hand-picked structural parameters (w, l, MET Binomial parameters) and an omitted density-evolution analysis; no code or data is released. TLE and MET are design techniques, not independently evidenced physical entities.

free parameters (5)
  • coupling window size w = 600
    Chosen empirically from w∈[400,1000] to balance coding efficiency and decoding latency (Part I Section III.B; Part II Section 4.1.3).
  • number of edges l = 4
    Set to 4 (one TLE + three MET edges); the paper says l is 'typically between 3 and 5' but gives no derivation of the value.
  • MET edge Binomial parameters (p2,p3,p4) = (1/2, 1/4, 1/8)
    Optimized via numerical density evolution that is not shown; these distributions control the claimed efficiency and are central to performance (Part I Section II.C.2; Part II Section 4.1.3).
  • tail compression factor = linear from 1 to 2 over last w balls
    Heuristic to halve tail loss; the paper states it is confirmed by evaluation but provides no analysis (Part II Section 4.2.1).
  • error-floor exclusion = epsilon^l per-symbol floor excluded from failures
    Isolated undecodable balls with probability ε^l are 'not counted as decoding failures,' which relaxes the stated 10^-3 failure target at high erasure (Part I Section III.E).
axioms (5)
  • standard math Hash functions are independent and uniform over their specified ranges, and the Tanner graph is random enough for peeling threshold behavior.
    Assumed throughout the scheme description (Part I Section II.A; Part II Section 2.1); standard in hashing-based codes but not verified for this specific construction.
  • domain assumption Density evolution accurately predicts finite-n simulation thresholds for this MET-LDGM ensemble.
    The paper relies on this to claim the chosen MET parameters are near-optimal, but the DE equations are omitted (Part II Section 3.4).
  • domain assumption The Gilbert-Elliott channel parameters taken from [9],[27],[28] are representative of real VoIP/WiMAX/videoconferencing erasure processes.
    Used to benchmark METTLE against realistic bursty channels (Part I Section III.A).
  • domain assumption The libRaptorQ implementation timing is representative of RaptorQ decoding speed.
    All RaptorQ decoding-time claims depend on this single C++ implementation and workstation (Part I Section III.D).
  • domain assumption Simulations with n=10^5 source packets and 1000 runs accurately approximate the asymptotic failure probability and latency.
    The evaluation uses n=10^5, and the paper asserts this is large enough to demonstrate the claimed thresholds (Part II Section 4.1).

pith-pipeline@v1.3.0-alltime-deepseek · 34865 in / 11558 out tokens · 112283 ms · 2026-08-03T02:35:29.958650+00:00 · methodology

0 comments
read the original abstract

In this work, we solve a long-standing open problem in coding theory with broad applications in networking and systems: designing an erasure code that simultaneously satisfies three requirements: (1) high coding efficiency, (2) low coding complexity, and (3) being a streaming code (defined as one with low decoding latency). We propose METTLE (Multi-Edge Type with Touch-less Leading Edge), the first erasure code to meet all three requirements. Compared to "streaming RaptorQ" (RaptorQ configured with a small source block size to ensure a low decoding latency), METTLE is only slightly worse in coding efficiency, but 47.7 to 84.6 times faster to decode.

Figures

Figures reproduced from arXiv: 2602.10020 by Jingfan Meng, Jun Xu (Jim), Qianru Yu, Tianji Yang.

Figure 1
Figure 1. Figure 1: Spatial coupling in Walzer’s scheme. As such, spatial coupling (SC) takes a very different form in SC-LDPC than in METTLE (and Walzer’s scheme). In SC-LDPC, coupling occurs between nearby variable and check vertices in a protograph, where each [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of MET coupling. The name MET comes from the following fact: since these l edges now have distinct (landing position) distri￾butions, they have different types in the density evolution (DE) analysis (not shown here in the interest of space). The final landing-position distributions, optimized (for coding efficiency) via numerical DE computations, verified by simulations, and adopted in METTLE … view at source ↗
Figure 1
Figure 1. Figure 1: Walzer’s Scheme. For each position 𝑝𝑥 ∈ 𝑃 = [0, 𝑛), select 𝑙 = 3 incident nodes (bins) independently and uniformly at random from the range [(1 + 𝑐)𝑝𝑥, (1 + 𝑐) (𝑝𝑥 + 𝑤)). During peeling decoding, the “west” and “east” coasts erode inward from both ends at each iteration. In other words, the decoding front advances from both sparse-degree ends toward “inland”, peeling the unrecovered region layer by layer. … view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of MET coupling: a source symbol at [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fraction of symbols undecoded (FSU) and failure probability vs. overhead under BEC. [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fraction of symbols undecoded (FSU) and failure probability vs. overhead under bursty channels. [PITH_FULL_IMAGE:figures/full_fig_p027_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Girth Distribution in METTLE. and perform breadth-first search (BFS) from one endpoint to determine the shortest cycle length containing that edge [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 5 canonical work pages

  1. [1]

    Bentaleb Abdelhak. 2024. Unifying real-time communications and content delivery with media-over-QUIC transport. https://events.vtools.ieee.org/m/406337

    2024

  2. [2]

    Laith Al-Jobouri, Martin Fleury, and Mohammed Ghanbari. 2013. Intra-Refresh Provision for WiMAX Data-Partitioned Video Streaming. Consumer Electronics Times 2, 3 (2013), 137–145

    2013

  3. [3]

    Congkai An, Huanhuan Zhang, Shibo Wang, Jingyang Kang, Anfu Zhou, Liang Liu, Huadong Ma, Zili Meng, Delei Ma, Yusheng Dong, and Xiaogang Lei. 2025. Tooth: toward optimal balance of video QoE and redundancy cost by fine-grained FEC in cloud gaming streaming. In Proceedings of the 22nd USENIX Symposium on Networked Systems Design and Implementation (Philade...

    2025

  4. [4]

    Ahmed Badr, Ashish Khisti, Wai-Tian Tan, and John Apostolopoulos. 2013. Streaming codes for channels with burst and isolated erasures. In 2013 Proceedings IEEE INFOCOM . IEEE, Turin, Italy, 2850–2858. https://doi.org/10.1109/ INFCOM.2013.6567095

    arXiv 2013

  5. [5]

    Ahmed Badr, Ashish Khisti, Wai-tian Tan, Xiaoqing Zhu, and John Apostolopoulos. 2017. FEC for VoIP using dual-delay streaming codes. In IEEE INFOCOM 2017 - IEEE Conference on Computer Communications . IEEE, Atlanta, GA, USA, 1–9. https://doi.org/10.1109/INFOCOM.2017.8057027

    arXiv 2017

  6. [6]

    Ahmed Badr, Pratik Patil, Ashish Khisti, Wai-Tian Tan, and John Apostolopoulos. 2016. Layered constructions for low-delay streaming codes. IEEE Transactions on Information Theory 63, 1 (2016), 111–141. METTLE: Native Streaming Code with Peeling Decodability 21

    2016

  7. [7]

    Netflix Technology Blog. 2023. All of Netflix’s HDR video streaming is now dynamically optimized. https:// netflixtechblog.com/all-of-netflixs-hdr-video-streaming-is-now-dynamically-optimized-e9e0cb15f2ba

    2023

  8. [8]

    Burton H. Bloom. 1970. Space/time trade-offs in hash coding with allowable errors. Commun. ACM 13, 7 (July 1970), 422–426. https://doi.org/10.1145/362686.362692

    arXiv 1970

  9. [9]

    Bogino, Pasquale Cataldi, Marco Grangetto, Enrico Magli, and Gabriella Olmo

    Mattia C.O. Bogino, Pasquale Cataldi, Marco Grangetto, Enrico Magli, and Gabriella Olmo. 2007. Sliding-Window Digital Fountain Codes for Streaming of Multimedia Contents. In 2007 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, New Orleans, LA, USA, 3467–3470. https://doi.org/10.1109/ISCAS.2007.378373

    arXiv 2007

  10. [10]

    Byers, Michael Luby, Michael Mitzenmacher, and Ashutosh Rege

    John W. Byers, Michael Luby, Michael Mitzenmacher, and Ashutosh Rege. 1998. A digital fountain approach to reliable distribution of bulk data. ACM SIGCOMM Computer Communication Review 28, 4 (1998), 56–67. Publisher: ACM New York, NY, USA

    1998

  11. [11]

    Pasquale Cataldi, Marco Grangetto, Tammam Tillo, Enrico Magli, and Gabriella Olmo. 2010. Sliding-Window Raptor Codes for Efficient Scalable Wireless Video Broadcasting With Unequal Loss Protection. IEEE Transactions on Image Processing 19, 6 (June 2010), 1491–1503

    2010

  12. [12]

    Daniel J

    Jr. Daniel J. Costello, Min Zhu, David G. M. Mitchell, and Michael Lentmaier. 2025. High-Rate Spatially Coupled LDPC Codes Based on Massey’s Convolutional Self-Orthogonal Codes. arXiv:2502.03774 [cs.IT] https://arxiv.org/abs/2502. 03774

    Pith/arXiv arXiv 2025

  13. [13]

    Frederic Didier. 2009. Efficient erasure decoding of Reed-Solomon codes. arXiv:0901.1886 [cs.IT] https://arxiv.org/ abs/0901.1886

    Pith/arXiv arXiv 2009

  14. [14]

    Martin Dietzfelbinger and Stefan Walzer. 2019. Dense Peelable Random Uniform Hypergraphs. arXiv:1907.04749 [cs.DS] https://arxiv.org/abs/1907.04749

    Pith/arXiv arXiv 2019

  15. [15]

    Yevgeniy Dodis, Leonid Reyzin, and Adam Smith. 2004. Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data. In Advances in Cryptology - EUROCRYPT 2004 , Christian Cachin and Jan L. Camenisch (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 523–540

    2004

  16. [16]

    Fong, and Ashish Khisti

    Elad Domanovitz, Silas L. Fong, and Ashish Khisti. 2022. An Explicit Rate-Optimal Streaming Code for Channels With Burst and Arbitrary Erasures. IEEE Transactions on Information Theory 68, 1 (2022), 47–65. https://doi.org/10.1109/ TIT.2021.3121101

    arXiv 2022

  17. [17]

    Edwin O Elliott. 1963. Estimates of error rates for codes on burst-noise channels. The Bell System Technical Journal 42, 5 (1963), 1977–1997

    1963

  18. [18]

    Goodrich, Frank Uyeda, and George Varghese

    David Eppstein, Michael T. Goodrich, Frank Uyeda, and George Varghese. 2011. What’s the difference? efficient set reconciliation without prior context. SIGCOMM Comput. Commun. Rev. 41, 4 (Aug. 2011), 218–229. https: //doi.org/10.1145/2043164.2018462

    arXiv 2011

  19. [19]

    A Jimenez Felstrom and Kamil Sh Zigangirov. 1999. Time-varying periodic convolutional codes with low-density parity-check matrix. IEEE Transactions on Information Theory 45, 6 (1999), 2181–2191

    1999

  20. [20]

    G Forney. 1971. Burst-correcting codes for the classic bursty channel. IEEE Transactions on Communication Technology 19, 5 (1971), 772–781

    1971

  21. [21]

    Gallager

    R. Gallager. 1962. Low-density parity-check codes. IRE Transactions on Information Theory 8, 1 (1962), 21–28. https://doi.org/10.1109/TIT.1962.1057683

    arXiv 1962

  22. [22]

    Goodrich and Michael Mitzenmacher

    Michael T. Goodrich and Michael Mitzenmacher. 2011. Invertible bloom lookup tables. In 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton) . IEEE, Monticello, IL, USA, 792–799. https://doi.org/ 10.1109/Allerton.2011.6120248

    arXiv 2011

  23. [23]

    Saqib Hakak, Thippa Reddy Gadekallu, Praveen Kumar Reddy Maddikunta, Swarna Priya Ramu, Parimala M, Chamitha De Alwis, and Madhusanka Liyanage. 2023. Autonomous vehicles in 5G and beyond: A survey. Vehicular Communica- tions 39 (2023), 100551. https://doi.org/10.1016/j.vehcom.2022.100551

    arXiv 2023

  24. [24]

    Hemani Kaushal and Georges Kaddoum. 2016. Underwater Optical Wireless Communication. IEEE Access 4 (2016), 1518–1547. https://doi.org/10.1109/ACCESS.2016.2552538

    arXiv 2016

  25. [25]

    Tomer Keniagin, Eitan Yaakobi, and Ori Rottenstreich. 2025. CertainSync: Rateless Set Reconciliation with Certainty. Proc. ACM Meas. Anal. Comput. Syst. 9, 2, Article 18 (June 2025), 33 pages. https://doi.org/10.1145/3727110

    work page doi:10.1145/3727110 2025

  26. [26]

    Krzakala, M

    F. Krzakala, M. Mézard, F. Sausset, Y. F. Sun, and L. Zdeborová. 2012. Statistical-Physics-Based Reconstruction in Compressed Sensing. Phys. Rev. X 2 (May 2012), 021005. Issue 2. https://doi.org/10.1103/PhysRevX.2.021005

    work page doi:10.1103/physrevx.2.021005 2012

  27. [27]

    Shrinivas Kudekar, Tom Richardson, and Rüdiger L. Urbanke. 2013. Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation. IEEE Transactions on Information Theory 59, 12 (2013), 7761–7813. https: //doi.org/10.1109/TIT.2013.2280915

    arXiv 2013

  28. [28]

    Shrinivas Kudekar, Thomas J Richardson, and Rüdiger L Urbanke. 2011. Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC. IEEE transactions on information theory 57, 2 (2011), 803–834

    2011

  29. [29]

    Richardson, and Rüdiger L

    Shrinivas Kudekar, Thomas J. Richardson, and Rüdiger L. Urbanke. 2015. Wave-Like Solutions of General 1-D Spatially Coupled Systems. IEEE Transactions on Information Theory 61, 8 (2015), 4117–4157. https://doi.org/10.1109/TIT.2015. 22 Yu et al. 2438870

    doi:10.1109/tit.2015 2015

  30. [30]

    M. Luby. 2002. LT codes. In The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. IEEE Comput. Soc, Vancouver, BC, Canada, 271–280. https://doi.org/10.1109/SFCS.2002.1181950

    Pith/arXiv arXiv 2002

  31. [31]

    Luby, Michael Mitzenmacher, M

    Michael G. Luby, Michael Mitzenmacher, M. Amin Shokrollahi, Daniel A. Spielman, and Volker Stemann. 1997. Practical loss-resilient codes. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing (El Paso, Texas, USA) (STOC ’97) . Association for Computing Machinery, New York, NY, USA, 150–159. https: //doi.org/10.1145/258533.258573

    arXiv 1997

  32. [32]

    Francisco Lázaro and Balázs Matuz. 2023. A Rate-Compatible Solution to the Set Reconciliation Problem. IEEE Transactions on Communications 71, 10 (2023), 5769–5782. https://doi.org/10.1109/TCOMM.2023.3296630

    arXiv 2023

  33. [33]

    D.J.C. MacKay. 1999. Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory 45, 2 (1999), 399–431. https://doi.org/10.1109/18.748992

    work page doi:10.1109/18.748992 1999

  34. [34]

    Emin Martinian and C-EW Sundberg. 2004. Burst erasure correction codes with low decoding delay. IEEE Transactions on Information theory 50, 10 (2004), 2494–2502

    2004

  35. [35]

    Emin Martinian and Mitchell Trott. 2007. Delay-Optimal Burst Erasure Code Construction. In 2007 IEEE International Symposium on Information Theory . IEEE, Nice, France, 1006–1010. https://doi.org/10.1109/ISIT.2007.4557355

    arXiv 2007

  36. [36]

    François Michel, Quentin De Coninck, and Olivier Bonaventure. 2019. QUIC-FEC: Bringing the benefits of Forward Erasure Correction to QUIC. In 2019 IFIP Networking Conference (IFIP Networking) . IEEE, Warsaw, Poland, 1–9. https://doi.org/10.23919/IFIPNetworking.2019.8816838

    arXiv 2019

  37. [37]

    David GM Mitchell, Michael Lentmaier, and Daniel J Costello. 2015. Spatially coupled LDPC codes constructed from protographs. IEEE Transactions on Information Theory 61, 9 (2015), 4866–4889

    2015

  38. [38]

    David G. M. Mitchell, Ali E. Pusane, Kamil Sh. Zigangirov, and Daniel J. Costello. 2008. Asymptotically good LDPC convolutional codes based on protographs. In 2008 IEEE International Symposium on Information Theory . IEEE, Toronto, ON, Canada, 1030–1034. https://doi.org/10.1109/ISIT.2008.4595143

    arXiv 2008

  39. [39]

    Thiago Camelo Mourão, Shady Saikali, Evan Patel, Mischa Dohler, Vipul Patel, and Márcio Covas Moschovas. 2025. Chapter 15 - Telesurgery applications, current status, and future perspectives in technologies and ethics. In Handbook of Robotic Surgery, Stênio de Cássio Zequi and Hongliang Ren (Eds.). Academic Press, 161–168. https://doi.org/10. 1016/B978-0-4...

    2025

  40. [40]

    Naruomi Obata, Yung-Yih Jian, Kenta Kasai, and Henry D. Pfister. 2013. Spatially-coupled multi-edge type LDPC codes with bounded degrees that achieve capacity on the BEC under BP decoding. In 2013 IEEE International Symposium on Information Theory. IEEE, Istanbul, Turkey, 2433–2437. https://doi.org/10.1109/ISIT.2013.6620663

    arXiv 2013

  41. [41]

    Leonardo Peroni and Sergey Gorinsky. 2025. An End-to-End Pipeline Perspective on Video Streaming in Best- Effort Networks: A Survey and Tutorial. ACM Comput. Surv. 57, 12, Article 322 (July 2025), 47 pages. https: //doi.org/10.1145/3742472

    doi:10.1145/3742472 2025

  42. [42]

    I. S. Reed and G. Solomon. 1960. Polynomial Codes Over Certain Finite Fields. J. Soc. Indust. Appl. Math. 8, 2 (1960), 300–304. https://doi.org/10.1137/0108018

    doi:10.1137/0108018 1960

  43. [43]

    Tom Richardson and Ruediger Urbanke. 2008. Modern Coding Theory . Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511791338

    work page doi:10.1017/cbo9780511791338 2008

  44. [44]

    Thomas J Richardson and Rüdiger L Urbanke. 2002. The capacity of low-density parity-check codes under message- passing decoding. IEEE Transactions on information theory 47, 2 (2002), 599–618

    2002

  45. [45]

    Michael Rink. 2013. Mixed Hypergraphs for Linear-Time Construction of Denser Hashing-Based Data Structures. In SOFSEM 2013: Theory and Practice of Computer Science , Peter van Emde Boas, Frans C. A. Groen, Giuseppe F. Italiano, Jerzy Nawrocki, and Harald Sack (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 356–368

    2013

  46. [46]

    Michael Rudow and KV Rashmi. 2022. Streaming codes for variable-size messages. IEEE Transactions on Information Theory 68, 9 (2022), 5823–5849

    2022

  47. [47]

    Yan, Abhishek Kumar, Ganesh Ananthanarayanan, Martin Ellis, and K.V

    Michael Rudow, Francis Y. Yan, Abhishek Kumar, Ganesh Ananthanarayanan, Martin Ellis, and K.V. Rashmi. 2023. Tambur: Efficient loss recovery for videoconferencing via streaming codes. In 20th USENIX Symposium on Networked Systems Design and Implementation (NSDI 23) . USENIX Association, Boston, MA, 953–971. https://www.usenix.org/ conference/nsdi23/presen...

    2023

  48. [48]

    Laurent Schmalen. 2015. Spatially Coupled LDPC Codes – Theory and Applications. Tutorial slides, Karlsruhe Institute of Technology (KIT). https://www.cel.kit.edu/english/370.php

    2015

  49. [49]

    Amin Shokrollahi. 2006. Raptor codes. IEEE Transactions on Information Theory 52, 6 (2006), 2551–2567. https: //doi.org/10.1109/TIT.2006.874390

    arXiv 2006

  50. [50]

    Amin Shokrollahi and Michael Luby. 2011. Raptor codes . Vol. 6. Now Publishers, Inc. 213–322 pages. https: //doi.org/10.1561/0100000060

    doi:10.1561/0100000060 2011

  51. [51]

    Shokrollahi, M

    A. Shokrollahi, M. Luby, M. Watson, T. Stockhammer, and L. Minder. 2011. RaptorQ Forward Error Correction Scheme for Object Delivery. RFC 6330. Available at https://datatracker.ietf.org/doc/html/rfc6330. METTLE: Native Streaming Code with Peeling Decodability 23

    2011

  52. [52]

    Singleton

    R. Singleton. 1964. Maximum distanceq-nary codes. IEEE Transactions on Information Theory 10, 2 (1964), 116–118. https://doi.org/10.1109/TIT.1964.1053661

    arXiv 1964

  53. [53]

    B. Sklar. 1997. Rayleigh fading channels in mobile digital communication systems. I. Characterization. IEEE Communi- cations Magazine 35, 9 (1997), 136–146. https://doi.org/10.1109/35.620535

    work page doi:10.1109/35.620535 1997

  54. [54]

    R. Tanner. 1981. A recursive approach to low complexity codes. IEEE Transactions on Information Theory 27, 5 (1981), 533–547. https://doi.org/10.1109/TIT.1981.1056404

    arXiv 1981

  55. [55]

    International Telecommunication Union. 2001. ITU-T Recommendation G.1010: End-user multimedia QoS categories . Technical Report G.1010 (11/2001). ITU-T. https://www.itu.int/rec/T-REC-G.1010-200111-I

    2001

  56. [56]

    Stefan Walzer. 2025. Peeling Close to the Orientability Threshold Spatial Coupling in Hashing-Based Data Structures. ACM Trans. Algorithms 21, 3, Article 33 (July 2025), 23 pages. https://doi.org/10.1145/3711822

    doi:10.1145/3711822 2025

  57. [57]

    Lei Yang, Yossi Gilad, and Mohammad Alizadeh. 2024. Practical Rateless Set Reconciliation. In Proceedings of the ACM SIGCOMM 2024 Conference (Sydney, NSW, Australia)(ACM SIGCOMM ’24). Association for Computing Machinery, New York, NY, USA, 595–612. https://doi.org/10.1145/3651890.3672219

    arXiv 2024

  58. [58]

    Shroff, and Hesham El Gamal

    Yang Yang, Jian Tan, Ness B. Shroff, and Hesham El Gamal. 2014. Delay Asymptotics With Retransmissions and Incremental Redundancy Codes Over Erasure Channels. IEEE Transactions on Information Theory 60, 3 (2014), 1932–1944. https://doi.org/10.1109/TIT.2014.2300485

    arXiv 2014

  59. [59]

    Nguyen, and Henry D

    Arvind Yedla, Yung-Yih Jian, Phong S. Nguyen, and Henry D. Pfister. 2012. A simple proof of threshold saturation for coupled scalar recursions. In 2012 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC). IEEE, Gothenburg, Sweden, 51–55. https://doi.org/10.1109/ISTC.2012.6325197

    arXiv 2012

  60. [60]

    Nguyen, and Henry D

    Arvind Yedla, Yung-Yih Jian, Phong S. Nguyen, and Henry D. Pfister. 2012. A simple proof of threshold saturation for coupled vector recursions. In 2012 IEEE Information Theory Workshop . IEEE, Lausanne, Switzerland, 25–29. https: //doi.org/10.1109/ITW.2012.6404671

    arXiv 2012