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Capacity-achieving sparse superposition codes with spatially coupled VAMP decoder

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Sparse superposition codes with a spatially coupled VAMP decoder are claimed to be capacity-achieving over the AWGN channel when the design matrices meet the spectra criterion.

desk verdict A plausible extension of VAMP to spatially coupled superposition codes whose capacity claim rests on an unproven state-evolution closure; worth refereeing if the SE step is addressed. read the letter →

arxiv 2504.13601 v1 pith:FUC3CMQV submitted 2025-04-18 cs.IT math.IT

Yuhao Liu , Teng Fu , Jie Fan , Panpan Niu , Chaowen Deng , Zhongyi Huang This is my paper · ORCID
classification cs.ITmath.IT MSC 94A1594A24
keywords sparsesuperpositioncodesspatialcouplingvectorapproximatemessagepassingstateevolutioncapacity-achievingAWGNchannelspectracriterionsectionerrorrate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a spatially coupled variant of the vector approximate message passing (VAMP) decoder for sparse superposition codes, a coding scheme in which each codeword is a sparse vector multiplied by a large random matrix. The authors claim that, when the design matrices satisfy the spectra criterion, this SC-VAMP decoder is capacity-achieving over the additive white Gaussian noise channel. The argument runs through a state evolution analysis showing that decoding errors are pushed from the boundary blocks inward and vanish after finitely many iterations for all rates below an information-theoretic threshold, which is then shown to equal channel capacity. A reader would care because this supplies a polynomial-time decoder that provably reaches the Shannon limit, and simulations show it beats the previous VAMP decoder with exponential power allocation at finite block lengths.

What carries the argument

The load-bearing mechanism is the rescaled state-evolution recursion given by equations (1)-(4), with variables $\sigma_r^k$, $\tau_c^k$, $\psi_c^k$, and $\phi_r^k$, together with the phase-transition behaviour of the Bayes denoiser: $\lim_{B\to\infty}E_2(\gamma)=\mathbb{I}\{(\lim \log B/\gamma)>1/2\}$. Proposition 1 turns this recursion into a threshold-saturation argument: with coupling width $W$ and block count $\Gamma$, if $R_{\mathrm{all}}<\vartheta^{-1}R_{\mathrm{IT}}$ and $W>\max\{\lceil1/l^*(\vartheta)\rceil,\lceil1/h^*(\vartheta,\Delta)\rceil\}$, then $\psi_c^k=0$ for an expanding set of blocks, so decoding succeeds. The capacity step is the identity $F(x)=\mathbb{E}_{\rho_0}[\lambda/(\lambda x+\sigma^2)]$, whose Cauchy-Schwarz bound $F(x)\le(\sigma^2+x)^{-1}$ yields $R_{\mathrm{IT}}\le C$, with equality exactly when $\rho_0=\delta_1$. The decoder itself is derived from the factor graph by expectation-consistent message passing with uniform diagonalization, which approximates per-block messages by Gaussians with a common precision.

What would settle it

Run SC-VAMP on a large but finite instance with a right-rotationally invariant design matrix whose limiting spectrum is the point mass $\delta_1$, at a rate below $\frac12\log(1+\mathrm{snr})$, and compare the measured per-block mean squared error with the state-evolution prediction; a mismatch that does not vanish as the dimensions grow would falsify the SE tracking and hence the capacity claim.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the spatially coupled sparse superposition (SC-SS) code, decoded by the proposed SC-VAMP decoder, is capacity-achieving over the additive white Gaussian noise channel when every design matrix satisfies the spectra criterion: the limiting spectral density $\rho_{\mathrm{supp},r}$ of $B^{-1}A_r^T A_r$ converges to the point mass $\delta_1$ as the section size $B\to\infty$ with aspect ratio $\alpha\to 0$. The proof works through state evolution: for rates $R_{\mathrm{all}}$ below the information-theoretic threshold $R_{\mathrm{IT}}=\frac12\int_0^1 F(x)\,dx$, Proposition 1 shows the per-block error indicator $\psi_c^k$ is driven to zero in a wave from the outermost blocks inward, so after $K=1+\lceil\Gamma/(2g)\rceil$ iterations every block is recovered. The Cauchy-Schwarz bound $F(x)\le(\sigma^2+x)^{-1}$ gives $R_{\mathrm{IT}}\le\frac12\log(1+\mathrm{snr})=C$, and equality is attained in the point-mass limit, so every rate $R_{\mathrm{all}}<C$ is decodable. This confirms the VAMP-based capacity conjecture for rotational invariant designs.

Load-bearing premise

The proof assumes the decoder's average error in each block is exactly what the state-evolution recursion predicts, and that the coupling can be made arbitrarily wide so the rate loss vanishes; if either fails for the concatenated SC-VAMP update, the capacity claim collapses.

Editorial extensions

If this is right

  • Under the paper's state-evolution analysis, any rate $R_{\mathrm{all}}<C$ is decodable with SC-VAMP provided the design matrices satisfy the spectra criterion and the coupling parameters are chosen sufficiently wide.
  • Decoding error disappears in an inward-moving wave: the outermost blocks are recovered first and the central blocks last, confirming threshold saturation for VAMP-based spatially coupled decoding.
  • The spectra criterion makes the result universal across right-rotationally invariant designs: Gaussian matrices and structured DCT/Hadamard matrices both admit capacity-achieving decoding, with fast transforms reducing per-iteration cost to $O(BL\log(BL))$.
  • In the large-system limit, SC-VAMP reaches the same capacity threshold as VAMP with exponential power allocation, while the simulations here show SC-VAMP attains a lower section error rate at practical finite block lengths.
  • If state-evolution tracking remains valid at finite sizes, the same threshold-saturation structure should yield non-asymptotic section error bounds, the extension the paper lists as future work.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the state-evolution tracking can be proven non-asymptotically, the threshold-saturation argument should produce finite-length section error bounds that decay exponentially in the block length; the paper does not prove this step.
  • The spectra criterion is a universality condition, so the theorem should be read as covering any right-rotationally invariant design whose spectrum concentrates well, not just the Gaussian and DCT matrices simulated.
  • Because the capacity argument rests only on the Cauchy-Schwarz bound for $F(x)$, the same structure should extend to memoryless channels whenever the denoiser has the required phase transition; the paper mentions this only informally.
  • The condition $\Gamma>W^2$ with $W\to\infty$ means the coupling overhead $\vartheta$ tends to one only asymptotically; quantifying the required coupling width for a fixed gap to capacity is a natural next step that the paper leaves open.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes a spatially coupled VAMP (SC-VAMP) decoder for sparse superposition codes with spatially coupled right-rotationally-invariant design matrices. The algorithm is derived from a factor graph with expectation-consistent message passing and a uniform-diagonalization approximation. The authors write state-evolution recursions for the per-block MSE and prove a threshold-saturation result (Proposition 1) for the limiting SE recursion. A Cauchy-Schwarz bound on the information-theoretic threshold R_IT is then used to conclude that the SC-SS code with SC-VAMP is capacity-achieving over the AWGN channel when the design spectra converge to δ1 as α→0. Numerical experiments compare SC-VAMP with plain VAMP and exponential-power-allocation VAMP, reporting a lower section error rate; the code is publicly available.

Significance. If the SE recursion is valid and the large-section limit is made precise, the paper would give a new capacity-achieving decoding scheme that combines spatial coupling with rotationally invariant designs, extending prior VAMP results from exponential power allocation to a spatially coupled construction. The empirical comparison is a genuine strength, and the public code makes the experiments reproducible. However, the central capacity claim is conditional on unproved state evolution for the specific overlapping-matrix, diagonalized update, and the asymptotic order of the coupling parameters is not quantified. The contribution is therefore a plausible and well-supported conjecture with a clear algorithmic proposal, rather than a fully demonstrated theorem.

major comments (4)
  1. [§IV (Algorithm 1, lines 20–21)] The SE equations are introduced with 'it follows' and no theorem establishes that the scalarized per-block MSE recursions track Algorithm 1. The concatenating/uniform-diagonalization step collapses the per-block precisions (η̂_{2,c}) into a single scalar η_{2,r} by harmonic mean. Because each block c feeds several overlapping matrices A_r, the messages entering a given r are not conditionally independent given x_c, so the VAMP/EC scalar closure conditions are not automatic. Please either prove SE for this exact update or cite a theorem that covers overlapping spatially coupled blocks with a section-wise denoiser; without this, Proposition 1 and the capacity conclusion apply only to the assumed SE.
  2. [§IV, Proposition 1 proof] The printed inequality ∑_{r=c}^{W-1} 1/r ≤ ln(W/c) is false for 1 ≤ c ≤ W; the correct direction is ≥. The subsequent upper bound on τ^0_c requires a lower bound on the harmonic sum, so the displayed proof of the initial saturation wave is not rigorous as written. This appears easily correctable, but it is load-bearing because it establishes the first set of zero ψ^0_c blocks.
  3. [§IV, large-section limit] The passage from finite-B SE to the limit equations uses the phase transition of E_2(γ) and assumes α = Θ(log B/B) → 0 without quantifying error terms. The statement that 'for sufficiently large W with Γ > W^2, ϑ → 1' does not specify how W, Γ, B, and L must scale relative to one another and to the target rate gap Δ. Please state explicit asymptotics, or provide a non-asymptotic bound, so that 'capacity-achieving' has a precise meaning and the iteration count K = 1 + ⌈Γ/(2g)⌉ is compatible with the code length.
  4. [§IV, after Proposition 1] The capacity conclusion relies on equality in the Cauchy-Schwarz bound, which occurs only when ρ0 = δ1, while Proposition 1 requires all F_r to coincide. The paper should clarify whether the claimed capacity result assumes a common limiting spectrum for all r or only that each ρ_supp,r → δ1 as α→0, and, in the latter case, explain how the proof adapts when F_r differs for finite r.
minor comments (4)
  1. [§IV, Proposition 1 proof] The phrase 'g is a integer greater than or equal to 1' contains a typo; it should be 'an integer'.
  2. [Fig. 3 caption] It would be more informative to state the numerical values of the algorithmic and information-theoretic thresholds used in the comparison.
  3. [Algorithm 1, line 14] The definition N(r) = |W_r| 1{r≤W} + W 1{r>W} is redundant; if N(r) = |W_r|, it may be simpler to say so explicitly.
  4. [Abstract] The GitHub URL contains a space ('SC-V AMP') due to formatting; ensure it is printed as a single clickable hyperlink.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the capacity-achieving claim is derived from an explicit information-theoretic threshold bound and SE threshold-saturation analysis, not from a fitted parameter or self-citation.

full rationale

The paper's central claim is that SC-SS with SC-VAMP is capacity-achieving when each design matrix satisfies the spectra criterion. The derivation chain is: (i) state evolution equations are posited to track per-block MSE; (ii) Proposition 1 shows under Rall < ϑ^{-1} R_IT the SE fixed point has ψ=0, i.e., successful decoding; (iii) Cauchy–Schwarz gives R_IT ≤ (1/2)log(1+snr)=C, with equality iff ρ_0=δ_1. None of these steps defines the target quantity in terms of itself: R_IT is a deterministic functional of the spectral density and σ², not a fitted parameter; the spectral criterion δ_1 is a stated sufficient condition, not an output of the proof; and the SE equations are not defined using capacity. The self-citations [1],[2],[32] supply the VAMP framework, the exponential-decay PA result, and the earlier conjecture, but the present proof does not delegate its central conclusion to them. The unproven SE tracking assumption and the incorrect inequality direction in the proof of Proposition 1 are genuine technical gaps, but they are correctness risks, not circularity: the argument would fail or need repair without making the conclusion equivalent to an input. No step was found where a prediction reduces by construction to its own premise, so the score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to data. The proof relies on standard inequalities, an assumed SE description, the E2 phase transition, and the spectral concentration condition. The main assumptions are the exactness of SE and the spectral criterion.

assumptions (5)
  • domain assumption State evolution (SE) exactly tracks the per-block MSE of the SC-VAMP decoder in the large-L limit.
    Section IV states 'the MSE metric can be tracked by the following SE equations' without proof; all subsequent analysis rests on this.
  • domain assumption The design matrices are right orthogonally invariant with a limiting spectral density ρ_r, and the spectra criterion ρ_supp,r → δ1 as α→0 holds.
    This is the core condition for capacity-achieving and is used in Section IV to set F(x) and bound R_IT.
  • domain assumption The phase transition of E2(γ) in the large-B limit: lim_{B→∞} E2(γ) = I{(lim logB/γ) > 1/2}.
    Used to obtain the limit SE equations (1)-(4) in Section IV.
  • ad hoc to paper The coupling parameters satisfy Γ > W^2 and W is sufficiently large so that ϑ = (Γ+W-1)/Γ → 1 as W→∞.
    Stated after Proposition 1 in Section IV to conclude capacity-achieving; no quantitative bounds are given.
  • standard math Standard analytic results: Cauchy-Schwarz inequality, uniqueness of solutions to equations (6) and (7), and monotonicity of F.
    Used in the proof of Proposition 1 and the derivation of R_IT ≤ C.

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Pith. "Pith review of Capacity-achieving sparse superposition codes with spatially coupled VAMP decoder." pith.science (2026). https://pith.science/paper/FUC3CMQV

@misc{pith2026250413601,
  author       = {Pith},
  title        = {Pith review of: Capacity-achieving sparse superposition codes with spatially coupled VAMP decoder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FUC3CMQV}},
  note         = {Machine review of arXiv:2504.13601}
}
read the original abstract

Sparse superposition (SS) codes provide an efficient communication scheme over the Gaussian channel, utilizing the vector approximate message passing (VAMP) decoder for rotational invariant design matrices. Previous work has established that the VAMP decoder for SS achieves Shannon capacity when the design matrix satisfies a specific spectral criterion and exponential decay power allocation is used. In this work, we propose a spatially coupled VAMP (SC-VAMP) decoder for SS with spatially coupled design matrices. Based on state evolution (SE) analysis, we demonstrate that the SC-VAMP decoder is capacity-achieving when the design matrices satisfy the spectra criterion. Empirically, we show that the SC-VAMP decoder outperforms the VAMP decoder with exponential decay power allocation, achieving a lower section error rate. All codes are available on https://github.com/yztfu/SC-VAMP-for-Superposition-Code.git.

Figures

Figures reproduced from arXiv: 2504.13601 by the authors.

Figure 1
Figure 1. A SC-SS with spatial coupling parameters [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Factor graph representation of the joint probability distribution of C [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Overall section error rate SERk = (PC c=1 SERk c )/C ran on a random single instance with L = 214 , B = 16 and snr = 15, as a function of the iterations. For SC-VAMP decoder, we set Γ = 16, W = 2 and ϑ = 17/16. The overall rate Rall = 1.60 is higher than the algorithm threshold, lower than the information-theoretic threshold proposed in [1]. Given that F(x) is decreasing in [0, 1], we have τ k+1 c ≤ Rallϑ " Z 1 c−gk… view at source ↗

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Works this paper leans on

40 extracted references · 35 canonical work pages

  1. [1]

    Sparse superposition codes under V AMP decoding with generic rotational invariant coding matrices,

    T. Hou, Y . Liu, T. Fu, and J. Barbier, “Sparse superposition codes under V AMP decoding with generic rotational invariant coding matrices,” in Proc. IEEE ISIT , June 2022, pp. 1372–1377

    work page 2022

  2. [2]

    Capacity- achieving sparse regression codes via vector approximate message pass- ing,

    Y . Xu, Y . Liu, S. Liang, T. Wu, B. Bai, J. Barbier, and T. Hou, “Capacity- achieving sparse regression codes via vector approximate message pass- ing,” in Proc. IEEE ISIT , June 2023, pp. 785–790

    work page 2023

  3. [3]

    Toward fast reliable communication at rates near capacity with gaussian noise,

    A. R. Barron and A. Joseph, “Toward fast reliable communication at rates near capacity with gaussian noise,” in Proc. IEEE ISIT , June 2010, pp. 315–319

    work page 2010

  4. [4]

    Analysis of fast sparse superposition codes,

    A. R. Barron and A. Joseph, “Analysis of fast sparse superposition codes,” in Proc. IEEE ISIT , July 2011, pp. 1772–1776

    work page 2011

  5. [5]

    Least squares superposition codes of moderate dictionary size are reliable at rates up to capacity,

    A. Joseph and A. R. Barron, “Least squares superposition codes of moderate dictionary size are reliable at rates up to capacity,” IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 2541–2557, May 2012

    work page 2012

  6. [6]

    Sparse regression codes,

    R. Venkataramanan, S. Tatikonda, A. Barron et al. , “Sparse regression codes,” Found. Trends® Commun. Inf. Theory , vol. 15, no. 1-2, pp. 1– 195, 2019

    work page 2019

  7. [7]

    Fast sparse superposition codes have near exponential error probability for R < C,

    A. Joseph and A. R. Barron, “Fast sparse superposition codes have near exponential error probability for R < C,” IEEE Trans. Inf. Theory , vol. 60, no. 2, pp. 919–942, Feb. 2014

    work page 2014

  8. [8]

    Approximate iterative Bayes optimal estimates for high-rate sparse superposition codes,

    S. Cho and A. Barron, “Approximate iterative Bayes optimal estimates for high-rate sparse superposition codes,” in Sixth Workshop on Inf. The. Methods in Sci. and Eng. , 2013, pp. 35–42

    work page 2013

Show all 40 references
  1. [9]

    Message-passing algo- rithms for compressed sensing,

    D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algo- rithms for compressed sensing,” Proc. Natl. Acad. Sci. U.S.A. , vol. 106, no. 45, pp. 18 914–18 919, 2009

    2009

  2. [10]

    The dynamics of message passing on dense graphs, with applications to compressed sensing,

    M. Bayati and A. Montanari, “The dynamics of message passing on dense graphs, with applications to compressed sensing,” IEEE Trans. Inf. Theory, vol. 57, no. 2, pp. 764–785, Feb. 2011

    2011

  3. [11]

    Replica analysis and approximate message passing decoder for superposition codes,

    J. Barbier and F. Krzakala, “Replica analysis and approximate message passing decoder for superposition codes,” in Proc. IEEE ISIT, June 2014, pp. 1494–1498

    2014

  4. [12]

    Approximate message-passing decoder and capacity achieving sparse superposition codes,

    J. Barbier and F. Krzakala, “Approximate message-passing decoder and capacity achieving sparse superposition codes,” IEEE Trans. Inf. Theory , vol. 63, no. 8, pp. 4894–4927, Aug. 2017

    2017

  5. [13]

    Proof of threshold saturation for spatially coupled sparse superposition codes,

    J. Barbier, M. Dia, and N. Macris, “Proof of threshold saturation for spatially coupled sparse superposition codes,” in Proc. IEEE ISIT , July 2016, pp. 1173–1177

    2016

  6. [14]

    Capacity-achieving sparse superposition codes via approximate message passing decoding,

    C. Rush, A. Greig, and R. Venkataramanan, “Capacity-achieving sparse superposition codes via approximate message passing decoding,” IEEE Trans. Inf. Theory, vol. 63, no. 3, pp. 1476–1500, Mar. 2017

    2017

  7. [15]

    The error probability of sparse superposition codes with approximate message passing decoding,

    C. Rush and R. Venkataramanan, “The error probability of sparse superposition codes with approximate message passing decoding,” IEEE Trans. Inf. Theory, vol. 65, no. 5, pp. 3278–3303, May 2019

    2019

  8. [16]

    Capacity-achieving spatially coupled sparse superposition codes with AMP decoding,

    C. Rush, K. Hsieh, and R. Venkataramanan, “Capacity-achieving spatially coupled sparse superposition codes with AMP decoding,” IEEE Trans. Inf. Theory, vol. 67, no. 7, pp. 4446–4484, July 2021

    2021

  9. [17]

    Generalized approximate message passing for estimation with random linear mixing,

    S. Rangan, “Generalized approximate message passing for estimation with random linear mixing,” in Proc. IEEE ISIT , July 2011, pp. 2168– 2172

    2011

  10. [18]

    A unifying tutorial on approximate message passing,

    O. Y . Feng, R. Venkataramanan, C. Rush, R. J. Samworth et al. , “A unifying tutorial on approximate message passing,” Found. Trends Mach. Learn, vol. 15, no. 4, pp. 335–536, 2022

    2022

  11. [19]

    Universal sparse superposition codes with spatial coupling and GAMP decoding,

    J. Barbier, M. Dia, and N. Macris, “Universal sparse superposition codes with spatial coupling and GAMP decoding,” IEEE Trans. Inf. Theory , vol. 65, no. 9, pp. 5618–5642, Sep. 2019

    2019

  12. [20]

    The error probability of spatially cou- pled sparse regression codes over memoryless channels,

    Y . Liu, Y . Xu, and T. Hou, “The error probability of spatially cou- pled sparse regression codes over memoryless channels,” arXiv preprint arXiv:2409.05745, 2024

    2024 arXiv

  13. [21]

    Techniques for improving the finite length performance of sparse superposition codes,

    A. Greig and R. Venkataramanan, “Techniques for improving the finite length performance of sparse superposition codes,” IEEE Trans. Com- mun., vol. 66, no. 3, pp. 905–917, Mar. 2017

    2017

  14. [22]

    Vector approximate message passing,

    S. Rangan, P. Schniter, and A. K. Fletcher, “Vector approximate message passing,” IEEE Trans. Inf. Theory , vol. 65, no. 10, pp. 6664–6684, Oct. 2019

    2019

  15. [23]

    Orthogonal AMP,

    J. Ma and L. Ping, “Orthogonal AMP,” IEEE Access, vol. 5, pp. 2020– 2033, Jan. 2017

    2020

  16. [24]

    Spatially coupled sparse regression codes: Design and state evolution analysis,

    K. Hsieh, C. Rush, and R. Venkataramanan, “Spatially coupled sparse regression codes: Design and state evolution analysis,” in Proc. IEEE ISIT, June 2018, pp. 1016–1020

    2018

  17. [25]

    Factor graphs and the sum-product algorithm,

    F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Trans. Inf. Theory , vol. 47, no. 2, pp. 498–519, Feb. 2001

    2001

  18. [26]

    A family of algorithms for approximate Bayesian inference,

    T. P. Minka, “A family of algorithms for approximate Bayesian inference,” Ph.D. dissertation, Dept. Elect. Eng. Comput. Sci., MIT, Cambridge, MA, USA, 2001

    2001

  19. [27]

    Expectation propagation for exponential families,

    M. Seeger, “Expectation propagation for exponential families,”

  20. [28]

    Orthogonal approximate message-passing for spatially coupled linear models,

    K. Takeuchi, “Orthogonal approximate message-passing for spatially coupled linear models,” IEEE Trans. Inf. Theory, vol. 70, no. 1, pp. 594– 631, Jan. 2023

    2023

  21. [29]

    Bayes-optimal estimation in generalized linear models via spatial coupling,

    P. P. Cobo, K. Hsieh, and R. Venkataramanan, “Bayes-optimal estimation in generalized linear models via spatial coupling,” IEEE Trans. Inf. Theory, vol. 70, no. 11, pp. 8343–8363, Nov. 2024

    2024

  22. [30]

    Expecta- tion consistent approximate inference: Generalizations and convergence,

    A. Fletcher, M. Sahraee-Ardakan, S. Rangan, and P. Schniter, “Expecta- tion consistent approximate inference: Generalizations and convergence,” in Proc. IEEE ISIT , July 2016, pp. 190–194

    2016

  23. [31]

    On the universality of noiseless linear estimation with respect to the measurement matrix,

    A. Abbara, A. Baker, F. Krzakala, and L. Zdeborová, “On the universality of noiseless linear estimation with respect to the measurement matrix,” Journal of Physics A: Mathematical and Theoretical , vol. 53, no. 16, p. 164001, 2020

    2020

  24. [32]

    Sparse superposition codes with rotational invariant coding matrices for memoryless channels,

    Y . Liu, T. Fu, J. Barbier, and T. Hou, “Sparse superposition codes with rotational invariant coding matrices for memoryless channels,” in Proc. IEEE ITW, Nov. 2022, pp. 267–272

    2022

  25. [33]

    Finite sample analysis of approximate message passing algorithms,

    C. Rush and R. Venkataramanan, “Finite sample analysis of approximate message passing algorithms,” IEEE Trans. Inf. Theory , vol. 64, no. 11, pp. 7264–7286, Nov. 2018

    2018

  26. [34]

    A non-asymptotic framework for approximate message passing in spiked models,

    G. Li and Y . Wei, “A non-asymptotic framework for approximate message passing in spiked models,” arXiv preprint arXiv:2208.03313 , 2022

    2022 arXiv

  27. [35]

    A non-asymptotic analysis of generalized vector approximate message passing algorithms with rotationally invariant designs,

    C. Cademartori and C. Rush, “A non-asymptotic analysis of generalized vector approximate message passing algorithms with rotationally invariant designs,” IEEE Trans. Inf. Theory , vol. 70, no. 8, pp. 5811–5856, Aug. 2024

    2024

  28. [36]

    Memory AMP,

    L. Liu, S. Huang, and B. M. Kurkoski, “Memory AMP,” IEEE Trans. Inf. Theory, vol. 68, no. 12, pp. 8015–8039, Dec. 2022

    2022

  29. [37]

    Approximate message passing algorithms for rotationally invari- ant matrices,

    Z. Fan, “Approximate message passing algorithms for rotationally invari- ant matrices,” The Annals of Statistics , vol. 50, no. 1, pp. 197–224, 2022

    2022

  30. [38]

    Universality of approximate message passing with semirandom matrices,

    R. Dudeja, Y . M. Lu, and S. Sen, “Universality of approximate message passing with semirandom matrices,” The Annals of Probability , vol. 51, no. 5, pp. 1616–1683, 2023

    2023

  31. [39]

    Spectral universality in regularized linear regression with nearly deterministic sensing matrices,

    R. Dudeja, S. Sen, and Y . M. Lu, “Spectral universality in regularized linear regression with nearly deterministic sensing matrices,” IEEE Trans. Inf. Theory, vol. 70, no. 11, pp. 7923–7951, Nov. 2024

    2024

  32. [2005]

    Available: https://infoscience.epfl.ch/handle/20.500

    [Online]. Available: https://infoscience.epfl.ch/handle/20.500. 14299/61899

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