Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding

Elsa Dupraz; Jiahui Wei; Philippe Mary

REVIEW 4 major objections 4 minor 23 references

Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper establishes that the finite-blocklength rate for the indirect Wyner-Ziv problem—where a decoder must reconstruct both an observed source and a latent, unobserved source—is the asymptotic rate-distortion function plus a…

desk verdict A promising first finite-blocklength treatment of indirect Wyner-Ziv with two distortion constraints, but the main theorem's proof has a genuine misstep in Eq. (63) that needs repair before the result is reliable. read the letter →

arxiv 2507.17432 v2 pith:FOB2WOFD submitted 2025-07-23 cs.IT math.IT

Jiahui Wei , Philippe Mary , Elsa Dupraz This is my paper

classification cs.ITmath.IT MSC 94A1594A2994A34 PACS 89.70.-a89.70.Cf

keywords indirectsourcecodingWyner-Zivfiniteblocklengthrate-distortiongoal-orientedcommunicationsdispersionPoissonmatchinglemmaBlahut-Arimotoalgorithm

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 derives the rate-distortion function for the indirect Wyner-Ziv problem, where a decoder with side information must reconstruct both an observed source and a latent, unobserved source. It then proves a finite-blocklength achievability bound: for blocklength $n$ and excess probability $\epsilon$, a rate near the asymptotic rate plus a dispersion penalty of order $1/\sqrt{n}$ suffices. Because the latent source can stand for semantic information such as a classification label, the results give practical rate-distortion-classification trade-offs for goal-oriented communications. The paper also supplies a Blahut-Arimoto algorithm to compute the region numerically.

What carries the argument

The argument rests on three pieces. The conditional Poisson Matching Lemma converts the probability that the encoder's and decoder's auxiliary random variables disagree into a bound involving a ratio of conditional densities, producing the one-shot excess-probability bound of Theorem 2. The multidimensional Berry-Esseen theorem is then applied to the three-dimensional information-density-distortion vector $(\iota(U;X)-\iota(U;Y),\, d(X,\hat{X}),\, d_s(S,\hat{S}))$, whose Gaussian limit defines the dispersion region $S(V,\epsilon)$ and yields the $1/\sqrt{n}$ term. The Blahut-Arimoto algorithm, obtained by differentiating the Lagrangian of the asymptotic optimization, provides the optimal test channel $P^\star_{U|X}$ used to evaluate the bound numerically for a classification example.

What would settle it

Compute the covariance matrix $V$ for a specific Gaussian-mixture example with parameters where $\theta_0$ and $\theta_1$ produce a nearly singular $V$, then run the Blahut-Arimoto algorithm and evaluate the excess probability from Theorem 2; if the actual excess probability exceeds the bound from Theorem 3 for moderate $n$, the claimed second-order rate would be falsified.

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Extended reading notes

Core claim

The central claim is that the finite-blocklength indirect Wyner-Ziv rate-distortion function is bounded above by $R_{WZ}(D,D_s) + e_1 S(V,\epsilon)/\sqrt{n} + 2\log n/n$ for $n$ sufficiently large, where $R_{WZ}(D,D_s)$ is the asymptotic function from Theorem 1, $e_1$ selects the rate coordinate, and $S(V,\epsilon)$ is the dispersion region of the Gaussian limit of the information-density-distortion vector. In the asymptotic regime, the paper characterizes $R_{WZ}(D,D_s)$ as the infimum of $I(X;U)-I(U;Y)$ over test channels satisfying two distortion constraints, one on the observed source $X$ and one on the latent source $S$ through a modified distortion measure. For finite $n$, the paper shows that codes exist whose rate tracks the asymptotic rate with a second-order penalty that vanishes as $n$ grows.

Load-bearing premise

The proof of Theorem 3 applies a multidimensional Berry-Esseen theorem to the information-density-distortion vector, which requires the covariance matrix $V$ to be positive definite and the third moments to exist for every parameter choice; if $V$ is singular or the densities have heavy tails, the Gaussian approximation may fail.

Editorial extensions

If this is right

If Theorem 3 is correct, there exist $(n,M,D,D_s,\epsilon)$-codes whose rate is within $e_1 S(V,\epsilon)/\sqrt{n} + 2\log n/n$ of the asymptotic indirect Wyner-Ziv rate.
The achievable non-asymptotic region expands toward the asymptotic region as blocklength $n$ or excess probability $\epsilon$ increases, matching the numerical behavior reported in the paper.
The proposed Blahut-Arimoto algorithm lets one compute the indirect rate-distortion region for source models such as Gaussian mixtures where no closed-form expression is available.
For binary classification labels with Hamming distortion, the method quantifies the rate needed to achieve a target semantic accuracy jointly with an observation-distortion constraint.
Because the Poisson matching bound avoids separate packing and covering arguments, the second-order term is tighter than bounds built from channel resolvability codes.

Reading between the lines

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

The same second-order technique should extend to $M$-ary latent labels and to tasks beyond classification, such as clustering or parameter estimation, as long as the distortion on $S$ is per-letter and the information-density-distortion vector has third moments.
The unstated requirement that $V$ be positive definite suggests that practical implementations should regularize the empirical covariance or use a truncated Gaussian approximation when distortions are nearly deterministic.
The random-guessing zero-rate baseline for $D_s>0.5$ could be folded directly into the optimization as a rate floor, which would sharpen the bound at small blocklengths.
A converse bound for the same indirect setup would let one test whether the $1/\sqrt{n}$ dispersion term is tight or merely an achievability artifact.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The take-home: this is a serious attempt at a first non-asymptotic achievability region for indirect Wyner-Ziv with two distortion constraints, and the Poisson-matching bound in Theorem 2 is clean. But the proof of the headline second-order result (Theorem 3) contains a misstep in Eq. (63) that, as written, invalidates the claimed bound. The paper should not be rejected; it should be revised carefully.

What's genuinely new: adapting the conditional Poisson matching lemma to the indirect setup where both the observation X and latent S are under distortion constraints. Theorem 2's excess-probability bound (19) is plausible and follows from the lemma in a standard way. The BA algorithm extending [5] to two Lagrangian constraints is useful, and the Gaussian-mixture classification example is a reasonable illustration. The asymptotic function in Theorem 1 is a straightforward extension, and the authors don't oversell it; the citation to [7] covers some overlap.

The soft spots, in order of severity. First, Eq. (63) claims the union event {A>γ ∪ B>nD_s ∪ C>nD} is bounded by the intersection event {A≥γ, B≥nD_s−logn, C≥nD−logn}. The stress test sent me concludes the inequality direction is wrong; the supporting reason there is itself off (the intersection is not a subset of the union; the two events are incomparable). But the conclusion stands: nothing justifies that upper bound, and in natural cases the union probability exceeds the intersection probability. The good news is the proof can likely be repaired by skipping (63) and arguing on the complement: the success event contains the lower-left orthant used in (67)-(70), so the Berry-Esseen step can be applied directly to that orthant. Still, as posted, Theorem 3 is unproved.

Second, the threshold vector in (63) lists nD_s second and nD third, while the vector in (59) has d(X,Xhat) in the second slot; the swap is real and needs fixing. Third, Theorem 3 omits the positive-definiteness of V and the moment conditions required by the multivariate Berry-Esseen theorem; for the general models the paper describes, the O(log n/√n) approximation is not guaranteed without them. Minor: no code for the numerics, and the BA algorithm's convergence is only stated, not analyzed.

For whom: anyone working on finite-blocklength semantic or goal-oriented source coding. The problem is relevant and the approach is worth engaging.

My recommendation: send it to peer review. A good referee should push for a corrected proof of Theorem 3, but this is the kind of paper that can be fixed rather than one in which the central idea is wrong.

Referee Report

4 major / 4 minor

Summary. The paper considers the indirect Wyner-Ziv source coding problem in which a length-n observation X is encoded with decoder-only side information Y, and the decoder must reconstruct both X and a latent source S under two distortion constraints. The authors state an asymptotic rate-distortion function (Theorem 1), a one-shot excess-probability bound obtained from the conditional Poisson matching lemma (Theorem 2), and a second-order achievability bound (Theorem 3) of the form R_WZ(D,D_s) plus a dispersion term over sqrt(n) plus 2 log n/n. They also propose a Blahut-Arimoto algorithm for the associated optimization and evaluate the finite-blocklength region numerically for a Gaussian-mixture classification model.

Significance. If proved, Theorem 3 would be a useful finite-blocklength result for indirect Wyner-Ziv coding and would extend the Poisson-matching approach to problems with two distortion constraints. The paper is transparent about its proof ingredients, namely the conditional Poisson matching lemma and the multivariate Berry-Esseen theorem, and no fitted parameters enter the bound; the numerical example is concrete and the BA algorithm is a reasonable extension of existing techniques. The main result is not established as written because of a direction error in the key probability bound in Appendix C and missing regularity conditions for the Berry-Esseen step. These issues appear local and correctable, so the contribution is potentially significant but needs a major revision.

major comments (4)

[Appendix C, Eqs. (62)-(63)] The inequality connecting (62) and (63) has the wrong direction. The event in (62) is a union of coordinatewise exceedances: {sum j_i,1 > log M - log n} union {sum j_i,2 > nD_s} union {sum j_i,3 > nD}. The event in (63) is the componentwise lower-orthant condition {sum j_i >= (log M, nD_s, nD) - log n}, which is an intersection-type event. For a general random vector Z=(A,B,C), P(A>a or B>b or C>c) is not bounded above by P(A>=a', B>=b', C>=c') for lowered thresholds; for example, a realization with only A large leaves the intersection event false. Therefore (63) does not upper-bound (62), and this step is the only bridge from the Poisson matching bound to the multivariate Berry-Esseen approximation. The proof should be rewritten so that Berry-Esseen is applied to the complement event {sum j_i <= threshold}, since 1 - P[excess] is exactly the probability that all three coordinates are below their thresholds; as written, Theorem 3 is unproved.
[Appendix C, Eqs. (59), (63), and (65)] The coordinate ordering is inconsistent. The vector (59) is (i(X;U)-i(U;Y), d(X,xhat), d_s(S,shat)), so the second coordinate is the observation distortion and the third is the semantic distortion. The threshold vector in (63) is (log M, nD_s, nD) - log n, which places nD_s on the d coordinate and nD on the d_s coordinate. The vector b* in (65) appears to use the order (log M/n, D, G), which would be consistent with (59) only if G = D_s. This makes the derivation and the definition of the dispersion set in (25) unverifiable; please fix the ordering and state clearly which coordinate is which.
[Theorem 3 and Appendix C, Theorem 4] The multidimensional Berry-Esseen theorem is invoked without its hypotheses. Theorem 4 requires the unnormalized summands U_i to have finite third moments and the covariance matrix V to be positive definite; Theorem 3 only says V is positive semi-definite in (25) and imposes no moment conditions on the distortion measures defined in (2)-(3). If V is singular, the Gaussian vector B in (25) is degenerate and the standard O(1/sqrt(n)) Berry-Esseen statement does not apply; if the source has heavy tails with respect to d or d_s, the third moments of the entries of (59) may be infinite. Please state explicit regularity conditions in Theorem 3, or restrict the theorem to models satisfying them and handle the singular case separately.
[Appendix A, Eqs. (30)-(34)] The binning error calculation in the asymptotic proof of Theorem 1 is not correct as written. The probability that a given codeword u(i') falls into the received bin B(1) is 2^{-nR_2}, not 2^{-n(R_1-R_2)}; and the number of codewords in the whole codebook that are jointly typical with a fixed y is of order 2^{n(R_1 - I(U;Y))}. The resulting exponent should be n(R_2 - R_1 + I(U;Y) - epsilon), and the condition for P[E4] -> 0 is R_2 > R_1 - I(U;Y), which is the standard Wyner-Ziv condition when R_1 is close to I(X;U). The printed condition R_1-R_2 < I(U;Y)+epsilon has the wrong direction and does not follow from the displayed calculation. This should be corrected, since Theorem 1 is one of the two central claims.

minor comments (4)

[Section IV-B, Eq. (24)] Eq. (24) states an additive term 2*gamma/M, but the proof of Theorem 3 uses and needs an additive term 1/n; no argument is given for the displayed constant. Please reconcile the two bounds.
[Theorem 3 statement] The notation inf_R in (26) is unclear: the left-hand side already takes an infimum over R in Definition 2, and the right-hand side's second term e_1 S(V,epsilon)/sqrt(n) is a set rather than a scalar unless a particular b* in S(V,epsilon) is chosen. Please spell out how R enters b* and the sense in which the set-valued dispersion region is used.
[References] Reference [11] duplicates reference [9]; the two entries should be merged or distinguished.
[After Theorem 3] The word "infinum" should be "infimum", and the sentence "The infinum is taken on the rate R that implicitly appears in the second term" is too terse to be useful without the clarification requested above.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the achievability bounds rest on the external Poisson matching lemma and the multidimensional Berry-Esseen theorem; the authors' self-citation [21] is not load-bearing.

full rationale

The paper's derivation chain is self-contained against external results. Theorem 1's asymptotic rate-distortion function is obtained in Appendix A from standard achievability and converse arguments for Wyner-Ziv coding, with the modified distortion measure credited to [3]; the result is not assumed in its own proof. Lemma 1 and Lemma 2 are proved directly from the optimization in Theorem 1. Theorem 2 is derived from the conditional Poisson matching lemma of [14], applied to the actual coding scheme; no fitted parameter, calibration, or target-dependent choice is used to obtain the excess-probability bound. Theorem 3 is proved in Appendix C by applying the multidimensional Berry-Esseen theorem of [23] to the information-density-distortion vector (59); the Gaussian approximation and the dispersion region are defined from the covariance of that vector, and the proof does not rely on a prior result whose content is equivalent to the theorem. The citation of the authors' own work [21] appears only as an ancillary reference for a standard technique ('as in [13], [21]') and is not load-bearing. The BA algorithm is used solely for numerical evaluation and does not enter the proofs of Theorems 2 or 3. The paper also openly notes the looseness of the finite-blocklength Gaussian approximation at small n, which is an accuracy limitation rather than a circularity. The skeptic's concern about the direction of inequality in Eq. (63) and the unstated positive-definiteness/moment conditions in Theorem 3 are proof-correctness issues, not instances of a claim reducing to its own inputs; therefore they do not raise the circularity score.

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

The paper introduces no new physical entities and no fitted constants in its theorems; the assumptions are standard i.i.d., Markov chain, absolute continuity, and external probabilistic lemmas. The numerical example uses hand-chosen source parameters and BA tuning parameters, which do not enter the theoretical claims.

assumptions (5)

domain assumption The triplet (S_i,X_i,Y_i) is i.i.d. from P_SXY = P_S P_{XY|S}, with P_XY positive where needed.
Section II-B defines the source model; the modified distortion d' in (13) divides by P_XY(x,y), which requires positivity on the support.
domain assumption The auxiliary random variable U satisfies the Markov chain U - X - Y and the test channel P_{U|X} satisfies absolute continuity P_UX << P_U x P_X and P_UY << P_U x P_Y.
Used in Theorem 1 and Theorem 2; the absolute continuity conditions are stated just before (19) but not proven for all source models.
standard math The Poisson matching lemma (Lemma 3) is correct for Polish alphabets with base measure nu.
External result from [14], used in the proof of Theorem 2 as a black box.
standard math The multidimensional Berry-Esseen theorem applies to the information-density-distortion vector with finite third moments and positive definite covariance V.
External result [23], used in Appendix C; Theorem 3 does not verify the conditions.
domain assumption For the classification example, S is binary uniform and (X,Y) is a Gaussian mixture with covariance matrices Sigma_0 and Sigma_1.
Section V-A defines this model for the numerical evaluation; not a general result.

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Cite this review

Pith. "Pith review of Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding." pith.science (2026). https://pith.science/paper/FOB2WOFD

@misc{pith2026250717432,
  author       = {Pith},
  title        = {Pith review of: Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FOB2WOFD}},
  note         = {Machine review of arXiv:2507.17432}
}

abstract

In the Wyner-Ziv source coding problem, a source $X$ has to be encoded while the decoder has access to side information $Y$. This paper investigates the indirect setup, in which a latent source $S$, unobserved by both the encoder and the decoder, must also be reconstructed at the decoder. This scenario is increasingly relevant in the context of goal-oriented communications, where $S$ can represent semantic information obtained from $X$. This paper derives the indirect Wyner-Ziv rate-distortion function in asymptotic regime and provides an achievable region in finite block-length. Furthermore, a Blahut-Arimoto algorithm tailored for the indirect Wyner-Ziv setup, is proposed. This algorithm is then used to give a numerical evaluation of the achievable indirect rate-distortion region when $S$ is treated as a classification label.

Figures

Figures reproduced from arXiv: 2507.17432 by the authors.

**Figure 2.** RW Z (D, Ds) in finite block-length regimes. asymptotic coding rate RW Z(D, Ds). Finally, the dispersion region is obtained by evaluating the covariance matrix V for the considered blocklength n. In the sequel, we set σ 2 X = 2, σ2 Y = 1, θ0 = 1, θ1 = −1. We use 100 discretization levels between −10 and 10, for both X and Y , in order to solve (17) by exhaustive search. Furthermore, the maximum iteration and tolera… view at source ↗

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Works this paper leans on

23 extracted references · 20 canonical work pages

[5]

A rate distortion approach to goal-oriented communication,

P. A. Stavrou and M. Kountouris, “A rate distortion approach to goal-oriented communication,” in2022 IEEE International Symposium on Information Theory (ISIT), 2022, pp. 590–595

work page 2022
[7]

Distributed indirect source coding with decoder side information,

J. Tang, Q. Yang, and D. G¨ und¨ uz, “Distributed indirect source coding with decoder side information,”arXiv preprint arXiv:2405.13483, 2024

arXiv 2024
[1]

The rate-distortion function for source coding with side information at the decoder,

A. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,”IEEE Transac- tions on information Theory, vol. 22, no. 1, pp. 1–10, 1976

work page 1976
[2]

Information transmission with additional noise,

R. Dobrushin and B. Tsybakov, “Information transmission with additional noise,”IRE Transactions on Information Theory, vol. 8, no. 5, pp. 293–304, 1962

work page 1962
[3]

Indirect rate distortion problems,

H. Witsenhausen, “Indirect rate distortion problems,”IEEE Transactions on Information Theory, vol. 26, no. 5, pp. 518– 521, 1980

work page 1980
[4]

A rate-distortion framework for characterizing semantic information,

J. Liu, W. Zhang, and H. V. Poor, “A rate-distortion framework for characterizing semantic information,” in2021 IEEE Inter- national Symposium on Information Theory (ISIT). IEEE, 2021, pp. 2894–2899

work page 2021
[6]

Semantic compression with side information: A rate-distortion perspective,

T. Guo, Y. Wang, J. Han, H. Wu, B. Bai, and W. Han, “Semantic compression with side information: A rate-distortion perspective,”arXiv:2208.06094, 2022

arXiv 2022
[8]

Indirect Lossy Source Coding with Observed Source Reconstruction: Nonasymptotic Bounds and Second-Order Asymptotics

H. Yang, Y. Shi, S. Shao, and X. Yuan, “Joint data and semantics lossy compression: Nonasymptotic and second-order achievability bounds,”arXiv preprint arXiv:2401.14962, 2024

work page Pith review arXiv 2024

Show all 23 references

[9]

Channel coding rate in the finite blocklength regime,

Y. Polyanskiy, H. V. Poor, and S. Verd´ u, “Channel coding rate in the finite blocklength regime,”IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2307–2359, 2010

2010
[10]

Fixed-length lossy compression in the finite blocklength regime,

V. Kostina and S. Verdu, “Fixed-length lossy compression in the finite blocklength regime,”IEEE Transactions on Information Theory, vol. 58, no. 6, pp. 3309–3338, 2012

2012
[11]

Channel coding rate in the finite blocklength regime,

Y. Polyanskiy, H. V. Poor, and S. Verdu, “Channel coding rate in the finite blocklength regime,”IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2307–2359, 2010

2010
[12]

On the dispersions of three network information theory problems,

V. Y. F. Tan and O. Kosut, “On the dispersions of three network information theory problems,”IEEE Transactions on Information Theory, vol. 60, no. 2, pp. 881–903, 2014

2014
[13]

Nonasymp- totic and second-order achievability bounds for coding with side-information,

S. Watanabe, S. Kuzuoka, and V. Y. Tan, “Nonasymp- totic and second-order achievability bounds for coding with side-information,”IEEE Transactions on Information Theory, vol. 61, no. 4, pp. 1574–1605, 2015

2015
[14]

A unified framework for one- shot achievability via the poisson matching lemma,

C. T. Li and V. Anantharam, “A unified framework for one- shot achievability via the poisson matching lemma,”IEEE Transactions on Information Theory, vol. 67, no. 5, pp. 2624– 2651, 2021

2021
[15]

Thomas and A

M. Thomas and A. T. Joy,Elements of information theory. Wiley-Interscience, 2006

2006
[16]

The rate-distortion function for source coding with side information at the decoder-ii: General sources,

A. D. Wyner, “The rate-distortion function for source coding with side information at the decoder-ii: General sources,”In- formation and control, vol. 38, pp. 60–80, 1978

1978
[17]

An algorithm for computing the capacity of ar- bitrary discrete memoryless channels,

S. Arimoto, “An algorithm for computing the capacity of ar- bitrary discrete memoryless channels,”IEEE Transactions on Information Theory, vol. 18, no. 1, pp. 14–20, 1972

1972
[18]

F. M. Willems,Computation of the Wyner-Ziv rate-distortion function. Technische Hoge-school Eindhoven, 1983

1983
[19]

Strong functional representation lemma and applications to coding theorems,

C. T. Li and A. E. Gamal, “Strong functional representation lemma and applications to coding theorems,” in2017 IEEE International Symposium on Information Theory (ISIT), 2017, pp. 589–593

2017
[20]

Non-asymptotic achievability bounds in multiuser information theory,

S. Verd´ u, “Non-asymptotic achievability bounds in multiuser information theory,” in2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2012, pp. 1–8

2012
[21]

Distributed source coding for parametric and non-parametric regression,

J. Wei, E. Dupraz, and P. Mary, “Distributed source coding for parametric and non-parametric regression,”arXiv preprint arXiv:2404.18688, 2024

2024 arXiv
[22]

Successive refinement of information,

W. Equitz and T. Cover, “Successive refinement of information,” IEEE Transactions on Information Theory, vol. 37, no. 2, pp. 269–275, 1991

1991
[23]

On the Rate of Convergence in the Multivariate CLT,

F. Gotze, “On the Rate of Convergence in the Multivariate CLT,”The Annals of Probability, vol. 19, no. 2, pp. 724 – 739, 1991. Appendix A Proof of Theorem 1 The proof is a combination of the rate-distortion prob- lem with two constraints [15] and the conventional Wyner- Ziv [1...

1991

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [5]

A rate distortion approach to goal-oriented communication,

P. A. Stavrou and M. Kountouris, “A rate distortion approach to goal-oriented communication,” in2022 IEEE International Symposium on Information Theory (ISIT), 2022, pp. 590–595

work page 2022

[2] [7]

Distributed indirect source coding with decoder side information,

J. Tang, Q. Yang, and D. G¨ und¨ uz, “Distributed indirect source coding with decoder side information,”arXiv preprint arXiv:2405.13483, 2024

arXiv 2024

[3] [1]

The rate-distortion function for source coding with side information at the decoder,

A. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,”IEEE Transac- tions on information Theory, vol. 22, no. 1, pp. 1–10, 1976

work page 1976

[4] [2]

Information transmission with additional noise,

R. Dobrushin and B. Tsybakov, “Information transmission with additional noise,”IRE Transactions on Information Theory, vol. 8, no. 5, pp. 293–304, 1962

work page 1962

[5] [3]

Indirect rate distortion problems,

H. Witsenhausen, “Indirect rate distortion problems,”IEEE Transactions on Information Theory, vol. 26, no. 5, pp. 518– 521, 1980

work page 1980

[6] [4]

A rate-distortion framework for characterizing semantic information,

J. Liu, W. Zhang, and H. V. Poor, “A rate-distortion framework for characterizing semantic information,” in2021 IEEE Inter- national Symposium on Information Theory (ISIT). IEEE, 2021, pp. 2894–2899

work page 2021

[7] [6]

Semantic compression with side information: A rate-distortion perspective,

T. Guo, Y. Wang, J. Han, H. Wu, B. Bai, and W. Han, “Semantic compression with side information: A rate-distortion perspective,”arXiv:2208.06094, 2022

arXiv 2022

[8] [8]

Indirect Lossy Source Coding with Observed Source Reconstruction: Nonasymptotic Bounds and Second-Order Asymptotics

H. Yang, Y. Shi, S. Shao, and X. Yuan, “Joint data and semantics lossy compression: Nonasymptotic and second-order achievability bounds,”arXiv preprint arXiv:2401.14962, 2024

work page Pith review arXiv 2024