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arxiv: 2604.20245 · v1 · submitted 2026-04-22 · 💻 cs.IT · cs.CR· cs.CV· eess.IV· math.IT

Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism

Gustaf {\AA}hlgren , Onur G\"unl\"u This is my paper

Pith reviewed 2026-05-09 23:37 UTC · model grok-4.3

classification 💻 cs.IT cs.CRcs.CVeess.IVmath.IT
keywords secure rate-distortion-perceptioncommon randomnessrandom binningbroadcast channelsside informationstrong secrecy
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The pith

For noiseless channels the exact secure rate-distortion-perception region is characterized and separate source-channel coding is optimal with unlimited common randomness.

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

The paper determines the fundamental trade-offs for secure rate-distortion-perception coding, where compressed data must be sent over public channels with negligible leakage while preserving perceptual quality. For noiseless channels the complete secure RDP region is exactly characterized, and separate source-channel coding achieves this region optimally when encoder and decoder share unlimited common randomness. The results matter for applications such as neural image compression over insecure networks, because they show that common randomness can reduce required rates in ways not seen in ordinary rate-distortion problems. Binary and Gaussian examples confirm that random binning simultaneously delivers strong secrecy, low distortion, and high perceptual quality.

Core claim

For noiseless channels, the exact secure RDP region is characterized. Separate source-channel coding is optimal for this exact secure RDP region with unlimited common randomness available. For broadcast channels with correlated noise components, an inner bound is derived and shown to be tight for a class of more-capable BCs. When both encoder and decoder have access to side information correlated with the source and the channel is noiseless, the exact RDP region is established. If only the decoder has correlated side information in the noiseless setting, an inner bound is derived along with a special case where the region is exact.

What carries the argument

Random binning-based coding scheme that simultaneously achieves strong secrecy, low distortion, and high perceptual quality.

If this is right

  • Common randomness significantly reduces the communication rate in secure RDP settings for both binary and Gaussian sources.
  • The inner bound derived for broadcast channels is tight for more-capable channels.
  • Side information at both encoder and decoder yields an exact RDP region over noiseless channels.
  • Side information only at the decoder yields an inner bound with at least one exact special case.

Where Pith is reading between the lines

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

  • Shared randomness could be generated in practice to lower bandwidth demands in secure perceptual compression systems.
  • The random-binning approach may extend to additional channel models where perception metrics replace or supplement distortion measures.
  • Security constraints appear to interact with perception goals differently than they do with pure distortion.

Load-bearing premise

Unlimited common randomness is available between encoder and decoder and the perception metric permits random binning to achieve strong secrecy, low distortion, and high perceptual quality at once.

What would settle it

A concrete calculation for the binary or Gaussian source showing that common randomness fails to reduce the communication rate while still meeting strong secrecy and the perception target.

Figures

Figures reproduced from arXiv: 2604.20245 by Gustaf {\AA}hlgren, Onur G\"unl\"u.

Figure 1
Figure 1. Figure 1: The system model of the secure RDP problem with transmis [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The system model of the secure noisy RDP problem with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: The system model of the secure noisy RDP problem with [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: The system model of the secure RDP problem where the side [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: We further assume that the side information [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: The achievable rate region’s boundary for the communication [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication channels, security risks emerge. We therefore study secure RDP under negligible information leakage over both noiseless channels and broadcast channels, BCs, with correlated noise components. For noiseless channels, the exact secure RDP region is characterized. For BCs, an inner bound is derived and shown to be tight for a class of more-capable BCs. Separate source-channel coding is further shown to be optimal for this exact secure RDP region with unlimited common randomness available. Moreover, when both encoder and decoder have access to side information correlated with the source and the channel is noiseless, the exact RDP region is established. If only the decoder has correlated side information in the noiseless setting, an inner bound is derived along with a special case where the region is exact. Binary and Gaussian examples demonstrate that common randomness can significantly reduce the communication rate in secure RDP settings, unlike in standard rate-distortion settings. Thus, our results illustrate that random binning-based coding achieves strong secrecy, low distortion, and high perceptual quality simultaneously.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper characterizes the exact secure rate-distortion-perception (RDP) region for noiseless channels and derives an inner bound for broadcast channels that is tight for more-capable BCs. It proves the optimality of separate source-channel coding under unlimited common randomness and analyzes side information scenarios. Binary and Gaussian examples are provided to show that common randomness can reduce the required communication rate while satisfying strong secrecy, distortion, and perception constraints simultaneously.

Significance. If the derivations hold, this work makes a significant contribution by integrating security into the RDP framework using a randomized distributed function computation approach. The exact characterizations and the demonstration that random binning achieves all three goals without rate penalty under unlimited common randomness are important for theoretical understanding and practical applications in secure perceptual data compression. The results on side information and channel models further broaden the applicability.

major comments (1)
  1. [Results for noiseless channels (Section 3)] The exact secure RDP region characterization in the noiseless case relies on unlimited common randomness for the random binning scheme to simultaneously achieve strong secrecy, the distortion constraint, and the perception constraint. This is load-bearing for the claim that the achievable region matches the converse without extra rate cost, as noted in the binary and Gaussian examples. The paper should clarify if any rate overhead is incurred when common randomness is limited.
minor comments (2)
  1. [Abstract] The abstract mentions 'randomized distributed function computation approach' but the introduction or Section 2 could better explain how this differs from standard random binning in secure rate-distortion theory.
  2. [Examples section] In the binary and Gaussian examples, the specific values of the perception metric and how it is computed should be detailed to allow readers to verify the rate reductions claimed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [Results for noiseless channels (Section 3)] The exact secure RDP region characterization in the noiseless case relies on unlimited common randomness for the random binning scheme to simultaneously achieve strong secrecy, the distortion constraint, and the perception constraint. This is load-bearing for the claim that the achievable region matches the converse without extra rate cost, as noted in the binary and Gaussian examples. The paper should clarify if any rate overhead is incurred when common randomness is limited.

    Authors: We thank the referee for this observation. The exact secure RDP region characterization for noiseless channels in Section 3 is derived under the assumption of unlimited common randomness, which enables the random binning scheme to simultaneously satisfy strong secrecy, the distortion constraint, and the perception constraint without additional rate cost. This assumption is stated explicitly in the manuscript (e.g., in the abstract and the optimality result for separate source-channel coding), and the binary and Gaussian examples are presented to illustrate the rate-reduction benefit that common randomness provides under this model. The paper does not analyze the limited common randomness case; determining whether rate overhead would be incurred in that setting would require a separate analysis and is beyond the current scope. We will add a clarifying remark in the revised manuscript to emphasize the unlimited common randomness assumption and to note that the limited case remains an open direction for future research. revision: yes

Circularity Check

0 steps flagged

No circularity: bounds derived from standard information inequalities and explicit modeling assumptions

full rationale

The paper characterizes the exact secure RDP region for noiseless channels by deriving matching inner bounds (via random binning with unlimited common randomness) and outer bounds (via standard converse arguments using mutual information and secrecy constraints). Separate source-channel coding optimality is shown under the explicit assumption of unlimited common randomness, which is a modeling choice stated upfront rather than derived from the result. Binary and Gaussian examples illustrate rate reductions but serve as verifications, not as fitted inputs renamed as predictions. No self-definitional equations, fitted parameters called predictions, load-bearing self-citations, or smuggled ansatzes appear in the derivation chain. The results are self-contained against external benchmarks from rate-distortion and secrecy theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard information-theoretic definitions of rate, distortion, perception, and secrecy constraints; no free parameters, invented entities, or ad-hoc axioms are explicitly introduced in the abstract.

axioms (1)
  • standard math Standard definitions and properties of mutual information, rate-distortion functions, and strong secrecy in information theory.
    The paper builds directly on established information theoretic concepts for characterizing regions.

pith-pipeline@v0.9.0 · 5529 in / 1270 out tokens · 45601 ms · 2026-05-09T23:37:39.404446+00:00 · methodology

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