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arxiv: 1907.04599 · v1 · pith:4YSLR352new · submitted 2019-07-10 · 💻 cs.IT · math.IT

Adding Common Randomness Can Remove the Secrecy Constraints in Communication Networks

Fan Li , Jinyuan Chen This is my paper

Pith reviewed 2026-05-24 23:37 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords common randomnesssecrecy constraintsgeneralized degrees of freedomGaussian interference channelwiretap channelmultiple access channelinterference neutralization
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The pith

Adding common randomness at transmitters removes the GDoF penalty from secrecy constraints in three Gaussian networks.

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

The paper establishes that sharing common randomness among transmitters eliminates the generalized degrees-of-freedom loss caused by secrecy requirements in three basic communication settings. This is shown for the two-user symmetric Gaussian interference channel with confidential messages, the symmetric Gaussian wiretap channel with a helper, and the two-user symmetric Gaussian multiple access wiretap channel. The method uses the randomness to jam eavesdroppers while neutralizing it at legitimate receivers through a Markov chain technique. Characterizing the minimal amount of such randomness needed further supports its practicality. If true, this means secrecy can be achieved without rate penalty in terms of GDoF by using shared random bits generated offline.

Core claim

In this work we show that adding common randomness at the transmitters can totally remove the penalty in GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to remove the secrecy constraints in communication networks in terms of GDoF performance. Common randomness can be generated offline. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness.

What carries the argument

Common randomness shared only among legitimate transmitters, used via Markov chain-based interference neutralization to jam eavesdroppers while being canceled at intended receivers.

If this is right

  • The GDoF region of the two-user symmetric Gaussian interference channel with confidential messages matches the non-secrecy case.
  • The GDoF of the symmetric Gaussian wiretap channel with a helper reaches the non-secrecy value.
  • The GDoF region of the two-user symmetric Gaussian multiple access wiretap channel is unaffected by secrecy.
  • The minimal GDoF of common randomness required to remove the secrecy penalty is characterized for most cases.

Where Pith is reading between the lines

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

  • The neutralization technique might extend to larger multi-user networks where secrecy typically reduces GDoF.
  • Pre-sharing the common randomness offline could be done through a one-time secure channel before data transmission begins.
  • The separation of jamming from rate loss suggests testing whether similar shared randomness removes secrecy penalties in non-Gaussian or fading settings.

Load-bearing premise

The common randomness is generated offline and shared only among the legitimate transmitters, enabling it to jam eavesdroppers while being neutralized at legitimate receivers via the proposed Markov chain method.

What would settle it

Showing that the secrecy-constrained GDoF in any one of the three channels remains strictly below the non-secrecy GDoF even after adding arbitrary amounts of common randomness would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.04599 by Fan Li, Jinyuan Chen.

Figure 1
Figure 1. Figure 1: The optimal secure sum GDoF vs. α, for two-user symmetric Gaussian interference channels without and with common randomness (CR), where α is a channel parameter indicating the interference-to-signal ratio. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. By jamming the information signal at the eavesd… view at source ↗
Figure 2
Figure 2. Figure 2: Markov chain-based interference neutralization at the receivers, for a two-user interference channel with [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

In communication networks secrecy constraints usually incur an extra limit in capacity or generalized degrees-of-freedom (GDoF), in the sense that a penalty in capacity or GDoF is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to remove the secrecy constraints in communication networks, i.e., how to remove the GDoF penalty due to secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to remove the secrecy constraints in communication networks in terms of GDoF performance. Common randomness can be generated offline. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we hope to use less common randomness to remove secrecy constraints in terms of GDoF performance. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to remove secrecy constraints, based on our derived converses and achievability.

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

0 major / 3 minor

Summary. The paper studies three symmetric Gaussian settings with secrecy constraints—the two-user interference channel with confidential messages, the wiretap channel with a helper, and the two-user multiple-access wiretap channel—and claims that common randomness generated offline and shared only among the legitimate transmitters (unknown to eavesdroppers) completely eliminates the GDoF penalty induced by secrecy. Achievability is obtained via a Markov-chain-based interference neutralization scheme that jams the eavesdropper while canceling at legitimate receivers; matching converses are derived for the minimal GDoF of common randomness needed in most cases.

Significance. If the derivations hold, the result is significant: it shows that a modest amount of common randomness suffices to remove secrecy-induced GDoF loss entirely in these canonical models, with explicit converses characterizing the minimal common-randomness GDoF. The combination of matching achievability and converse bounds, together with the explicit neutralization construction, provides a clean and falsifiable contribution to the GDoF literature on secure networks.

minor comments (3)
  1. The description of the Markov-chain neutralization step would benefit from an explicit statement of the required joint distribution (or the precise Markov chain) in the achievability scheme for at least one of the three settings.
  2. Notation for the common-randomness GDoF (e.g., whether it is normalized per transmitter or total) should be defined once at the beginning and used consistently across all three models.
  3. A compact table comparing the secrecy-constrained GDoF, the GDoF with common randomness, and the minimal common-randomness GDoF for each of the three channels would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of the manuscript, including the accurate summary of the contributions and the recommendation for minor revision. No specific major comments are listed in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper derives GDoF achievability via explicit constructions that employ offline common randomness and a Markov-chain neutralization scheme designed to cancel at legitimate receivers while jamming eavesdroppers, together with matching converses obtained from standard information-theoretic bounding techniques on the channel models. These steps are grounded directly in the Gaussian interference, wiretap, and MAC settings without reducing any claimed prediction or minimal common-randomness GDoF to a fitted parameter, self-definition, or load-bearing self-citation. The central claim therefore follows from independent constructions and bounds rather than by construction from its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard domain assumptions for Gaussian channels and the offline generation of common randomness available only to transmitters; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The networks are symmetric Gaussian channels with additive white Gaussian noise independent across links.
    This is the standard modeling assumption invoked for the three settings in the abstract.

pith-pipeline@v0.9.0 · 5829 in / 1288 out tokens · 44499 ms · 2026-05-24T23:37:20.727127+00:00 · methodology

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Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 3 internal anchors

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