Source-linked AI summary
Interference-Assisted Secret Communication
Xiaojun Tang, Ruoheng Liu, Predrag Spasojevic, H. Vincent Poor
TL;DR
Wireless broadcast transmission makes confidential communication susceptible to eavesdropping. This paper studies a wiretap channel with an independent helping interferer and gives an achievable secrecy rate; its results show that interference can assist secrecy, including when the source-destination channel is worse than the source-eavesdropper channel.
Problem
Broadcast transmission makes wireless communication susceptible to eavesdropping, motivating study of confidential transmission with a passive eavesdropper and an independent helper.
Source: §I · p. 1Method
The paper models a wiretap channel with a helping interferer and gives an achievable secrecy rate using independent stochastic codebooks.
Source: §I · p. 1, §II · p. 2, §III · p. 2Results
The results show that the interferer can increase secrecy, with a positive secrecy rate possible even when the source-destination channel is worse than the source-eavesdropper channel.
Source: §I · p. 1Takeaways & Limitations
Independent interference can be exploited to benefit secret wireless communication by counteracting the eavesdropping threat associated with broadcast transmission.
Source: §I · p. 1, §VII · p. 5
Abstract
from arXiv · showhide
Wireless communication is susceptible to adversarial eavesdropping due to the broadcast nature of the wireless medium. In this paper it is shown how eavesdropping can be alleviated by exploiting the superposition property of the wireless medium. A wiretap channel with a helping interferer (WT-HI), in which a transmitter sends a confidential message to its intended receiver in the presence of a passive eavesdropper, and with the help of an independent interferer, is considered. The interferer, which does not know the confidential message, helps in ensuring the secrecy of the message by sending independent signals. An achievable secrecy rate for the WT-HI is given. The results show that interference can be exploited to assist secrecy in wireless communications. An important example of the Gaussian case, in which the interferer has a better channel to the intended receiver than to the eavesdropper, is considered. In this situation, the interferer can send a (random) codeword at a rate that ensures that it can be decoded and subtracted from the received signal by the intended receiver but cannot be decoded by the eavesdropper. Hence, only the eavesdropper is interfered with and the secrecy level of the confidential message is increased.
I. INTRODUCTION
The paper studies whether an independent interferer can use wireless superposition to counter eavesdropping caused by broadcast transmission. It models a transmitter, intended receiver, helper, and passive eavesdropper, then presents achievable secrecy results and a Gaussian case in which the helper can be decoded by the receiver but not the eavesdropper.
I. INTRODUCTION
- Broadcast transmission enables eavesdropping, while superposition also permits adversarial interference that can block intended communication.The paper proposes using superposition in the helper's independent transmission to counter the broadcast-related security threat.Source: §I · p. 1
- The helper can increase secrecy, including achieving a positive secrecy rate when the source-destination channel is worse than the source-eavesdropper channel.In the Gaussian example, the helper's codeword can be decoded and subtracted by the intended receiver but not decoded by the eavesdropper.Source: §I · p. 1
- For the WT-HI, the paper gives an achievable secrecy rate under perfect secrecy and a geometrical interpretation; for a symmetric Gaussian WT-HI, it gives an achievable secrecy rate and power control.Positive secrecy is achievable even when the source-destination channel is worse than the source-eavesdropper channel.Source: §I · p. 1
II. SYSTEM MODEL
- The WT-HI model has a transmitter sending a confidential message to an intended receiver with an independent helper and a passive eavesdropper.The helper does not know the confidential message, and the eavesdropper knows both codebooks.Source: §II · p. 2
III. ACHIEVABLE SECRECY RATE
The section gives an achievable secrecy rate for the WT-HI using independent stochastic codebooks. The transmitter's rate is split between confidential information and redundancy, while the helper sends dummy information that can further confuse the eavesdropper.
III. ACHIEVABLE SECRECY RATE
- The achievable MAC rate region at the intended receiver is defined by individual rate bounds and a sum-rate bound.The section also gives corresponding eavesdropper MAC bounds and additional rate constraints involving its individual decoding conditions.Source: §III · p. 2
- An achievable secrecy rate for the WT-HI is stated using independent input distributions and the channel transition law.The coding construction uses independent stochastic codebooks for the transmitter and helper, with the transmitter's codewords randomly binned by confidential message.Source: §III · p. 2
- The transmitter splits its rate into secrecy information and redundancy, while the helper sends dummy information to confuse the eavesdropper.The transmitter randomly selects a codeword from the bin for the confidential message, and the helper randomly selects a codeword from its codebook.Source: §III · p. 2
IV. GEOMETRIC INTERPRETATIONS
The geometrical interpretation compares code-rate regions for the intended receiver and eavesdropper. The receiver may decode both codewords or treat the helper's codeword as noise, while a suitable helper rate can put the eavesdropper in an unfavorable condition.
IV. GEOMETRIC INTERPRETATIONS
- The receiver does not need to decode the helper's codeword in the treat-as-noise case.The region is described as a union that includes both the MAC capacity region and the region where the receiver decodes C1 alone.Source: §IV · p. 3
- The intended receiver's achievable rate region combines decoding both codewords with decoding the transmitter's codeword while treating the helper's as noise.The figure plots code rate R1 versus R2 for the intended receiver and eavesdropper.Source: §IV · p. 3, Figure 1 · p. 3
- The eavesdropper has corresponding decoding-region cases, and choosing the helper rate R2 appropriately can place it in an unfavorable condition.The analysis considers very strong, strong, and weak interference; the general-case analysis is cited to.Source: §IV · p. 3
A. Very Strong Interference
In the very strong interference case considered here, no positive secrecy rate is obtained.
A. Very Strong Interference
- The result is specifically scoped to the very strong interference case.The section introduces this setting alongside Fig. 2.Source: A. Very Strong Interference · p. 3, Figure 2 · p. 3
- The paper reports that no positive secrecy rate can be obtained in this case.This is the stated outcome for the very strong interference case.Source: A. Very Strong Interference · p. 3
- Fig. 2 depicts the very strong interference channel.The supplied passage identifies the figure's setting but gives no further plotted details.Source: Figure 2 · p. 3
B. Strong Interference
In the strong-interference setting, the eavesdropper’s channel can be more capable than the intended receiver’s without help, leaving the achievable secrecy rate potentially zero. A helping interferer can nevertheless support positive secrecy by enabling receiver decoding while confusing the eavesdropper.
B. Strong Interference
- Without the interferer, the strong-interference condition makes X1 → Y2 more capable than X1 → Y1, so the achievable secrecy rate may be zero.The condition is stated for all product distributions on X1 and X2.Source: B. Strong Interference · p. 3
- With the helper, the selected rate pair lets the intended receiver decode C2 before C1 while dummy-rate randomness confuses the eavesdropper.The figure identifies the strong-interference channel and states I(X1, X2; Y1) > I(X1, X2; Y2).Source: B. Strong Interference · p. 3, Figure 3 · p. 3
C. Weak Interference
The section describes weak-interference conditions under which the helper can increase secrecy, and then introduces a symmetric Gaussian WT-HI setting for rate analysis.
C. Weak Interference
- When ∆1 ≤ ∆2, the helper can increase achievable secrecy; the weak-interference conditions compare the conditional receiver and eavesdropper information rates.For ∆1 > ∆2, the text says the helper can facilitate transmission by choosing X2 to maximize ∆1.Source: C. Weak Interference · p. 3, Figure 4 · p. 3
V. SYMMETRIC GAUSSIAN CHANNELS
- The symmetric Gaussian setting equates the source–eavesdropper and interferer–receiver channel conditions, with unit-variance Gaussian noise and average block-power constraints.The paper notes that general parameter settings are treated in.Source: §V · p. 4, Figure 5 · p. 4
A. Achievable Secrecy Rate
For a symmetric Gaussian WT-HI using Gaussian codebooks, the paper gives an achievable secrecy rate across interference regimes. It finds that helper power can permit positive secrecy beyond the no-helper condition.
A. Achievable Secrecy Rate
- Theorem 2 gives the achievable Gaussian secrecy rate in cases determined by a and the powers P1 and P2.For a ≥ 1 + P2, the rate is zero; the remaining cases are stated separately for 1 ≤ a < 1 + P2 and a < 1.Source: A. Achievable Secrecy Rate · p. 4
- The achievability scheme uses Gaussian input distributions, with Gaussian codebooks of average block powers P1 and P2.The powers are constrained by their respective upper bounds.Source: A. Achievable Secrecy Rate · p. 4
- With sufficiently large interferer power, positive secrecy is achievable for any a > 0; without a helper, positive secrecy requires a < 1.The no-helper comparison is the Gaussian wiretap channel.Source: A. Achievable Secrecy Rate · p. 4
B. Power Control
The section presents power control as a way to maximize the Gaussian WT-HI secrecy rate. Its effect depends on whether a is below or above one.
B. Power Control
- The maximizing power-control scheme is stated separately for a ≥ 1 and a < 1.The supplied theorem excerpts give the regime split but do not provide a complete readable expression for both choices.Source: B. Power Control · p. 4
- When a < 1, the interferer limits its power to avoid bringing too much interference to the primary transmission.When a ≥ 1, transmitter power control both reduces leakage to the eavesdropper and allows the intended receiver to decode and cancel interference.Source: B. Power Control · p. 4
C. Power-Unconstrained Secrecy Rate
The section considers the achievable secrecy rate when transmitter power is unconstrained and gives a result for the symmetric Gaussian WT-HI. Its rate depends on interference strength: weak interference doubles the achievable secrecy rate, while strong interference gives a rate matching a specified wiretap scenario.
C. Power-Unconstrained Secrecy Rate
- The power-unconstrained secrecy rate is tied to channel conditions and is the maximal achievable rate regardless of how large the transmit power is.The section introduces this quantity as a fundamental parameter of wireless secrecy systems.Source: C. Power-Unconstrained Secrecy Rate · p. 4
- Theorem 4 gives the achievable power-unconstrained secrecy rate for the symmetric GWT-HI.The supplied theorem statement does not include the full rate expression.Source: C. Power-Unconstrained Secrecy Rate · p. 5
- When interference is weak (a < 1), the interferer doubles the achievable secrecy rate; when it is strong (a > 1), the rate is (1/2) log2 a.For strong interference, this also equals the power-unconstrained secrecy rate when confidential messages are sent from the interferer to the intended receiver, without assuming a source-interferer channel.Source: C. Power-Unconstrained Secrecy Rate · p. 5
VI. NUMERICAL EXAMPLES
The numerical examples show how power control and interference strength affect achievable secrecy rates, including comparisons between the Gaussian WT-HI and the Gaussian wiretap channel. The conclusion is that independent interference can benefit secret wireless communication.
VI. NUMERICAL EXAMPLES
- With P1=2, at a=2 the power control scheme uses maximum interferer power and P1*=1; at a=1/2 it caps interferer power at P2*=2/3.The first setting lets the intended receiver decode interference first; in the second, the intended receiver treats interference as noise.Source: §VI · p. 5
- With P1=P2=2, GWT-HI Rs decreases for a < 1, rises for 1 < a ≤ 1.73, then falls; Rs=0 for a ≥ 3, while GWT Rs=0 for a ≥ 1.At a ≥ 3, the eavesdropper can decode the primary transmission by treating interference as noise.Source: Figure 7 · p. 5, §VI · p. 5
VII. CONCLUSIONS
- The paper concludes that independent interference can be exploited to benefit secret wireless communication.The conclusion attributes this approach to using the wireless medium's superposition property against eavesdropping associated with its broadcast nature.Source: §VII · p. 5