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Secure Short-Packet Communications for Mission-Critical IoT Applications

Hui-Ming Wang, Qian Yang, Zhiguo Ding, H. Vincent Poor

arXiv:1903.01433v1cs.IT

TL;DR

Short-packet IoT communications must satisfy stringent latency and reliability requirements, while the security implications of finite blocklength and secrecy-throughput behavior remain insufficiently understood. The paper develops analytical finite-blocklength approximations for secure IoT systems with multi-antenna eavesdroppers, then derives closed-form single-antenna results and blocklength optimizations. The analysis characterizes secrecy-throughput tradeoffs under secrecy, reliability, and latency constraints.

  • Problem

    The secrecy system throughput and blocklength design needed to balance latency and reliability under secrecy constraints remain unclear for short-packet IoT communications.

  • Method

    The paper proposes a finite-blocklength analytical framework for average secrecy throughput, including closed-form approximations and blocklength optimization for single-antenna and multi-antenna AP systems.

  • Results

    The analysis derives closed-form secrecy-throughput approximations and optimal blocklength results, with secrecy throughput first increasing and then decreasing with N in the stated continuous single-antenna analysis.

  • Takeaways & Limitations

    The obtained analytical results characterize how system parameters and reliability and latency constraints affect secrecy-throughput blocklength design in secure short-packet IoT systems.

Abstract

from arXiv · show

In pervasive Internet of Things (IoT) applications, the use of short packets is expected to meet the stringent latency requirement in ultra-reliable low-latency communications; however, the incurred security issues and the impact of finite blocklength coding on the physical-layer security have not been well understood. This paper comprehensively investigates the performance of secure short-packet communications in a mission-critical IoT system with an external multi-antenna eavesdropper. An analytical framework is proposed to approximate the average achievable secrecy throughput of the system with finite blocklength coding. To gain more insight, a simple case with a single-antenna access point (AP) is considered first, in which the secrecy throughput is approximated in a closed form. Based on that result, the optimal blocklengths to maximize the secrecy throughput with and without the reliability and latency constraints, respectively, are derived. For the case with a multi-antenna AP, following the proposed analytical framework, closed-form approximations for the secrecy throughput are obtained under both beamforming and artificial-noise-aided transmission schemes. Numerical results verify the accuracy of the proposed approximations and illustrate the impact of the system parameters on the tradeoff between transmission latency and reliability under the secrecy constraint.

I. INTRODUCTION

Mission-critical IoT requires short packets for stringent latency and reliability, but finite blocklength changes secure communication analysis and design. This paper develops analytical approximations and blocklength optimization for secrecy throughput in IoT systems with eavesdroppers.

  • Motivation: Mission-critical IoT applications impose stringent latency and reliability constraints, motivating short-packet communications.These requirements arise in applications such as intelligent transportation and industry automation.
  • Motivation: Short packets invalidate conventional long-blocklength channel and wiretap-code analyses because finite blocklength prevents direct use of asymptotic information-theoretic results.IoT packets can potentially contain only hundreds of bits, whereas conventional codes target packet sizes much larger than 10^3 bytes.
  • Research Gap: The paper addresses the limited understanding of secrecy system throughput and blocklength design for balancing latency and reliability under secrecy constraints.Prior finite-blocklength work studied secrecy rates and bounds, but the cited passage states that secrecy system throughput and blocklength design remained unclear.
  • Contributions: An analytical framework approximates average secrecy throughput for secure IoT communication with finite blocklength and a multi-antenna eavesdropper.The framework covers single-antenna and multi-antenna AP cases, with closed-form approximations developed for selected settings.
  • Finite-Blocklength Model: Finite-blocklength secrecy rate approaches secrecy capacity as N grows, while stricter reliability and secrecy constraints reduce achievable secrecy rate.The finite-blocklength penalty diminishes as N approaches infinity; smaller ε and δ represent more stringent constraints.

C. Performance Metrics and Problem Formulation

The paper defines secrecy throughput for finite-blocklength IoT transmission and develops approximations for the single-antenna case. These approximations support analysis of how blocklength and system parameters affect secrecy throughput under reliability, latency, and secrecy constraints.

  • C. Performance Metrics and Problem Formulation: Secrecy throughput is the average secrecy rate at which a B-bit packet is reliably transmitted under a specified information-leakage constraint.The transmission rate is R = B/N, where N is the blocklength.
  • C. Performance Metrics and Problem Formulation: For fixed B, increasing N lowers decoding error probability but also reduces data rate and increases transmission latency.Thus, blocklength captures the latency–reliability tradeoff in the secrecy-throughput metric.
  • A. Secrecy Throughput Approximation: The single-antenna channel model uses Rayleigh fading, with γA exponentially distributed and γE gamma distributed according to the eavesdropper’s antenna count.The analytical framework is summarized in Table I and is used to study finite-blocklength secrecy throughput.
  • A. Secrecy Throughput Approximation: The analytical framework begins by approximating the conditional decoding-error integral that makes the secrecy-throughput calculation intractable.A first-order approximation is introduced before further integration-based simplifications.
  • A. Secrecy Throughput Approximation: Theorem 1 provides an approximation applicable to arbitrary blocklength, although its analytical form is complicated.The approximation is obtained by simplifying the integral lower limit and substituting the resulting expression into the secrecy-throughput formula.
  • A. Secrecy Throughput Approximation: For moderate blocklengths 10^2 ≤ N ≤ 10^3, the paper derives a closed-form single-antenna approximation when |kρA| is large.This regime corresponds to packets containing hundreds of bits and is emphasized for latency-critical IoT applications.
  • A. Secrecy Throughput Approximation: A further simplified approximation applies when both |kρA| and the average eavesdropper SNR E[γE] = KEρE are large.The simplification sets M1 = 0 in the preceding expression and is intended to facilitate performance insight and optimization.
  • A. Secrecy Throughput Approximation: The proposed approximations match simulations over a wide range of N; secrecy throughput increases with ρA and information-leakage tolerance δ but decreases with KE.The results also indicate an optimal blocklength, and Proposition 2 is used for subsequent optimization because of its accuracy and tractability.

B. High-SNR Regime

In the high-SNR regime, the proposed secrecy-throughput approximation remains accurate over a wide range of blocklengths. The average decoding error cannot vanish because the legitimate and eavesdropper SNRs increase together.

  • High-SNR approximation: The approximation in (14) remains accurate over a wide range of N when transmit power approaches infinity.This follows under the condition in Proposition 2.
  • High-SNR behavior: The average decoding error probability cannot decrease to zero as transmit power approaches infinity because both SNRs increase simultaneously.
  • Parameter effects: Secrecy throughput increases with dE and δ but decreases with dA and KE in the high-SNR regime.

C. The Classical Case with Infinite Blocklength

With infinite blocklength, decoding error vanishes when the actuator SNR exceeds the eavesdropper SNR, and the finite-blocklength approximation converges to the classical result. Thus, the derived expression is validated in the large-blocklength regime.

  • Infinite-blocklength behavior: As N approaches infinity, decoding error probability approaches zero when γA > γE and one otherwise.
  • Approximation validation: The result in (17) is obtained from (14) as N approaches infinity, verifying the approximation in the large-blocklength regime.
  • Secrecy condition: When γA > γE, the transmission rate B/N is achievable without information leakage for any positive δ.The rate B/N becomes smaller than the secrecy capacity as N approaches infinity.
  • Optimization scope: The analysis optimizes secrecy throughput first without constraints and then with reliability and latency constraints.

A. Unconstrained Secrecy Throughput Optimization

The single-antenna analysis optimizes blocklength for secrecy throughput while balancing latency and decoding error, first without and then with practical constraints. The throughput is quasi-concave in continuous blocklength, enabling characterization of an optimal solution and parameter-dependent trends.

  • Optimization objective: The blocklength N balances transmission latency and decoding error for a fixed message size B.
  • Unconstrained optimization: Secrecy throughput is quasi-concave in relaxed continuous blocklength N, so the best integer blocklength is selected from {⌈N∗⌉, ⌊N∗⌋}.
  • Optimal blocklength trends: The optimal N∗ increases with ρE, KE, and B, but decreases as P, ρA, and δ increase when δ < 0.5.
  • Interpretation of trends: Larger KEρE or B makes decoding error more pronounced relative to latency, whereas larger P, ρA, or δ reduces error and favors shorter blocklengths.
  • Optimal throughput trends: The optimal secrecy throughput T(N∗) decreases with ρE or KE and increases with B, δ, P, or ρA.
  • Message-size effect: After choosing optimal N, T(N∗) increases monotonically with B rather than remaining quasi-concave in B.
  • Constrained optimization: Under reliability and latency constraints, feasibility requires ¯ε^-1(ζε) ≤ ⌊ζN⌋, and the optimal blocklength follows from the quasi-concavity result.The latency constraint is represented by the maximum tolerable blocklength ζN, while ζε limits average decoding error.

V. ANALYSIS FOR THE MULTI-ANTENNA CASE

For a multi-antenna AP, the paper derives finite-blocklength secrecy-throughput approximations under beamforming and artificial-noise transmission. The approximation closely matches simulation, while more AP antennas and appropriately allocated artificial noise improve secrecy throughput.

  • System model: Multiple AP antennas can improve transmission security by providing extra spatial degrees of freedom.
  • Transmission schemes: MRT transmits the confidential signal, while AN is injected into the legitimate channel's nullspace to confuse the eavesdropper.
  • Transmission schemes: The AN-aided scheme reduces to MRT beamforming when η = 1.
  • Channel information: The AP assumes statistical eavesdropper CSI because it is more practical and varies more slowly than instantaneous CSI.
  • Analytical approximation: Theorem 3 provides a finite-blocklength approximation for secrecy throughput with a multi-antenna AP, using parameters that trade computational complexity against accuracy.M1 ensures VE ≈ 1 when γE > M1, while M2 controls the complexity-accuracy tradeoff.
  • Numerical validation: The theoretical approximation is close to simulation, verifying the accuracy of the proposed multi-antenna analysis.
  • Numerical findings: Secrecy throughput increases with the AP antenna number, and appropriate AN power allocation makes AN-aided transmission superior to plain MRT beamforming.

VI. NUMERICAL RESULTS

The numerical study evaluates secure short-packet communication using fixed simulation settings and extensive channel averaging.

  • Simulation settings: The default configuration uses B = 200, δ = 10−2, KA = 2, and KE = 3.The settings also include ρA = 10 dB, ρE = 3 dB, η = 0.7, M1 = 10, and M2 = 20.
  • Simulation settings: 100,000 channel realizations are used to obtain all simulation results.

A. Single-Antenna Case

The results show that analytical approximations accurately capture secrecy-throughput optimization, while blocklength, antennas, power allocation, and constraints shape the latency–reliability tradeoff.

  • Single-antenna case: For fixed B, secrecy throughput is quasi-concave in blocklength, with an optimal N that increases as B increases.The optimal secrecy throughput also increases with B.
  • Single-antenna case: The analytical results coincide well with simulations for optimal secrecy throughput and blocklength across transmit-power settings.The comparison uses analytical lines and simulation or one-dimensional-search markers.
  • Single-antenna case: Under reliability and latency constraints, secrecy throughput becomes zero beyond a critical B when no feasible blocklength remains.More stringent secrecy or reliability constraints, or larger ρE, reduce both the optimal throughput and the critical point.
  • Multi-antenna case: Increasing KA significantly improves secrecy throughput and decreases the optimal blocklength; increasing KA from one to two approximately doubles maximum throughput.For N > 600, finite- and infinite-blocklength throughputs coincide well, especially for KA ≥3.
  • Multi-antenna case: In AN-aided transmission, η∗ increases with B and decreases with KA and N.When decoding performance deteriorates, η∗ increases; with smaller decoding error probability, more artificial noise is injected.
  • Conclusion: The study concludes that multiple transmitter antennas improve secrecy throughput and reduce the optimal blocklength in short-packet communications.The analytical framework is extended from the single-antenna AP to multi-antenna AN-aided transmission.

APPENDIX A PROOF OF PROPOSITION 1

The proof develops an approximation for secrecy throughput and establishes the structure needed to optimize it over blocklength.

  • Approximation: The secrecy-throughput expression is further approximated because the complicated x0(y) prevents a direct closed-form expression.The approximation uses the fact that VE approaches 1 when γE is sufficiently large.
  • Approximation: Gaussian-Chebyshev quadrature is used to approximate the integral Ω1.
  • Blocklength optimization: The optimal blocklength is found by relaxing integer N to a positive real number and differentiating secrecy throughput with respect to N.
  • Blocklength optimization: Secrecy throughput first increases and then decreases with continuous N, making it quasi-concave.The optimal relaxed N is the unique zero-crossing point of Ξ(N).

APPENDIX C PROOF OF COROLLARY 1

The proof analyzes how system parameters shift the optimal blocklength through the implicit condition Ξ(N) = 0.

  • Parameter dependence: The effect of any parameter χ on N∗ is analyzed using the derivative rule for implicit functions with Ξ(N) = 0.
  • Parameter dependence: For χ ∈ {P, ρA}, the proof obtains dN∗/dχ < 0.
  • Parameter dependence: For χ ∈ {ρE, KE, B}, the proof obtains dN∗/dχ > 0.

APPENDIX D PROOF OF COROLLARY 2

The proof analyzes how optimized secrecy throughput changes with system parameters by applying the chain rule and evaluating parameter-specific derivatives. It establishes monotonicity with respect to reliability, power, antenna-related parameters, and eavesdropper conditions.

  • The chain rule relates each parameter’s effect on T∗≜T(N∗(χ), χ) to partial derivatives evaluated at the optimized blocklength.The analysis sets N=N∗ when assessing the parameter impact on T(N∗).
  • T(N∗) with respect to δ: T(N∗) increases with δ, yielding dT∗/dδ > 0 for any N > 0.
  • T(N∗) with respect to P and ρA: When δ < 0.5, T(N∗) increases with χ ∈{P, ρA}, yielding dT∗/dχ > 0.This follows from the stated positivity condition for the relevant derivative.
  • T(N∗) with respect to B: The derivative analysis establishes dT∗/dB > 0 for the parameter B.The result uses Ξ(N∗) = 0 from Theorem 2.
  • T(N∗) with respect to ρE and KE: T(N∗) decreases with ρE and KE, with dT∗/dχ < 0 for χ ∈{ρE, KE}.

APPENDIX E PROOF OF THEOREM 3

The proof derives approximations for secrecy-throughput integrals across antenna and artificial-noise configurations. It uses partial integration, variable changes, Gaussian-Chebyshev quadrature, and large-parameter approximations before substituting the resulting expressions into the target formula.

  • Partial integration is used to further calculate the secrecy throughput in (28) and derive the integral expressions required for the approximation.
  • The integral Φ1 is approximated via Gaussian-Chebyshev quadrature, while Φ2 uses x0(y) ≈ 1(1+y)−1 and x′0(y) ≈ 1 for sufficiently large M1.M1 is treated as a sufficiently large parameter, as in the single-antenna case.
  • The case of η = 1: For η = 1, the AP allocates all transmitting power to the information-bearing signal, there is no injected AN, and τ = 0 gives An(x) = 1.
  • The case of η ≠ 1 and KE < KA: When η ≠ 1 and KE < KA, the eavesdropper has fewer antennas than the AP, defining one case for evaluating the integral Θn.
  • The proof concludes by substituting expressions (47)–(49) into (46).
  • The case of η ≠ 1 and KE ≥ KA: When η ≠ 1 and KE ≥ KA, Θn is separated into Θ1,n and Θ2,n over the index ranges 1 ≤ n ≤ KE − KA + 1 and KE − KA + 2 ≤ n ≤ KE.
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