Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Practical Design of Probabilistic Constellation Shaping for Physical Layer Security in Visible Light Communications

Thanh V. Pham, Susumu Ishihara

TL;DR

This work tackles practical probabilistic constellation shaping (PCS) for physical layer security in a SISO VLC wiretap channel, formulating modulation-constrained secrecy optimization under reliability, flicker-mitigation, and symmetry constraints. It derives tractable closed-form upper-bound and approximate BER expressions for PCS-PAM under arbitrary symbol distributions and proves their concavity, enabling a CCCP-based solution for cases with known and unknown Eve CSI. A QoS-based PCS design is also proposed to maximize Eve’s BER, and a set of practical constraints, including symmetry and flicker mitigation, are enforced via convex relaxations. Numerical results show PCS can outperform uniform signaling in secrecy performance across the practical LED power range, with the caveat that low-power regimes may favor sparse symbol usage to satisfy pre-FEC BER constraints. The methods provide a viable path toward secure VLC deployments with practical modulation and illumination requirements.

Abstract

This paper studies a practical design of probabilistic constellation shaping (PCS) for physical layer security in visible light communications (VLC). In particular, we consider a wiretap VLC channel employing a probabilistically shaped $M$-ary pulse amplitude modulation (PAM) constellation. Considering the requirements for reliability of the legitimate user's channel, flickering-free transmission, and symmetric constellation distribution, the optimal constellation distributions to maximize modulation-constrained secrecy capacity or the bit error rate (BER) of eavesdropper's channel are investigated for both scenarios of known and unknown eavesdropper's channel state information (CSI). To formulate the constraint on the channel reliability, tractable closed-form expressions for the upper bound and approximate BER of $M$-ary PAM under an arbitrary symbol probability are derived. The design problem is shown to be non-convex due to the non-convex BER constraint. By proving that the upper bound BER is a concave function of the constellation distribution, a suboptimal solution based on the convex-concave procedure (CCCP) is presented. Our findings reveal that while the uniform signaling can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in the entire region of the optical power. Some insights into the optimal constellation distribution with respect to the emitted optical power are also discussed.

Practical Design of Probabilistic Constellation Shaping for Physical Layer Security in Visible Light Communications

TL;DR

This work tackles practical probabilistic constellation shaping (PCS) for physical layer security in a SISO VLC wiretap channel, formulating modulation-constrained secrecy optimization under reliability, flicker-mitigation, and symmetry constraints. It derives tractable closed-form upper-bound and approximate BER expressions for PCS-PAM under arbitrary symbol distributions and proves their concavity, enabling a CCCP-based solution for cases with known and unknown Eve CSI. A QoS-based PCS design is also proposed to maximize Eve’s BER, and a set of practical constraints, including symmetry and flicker mitigation, are enforced via convex relaxations. Numerical results show PCS can outperform uniform signaling in secrecy performance across the practical LED power range, with the caveat that low-power regimes may favor sparse symbol usage to satisfy pre-FEC BER constraints. The methods provide a viable path toward secure VLC deployments with practical modulation and illumination requirements.

Abstract

This paper studies a practical design of probabilistic constellation shaping (PCS) for physical layer security in visible light communications (VLC). In particular, we consider a wiretap VLC channel employing a probabilistically shaped -ary pulse amplitude modulation (PAM) constellation. Considering the requirements for reliability of the legitimate user's channel, flickering-free transmission, and symmetric constellation distribution, the optimal constellation distributions to maximize modulation-constrained secrecy capacity or the bit error rate (BER) of eavesdropper's channel are investigated for both scenarios of known and unknown eavesdropper's channel state information (CSI). To formulate the constraint on the channel reliability, tractable closed-form expressions for the upper bound and approximate BER of -ary PAM under an arbitrary symbol probability are derived. The design problem is shown to be non-convex due to the non-convex BER constraint. By proving that the upper bound BER is a concave function of the constellation distribution, a suboptimal solution based on the convex-concave procedure (CCCP) is presented. Our findings reveal that while the uniform signaling can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in the entire region of the optical power. Some insights into the optimal constellation distribution with respect to the emitted optical power are also discussed.
Paper Structure (22 sections, 3 theorems, 56 equations, 7 figures)

This paper contains 22 sections, 3 theorems, 56 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Related Work
  4. Our Contributions
  5. Organization
  6. System and Channel Model
  7. Modulation-constrained Secrecy Capacity Analysis
  8. Practical PCS Design
  9. Bit-Error Rate of PCS-PAM
  10. Upper Bound
  11. Approximation
  12. Numerial Examples
  13. Flickering Mitigation
  14. Symmetric Constellation Distribution
  15. PCS Design and Solution
  16. ...and 7 more sections

Key Result

Proposition 1

A closed-form expression for SEP1 is given by where $d_{{\rm{U}}, m,n} = h_{{\rm{U}}}\gamma\eta(a_m - a_{n})$.

Figures (7)

  • Figure 1: SISO VLC wiretap channel.
  • Figure 2: Upper bound and approximate SER of PCS-PAM.
  • Figure 3: CCCP algorithm to solve \ref{['OptProb2']}
  • Figure 4: Convergence behavior of Algorithm 1.
  • Figure 5: Comparison between PCS designs and uniform signaling: Known Eve's CSI.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3