Physical Layer Security Autoencoder

The autoencoder is trained on a multi-terminal channel model consisting of a legitimate receiver (Bob) and an eavesdropper (Eve). The loss function explicitly maximizes mutual information with Bob while minimizing information leakage to Eve.

• Objective: max I(X; Y_Bob) - λ·I(X; Y_Eve)
• The Lagrangian multiplier λ controls the secrecy-rate trade-off
• Learns a secrecy capacity-approaching coding scheme without explicit algebraic code design
• Adapts to arbitrary eavesdropper channel conditions, including cases where Eve has a higher SNR than Bob

Unlike traditional systems that cascade a separate encryption algorithm (e.g., AES) with a channel code, the autoencoder learns a unified latent representation that simultaneously provides error correction and confidentiality.

• The encoder maps plaintext bits directly to secure channel symbols
• No distinguishable encryption layer exists for an attacker to isolate
• The decoder implicitly performs joint decryption and decoding
• Eliminates the overhead of key exchange protocols and synchronization

Training employs a three-player adversarial game between the transmitter (Alice), the legitimate receiver (Bob), and an eavesdropper network (Eve) that actively learns to intercept.

• Eve's network is trained concurrently to maximize its decoding accuracy
• Alice and Bob are trained to minimize Eve's success rate while maintaining Bob's reliability
• This min-max optimization converges to a Nash equilibrium where no better eavesdropping strategy exists
• Provides robustness against adaptive, learning-capable adversaries

In time-division duplex (TDD) systems, the autoencoder leverages physical channel reciprocity as a source of common randomness between Alice and Bob that is decorrelated from Eve's channel.

• The legitimate channel's CSI acts as an implicit key
• No key distribution protocol is required—secrecy emerges from the physical environment
• Effective when Eve is spatially separated by more than half a wavelength
• Can be combined with artificial noise injection into the null space of Bob's channel

The learned transmitter produces a deliberately distorted constellation that appears as random noise to Eve while remaining decodable by Bob's matched neural receiver.

• Transmitted symbols do not map to any standard QAM or PSK grid
• The constellation is a continuous, non-linear warping of the message space
• Eve's received symbols exhibit near-uniform distribution with no cluster structure
• Bob's receiver learns the inverse warping function conditioned on the legitimate channel

Training requires differentiable approximations of information-theoretic secrecy measures that can backpropagate gradients through the channel model.

• Uses a Mutual Information Neural Estimator (MINE) to approximate I(X; Y_Eve)
• Cross-entropy loss on Bob's decoder approximates reliability constraint
• The Csiszár-Körner secrecy capacity formula guides the loss weighting
• Enables gradient-based optimization of the entire end-to-end secrecy chain