Litter-Masked Block z-Channel: Designing Cover Distributions Against Public-Design Observers

2026-09-24

AI Summary

This study addresses the vulnerability of cover traffic in physical-layer idle slots to passive detection by proposing a waveform shaping method based on "garbage masking." A Stackelberg game framework under Kullback–Leibler indistinguishability constraints is constructed to jointly optimize security and transmission performance. The resulting problem is solved via an alternating convex relaxation algorithm and validated in LDPC-coded systems using reinforcement learning strategies. Experimental results demonstrate that the proposed approach reduces the observer's Stein detection exponent by 41%–48% while incurring only approximately 1% throughput loss, with no significant penalty above the reliable link operating point. These findings confirm the effectiveness of the method in achieving low-overhead covert communication at the physical layer.

Abstract

Networking defenses against traffic analysis fill idle slots with cover traffic, yet the physical layer carrying it still hands upper layers the erasure-only model of a silent-idle link, leaving the cover content unexploited. We shape that content: the idle-slot waveform is drawn from the codebook complement under a design distribution, the \emph{litter distribution}, chosen to defeat a public-design passive observer while the upper layer keeps its block z-channel model. The maximum a posteriori (MAP) receiver reduces to a single threshold on the log-likelihood ratio between the best codeword and the prior-weighted litter aggregate; its errors are silent corruptions the upper layer cannot detect and erasures that retransmission absorbs. Receiver design is thus one-dimensional, minimizing erasure under a cap on silent corruption, and the joint design a Stackelberg game against a Kullback-Leibler (KL) indistinguishability metric, solved by an alternating convex relaxation and corroborated by an independent reinforcement-learning policy. On a rate-$3/4$ $(16,12)$ parity-check (LDPC) code against an observer who knows her own channel but whose channel the transmitter knows only statistically, shaped litter cuts the observer's Stein detection exponent by $41$ to $48\%$ relative to uniform cover, flat over a $10$~dB span and in the activity rate. Below the point where the legitimate link turns reliable, no cover distribution admits an operating point; at that point shaping costs about one percent of throughput, and nothing measurable $2$~dB above it.

Problem

• traffic analysis defense
• cover distribution design
• block z-channel
• passive observer
• covert communication

Innovation

• Litter Distribution
• Block z-Channel
• Stackelberg Game
• Traffic Analysis Defense
• Alternating Convex Relaxation