Covert Communication via Action-Dependent States

TL;DR

The paper addresses covert communication over action-dependent-state channels (ADSIs) with transmitter access to the state either non-causally or causally. It develops block-Markov encoding combined with secret-key generation from the ADSI to achieve reliable and covert communication at rates on the order of $N$ (beyond the square-root law), and it derives matching upper bounds in several regimes. The authors unify channel-resolvability, Gel'fand-Pinsker coding, and Wyner-Ziv secret-key techniques to construct viable schemes, and they apply the framework to rewrite-memory problems and Gaussian channels, including cooperative Gaussian settings. Key contributions include explicit lower and upper bounds for both non-causal and causal ADSI cases, intuitive explanations and numerical illustrations, and extensions to general ADSI-driven channels and memory rewriting. The results demonstrate that ADSI, together with secret-key generation, enables positive covert rates in a broad class of channels, with practical implications for memory-recording and cooperative communications.

Abstract

This paper studies covert communication over channels with ADSI when the state is available either non-causally or causally at the transmitter. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring a low probability of detection by an adversary, which we refer to as `warden'. It is well known that in a point-to-point DMC, it is possible to communicate on the order of $\sqrt{N}$ bits reliably and covertly over $N$ channel uses while the transmitter and the receiver are required to share a secret key on the order of $\sqrt{N}$ bits. This paper studies achieving reliable and covert communication of positive rate, i.e., reliable and covert communication on the order of N bits in N channel uses, over a channel with ADSI while the transmitter has non-causal or causal access to the ADSI, and the transmitter and the receiver share a secret key of negligible rate. We derive achievable rates for both the non-causal and causal scenarios by using block-Markov encoding and secret key generation from the ADSI, which subsumes the best achievable rates for channels with random states. We also derive upper bounds, for both non-causal and causal scenarios, that meet our achievable rates for some special cases. As an application of our problem setup, we study covert communication over channels with rewrite options, which are closely related to recording covert information on memory, and show that a positive covert rate can be achieved in such channels. As a special case of our problem, we study the AWGN channels and provide lower and upper bounds on the covert capacity that meet when the transmitter and the receiver share a secret key of sufficient rate and when the warden's channel is noisier than the legitimate receiver channel. As another application of our problem setup, we show that cooperation can lead to a positive covert rate in Gaussian channels.

Figures (13)

• Figure 1: Covert communication over channels with action-dependent states
• Figure 2: The encoding and decoding scheme for block $b$, assuming that the encoder and the decoder have generated a secret key $\bar{K}$ in the previous block. The encoder first generates the reconciliation index $L$ and the secret key $K$ from a description of the ADSI, i.e., $V_{b-1}^N$, generated in the previous block. To transmit the message $M$ and the reconciliation index $L$, the likelihood encoder performs Gel'fand-Pinsker encoding. It computes the sequence $U_b^N$ according to the indices $(\bar{K},M,L)$ such that $U_b^N$ is iid with the ADSI. Also, the likelihood encoder computes the sequence $V_b^N$ that is iid with the ADSI, which will be used in the next block for the secret key generation. By decoding the indices $M$ and $L$ and accessing $Y_{b-1}^N$ the decoder will be able to reconstruct the sequence $V_{b-1}^N$ by using a Wyner-Ziv decoder, and therefore it can generate the secret key $K$.
• Figure 3: The encoding and decoding scheme for block $b$, assuming that the encoder and the decoder have generated a secret key $\bar{K}$ in the previous block. The encoder first generates the reconciliation index $L$ and the secret key $K$ from a description of the ADSI, i.e., $V_{b-1}^N$, generated in the previous block. To transmit the message $M$ and the reconciliation index $L$, according to the secret key $\bar{K}$, the encoder computes $U^N_b(M,L,\bar{K})$ and transmits $X_b^N$, where $X_{b,i}$ is generated by passing $U_{b,i}$ and $S_{b,i}$ through the test channel $P_{X|US}$. At the end of block $b$ accessing the action $A_b^N$, the ADSI $S_b^N$, and the indices $(M,L,\bar{K})$ the likelihood encoder computes the sequence $V_b^N$ that is iid with the ADSI $S_b^N$, which will be used in the next block for the secret key generation. By decoding the indices $M$ and $L$ and accessing $Y_{b-1}^N$ the decoder will be able to reconstruct the sequence $V_{b-1}^N$ by using a Wyner-Ziv decoder, and therefore it can generate the secret key $K$.
• Figure 4: BSCO with ADSI
• Figure 5: Channels with rewrite option and noiseless feedback

Theorems & Definitions (46)

• Definition 1
• Lemma 1
• Theorem 1
• Remark 1: Optimal Distributions
• Remark 2: Comparison with Channels with Action-Dependent States Without Covert Constraint
• Remark 3: Comparison with Covert Communications Over Channels with States
• Remark 4: The Effect of the Secret Shared Key of Negligible Rate
• Corollary 1
• Theorem 2
• Remark 5