Secret-Key Generation using Correlated Sources and Channels

We study the problem of generating a shared secret key between two terminals in a joint source-channel setup – the sender communicates to the receiver over a discrete memoryless wiretap channel and additionally the terminals have access to correlated discrete memoryless source sequences. We establish lower and upper bounds on the secret-key capacity. These bounds coincide, establishing the capacity, when the underlying channel consists of independent, parallel and reversely degraded wiretap channels. In the lower bound, the equivocation terms of the source and channel components are functionally additive. The secret-key rate is maximized by optimally balancing the the source and channel contributions. This tradeoff is illustrated in detail for the Gaussian case where it is also shown that Gaussian codebooks achieve the capacity. When the eavesdropper also observes a source sequence, the secret-key capacity is established when the sources and channels of the eavesdropper are a degraded version of the legitimate receiver. Finally the case when the terminals also have access to a public discussion channel is studied. We propose generating separate keys from the source and channel components and establish the optimality of this approach when the when the channel outputs of the receiver and the eavesdropper are conditionally independent given the input.

💡 Research Summary

The paper investigates the fundamental limits of secret‑key agreement when two legitimate terminals have access to both a discrete‑memoryless wiretap channel and correlated discrete‑memoryless source sequences. The sender transmits over a wiretap channel to the receiver while both parties observe correlated source symbols; the eavesdropper observes the channel output and, optionally, its own correlated source. The goal is to generate a common secret key that is uniformly random and asymptotically independent of everything the eavesdropper sees.

Main contributions

1. Achievable secret‑key rate (lower bound). The authors construct a two‑layer coding scheme. The first layer performs wiretap channel coding, achieving a “channel secrecy rate” (R_c = I(U;Y) - I(U;Z)) where (U) is an auxiliary random variable that captures the optimal input distribution. The second layer extracts common randomness from the correlated sources, yielding a “source secrecy rate” (R_s = H(S| \hat S) - H(S|E)) (or (H(S|\hat S)-H(S|S_E)) when the eavesdropper also has a source). Because the channel and source components are independent, the total secret‑key rate is simply the sum (R = R_c + R_s). The paper emphasizes that the equivocation contributions of the source and the channel are functionally additive, allowing an explicit trade‑off between the two resources.

2. Converse (upper bound). Using Fano’s inequality and standard information‑theoretic arguments, the authors show that any secret‑key scheme must satisfy
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