Wiretap Channel With Causal State Information

Abstract

Abstract-A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.

Wiretap channel with causal state information and secure rate-limited feedback

“…, is similar to that in [7], the analysis of the error probability is similar, and the jointly typical u n (l) is identified with high probability. The probability that a different sequence is identified is arbitrarily close to zero.…”

“…B}, we split the message to three parts as before, yet protect the first two with the state key. The state information key k s j−1 is split to two independent parts, k s (j−1,0) and k s (j−1,1) at rates which coincides with case 2 of R S−CSI−1 in [7]. Thus, compared with the first case ofR 1 , to send message…”

“…Similar to [7], we perform the maximization inR 1 through distributions p(u ), p(x|u, s) and functions of the form u(u , s), using the functional representation lemma [26]. This way, the achievability can be proved for an equivalent − q) is the (memoryless) probability distribution for the state sequence.…”

“…Note that M 0 , similar to [7], is protected using the Wyner coding scheme, therefore the eavesdropper cannot comprehend this part from the message when I(U ; Y, S 1 ) − I(U ; Z, S 2 ) > 0. The second part, M 1 , is encrypted with the key k s j−1 and the third part, M 2 , is encrypted with the key…”

Exploiting Partial Channel State Information for Secrecy over Wireless Channels

“…The model and results bear some similarities with those of the concurrent work in [16], [17] and we draw similar conclusions regarding the usefulness of CSIT. Strictly speaking, all the models studied in the remainder of the paper can be viewed as direct extensions of the discrete memoryless wiretap channels with causal CSI [18], [19], for which the secrecy capacity and secret-key capacity are often known; however, these results depend on auxiliary random variables and are not easily evaluated. In this paper, we extend these results by providing numerically computable expressions of achievable secure communication rates and secret-key capacity, which provide insight beyond that of the known singleletter expressions; we also establish strong secrecy rates by leveraging recent results on the secrecy capacity of arbitrary channels [20], [21].…”