Wiretap Channel with Action-Dependent Channel State Information

Abstract

In this paper, we investigate the model of wiretap channel with action-dependent channel state information. Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then generates the channel input sequence based on the state sequence and the message. The main channel and the wiretap channel are two discrete memoryless channels (DMCs), and they are connected with the legitimate receiver and the wiretapper, respectively. Moreover, the transition probability distribution of the main channel depends on the channel state. Measuring wiretapper's uncertainty about the message by equivocation, inner and outer bounds on the capacity-equivocation region are provided both for the case where the channel inputs are allowed to depend non-causally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are bounded, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example.

Wiretap Channel with Information Embedding on Actions

“…In this example, the parameter, α, is fixed as 0.2 (the other value of α could also be assumed). Similar to the arguments in [1,18,19]…”

“…C ′ uc coincides with the upper bound on the secrecy capacity of the model in [18] with causal states.…”

“…The corresponding lower and upper bounds on the sum secrecy capacity are also obtained. Besides, through a special case, we get a new upper bound on the secrecy capacity of the wiretap channel with action-dependent states and show that it is tighter than the upper bound obtained in [18]. We also discuss the tradeoff between the sum secrecy rate and the information embedding rate under the secrecy constraint.…”

“…Similar to [18], two cases are considered. Since the channel states are noncausally known to the channel encoder, Gel'fand and Pinsker's coding technique [22] will be used in the encoding process.…”

“…When no message needs to be embedded in the actions, the model in Figure 2 turns to the wiretap channel with action-dependent states [18]; see Figure 3. [18] gave an upper bound on the secrecy capacity of the model with noncausal states as:…”