Action-dependent States Research Articles

The Sender-Excited Secret Key Agreement Model: Capacity, Reliability, and Secrecy Exponents

We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the channel state may be influenced by some of the parties involved. We derive single-letter expressions for the secret key capacity through a type of source emulation analysis. We also derive lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage. These exponents allow us to determine a set of strongly-achievable secret key rates. For degraded eavesdroppers the maximum strongly-achievable rate equals the secret key capacity; our exponents can also be specialized to previously known results. In deriving our strong achievability results we introduce a coding scheme that combines wiretap coding (to excite the channel) and key extraction (to distill keys from residual randomness). The secret key capacity is naturally seen to be a combination of both source- and channel-type randomness. Through examples we illustrate a fundamental interplay between the portion of the secret key rate due to each type of randomness. We also illustrate inherent tradeoffs between the achievable reliability and secrecy exponents. Our new scheme also naturally accommodates rate limits on the public discussion. We show that under rate constraints we are able to achieve larger rates than those that can be attained through a pure source emulation strategy.

Wiretap Channel with Information Embedding on Actions

Information embedding on actions is a new channel model in which a specific decoder is used to observe the actions taken by the encoder and retrieve part of the message intended for the receiver. We revisit this model and consider a different scenario where a secrecy constraint is imposed. By adding a wiretapper in the model, we aim to send the confidential message to the receiver and keep it secret from the wiretapper as much as possible. We characterize the inner and outer bounds on the capacity-equivocation region of such a channel with noncausal (and causal) channel state information. Furthermore, the lower and upper bounds on the sum secrecy capacity are also obtained. Besides, by eliminating the specific decoder, we get a new outer bound on the capacity-equivocation region of the wiretap channel with action-dependent states and prove it is tighter than the existing outer bound. A binary example is presented to illustrate the tradeoff between the sum secrecy rate and the information embedding rate under the secrecy constraint. We find that the secrecy constraint and the communication requirements of information embedding have a negative impact on improving the secrecy transmission rate of the given communication link.

Wiretap Channel with Action-Dependent States and Rate-Limited Feedback

We introduce the wiretap channel with action-dependent states and rate-limited feedback. In the new model, the state sequence is dependent on the action sequence which is selected according to the message, and a secure rate-limited feedback link is shared between the transmitter and the receiver. We obtain the capacity-equivocation region and secrecy capacity of such a channel both for the case where the channel inputs depend noncausally on the state sequence and the case where they are restricted to causal dependence. We construct the capacity-achieving coding schemes utilizing Wyner's random binning, Gel'fand and Pinsker’s coding technique, and rate splitting. Furthermore, we compare our results with the existing approaches without feedback, with noiseless feedback, and without action-dependent states. The simulation results show that the secrecy capacity of our model is bigger than that of the first two existed approaches. Besides, it is also shown that, by taking actions to affect the channel states, we guarantee the data integrity of the message transmitted in the two-stage communication systems although the tolerable overhead of transmission time is brought.

Random-Coding Exponential Error Bounds for Channels with Action-Dependent States

Random-Coding Exponential Error Bounds for Channels with Action-Dependent States

Wiretap Channel in the Presence of Action-Dependent States and Noiseless Feedback

We investigate the wiretap channel in the presence of action-dependent states and noiseless feedback. 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, the message, and the noiseless feedback, where the noiseless feedback is from the output of the main channel to the channel encoder. 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. The transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, the capacity equivocation regions are provided both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are formulated, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example.

Capacity of Channels With Action-Dependent States

We consider channels with action-dependent states: Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then creates the channel input sequence based on the state sequence. We characterize the capacity of such a channel both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Our setting covers previously considered scenarios involving transmission over channels with states known at the encoder, as well as various new coding scenarios for channels with a “rewrite” option that may arise naturally in storage for computer memories with defects or in magnetic recoding. A few examples are worked out in detail.