How useful is adaptive action?

Abstract

Channels with action-dependent states, as defined in [1], are considered. While [1] investigated the scenario of message dependent non-adaptive action sequences, this work focuses on adaptive action sequences, where the action is a strictly causal function of the message and the state sequences. The capacity of such a channel is characterized for the case when the state information is available non-causally at the channel encoder and it is shown that the adaptive action is not useful in increasing the capacity. The capacity of the action-dependent additive Gaussian channel, which was left open in [1], is then characterized by showing the equivalence of the current setting to the problem of the cooperative multiple access channel (MAC) with asymmetric state information at the encoders [2]. The problem setting is then extended to characterize the rate-distortion region of the source coding dual of the adaptive action-dependent channel coding setup, where a source is to be communicated with some fidelity to a decoder with adaptive action-dependent side information. In this setting adaptivity offers no help in enlarging the ratedistortion region.

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

“…It is valuable to study the adaptive action in our model. From [22], we have already known that adaptive action is not useful in increasing the point-to-point channel capacity. We will study whether it influences the secrecy capacity of our channel model.…”

Wiretap Channel with Information Embedding on Actions

“…It is valuable to study the adaptive action in our model. From [10], we have already known that adaptive action is not useful in increasing the point-to-point channel capacity. We will study whether it influences the sum secrecy capacity of our channel model under the secrecy constraint.…”

“…For the noncausal case, only inner and outer bounds on the capacity region were obtained [4]. Other extensions of the channel with action-dependent states can be seen in [5][6][7][8][9][10]. From the perspective of secure communication, we consider a different communication model in Figure 2, i.e., the wiretap channel with information embedding on actions.…”

On cascade source coding with a side information “vending machine”

“…Many problems remain open such as characterizing the performance of the system in Fig. 1 with adaptive actions in the sense of [14] and in Fig. 2 with side information also available at Node 3.…”