On channels with action-dependent states

Abstract

Action-dependent channels model scenarios in which transmission takes place in two successive phases. In the first phase, the encoder selects an "action" sequence, with the twofold aim of conveying information to the receiver and of affecting in a desired way the state of the channel to be used in the second phase. In the second phase, communication takes place in the presence the mentioned actiondependent state. In this work, two extensions of the original action-dependent channel are studied. In the first, the decoder is interested in estimating not only the message, but also the state sequence within an average per-letter distortion. Under the constraint of common reconstruction (i.e., the decoder's estimate of the state must be recoverable also at the encoder) and assuming non-causal state knowledge at the encoder in the second phase, we obtain a single-letter characterization of the achievable rate-distortioncost trade-off. In the second extension, we study an action-dependent degraded broadcast channel. Under the assumption that the encoder knows the state sequence causally in the second phase, the capacitycost region is identified. Various examples, including Gaussian channels and a model with a "probing" encoder, are also provided to show the advantage of a proper joint design of the two communication phases.

Channels with Action Dependent States and Additional Private Messages

“…Nevertheless, the capacity region in the Gaussian case without common reconstructions is the same as that established in Theorem 4 and Corollary 3 of [13]. The novelty in our model is that we are interested in common reconstruction of the state process in the action-dependent setting with additional messages, which also settles the optimality of Gaussian auxiliaries for the model studied in [7].…”

“…• We prove the optimality of Gaussian auxiliaries for the Gaussian action dependent model with CR constraints [7].…”

“…Choudhuri et al [6] considered causal state communication over an action-dependent channel and characterized the trade-off between message communication and state estimation distortion. Ahmadi et al [7] studied action-dependent channels with the additional constraint of common reconstructions (CR) [8] of the state at the encoder and decoder. Recently, Kittichokechai et al [9] studied source and channel coding settings with action-dependent states and CR constraints, wherein the actions control the partial channel state information available at the encoder and decoder.…”

“…Notice that single letter capacity characterizations for the discrete-memoryless action dependent state channel (DMADSC) as well as the DMADSC with CR constraints were presented in [3] and [7] respectively. However, the Gaussian counterparts are listed therein as open problems.…”

Wiretap Channel with Information Embedding on Actions

“…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.…”