Capacity-distortion trade-off in channels with state

Abstract

A problem of state information transmission over a state-dependent discrete memoryless channel (DMC) with independent and identically distributed (i.i.d.) states, known strictly causally at the transmitter is investigated. It is shown that block-Markov encoding coupled with channel state estimation conditioned on treating the decoded message and received channel output as side information at the decoder yields the minimum state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. The optimal tradeoff between the rate of the independent information that can be reliably transmitted and the state estimation error is characterized via the capacity-distortion function. It is shown that any optimal tradeoff pair can be achieved via a simple rate-splitting technique, whereby the transmitter appropriately allocates its rate between pure information transmission and state estimation.

Action dependent strictly causal state communication

“…Before proving the Theorem 1, we recall a lemma from [3] and summarize a few useful properties of C A SC (D) (similar to the [3, Corollary 1], [2]), which will be useful in proving the converse.…”

“…The capacitydistortion tradeoff of such a channel is characterized for the case when the state information is available strictly causally at the channel encoder. The problem setting extends the action dependent framework of [1] and as a special case recovers the results of few previously considered joint communication and estimation scenarios in [2], [3], [4]. The scenario when the action is also allowed to depend on the past observed states (adaptive action) is also considered.…”

“…Alternatively, our work extends that of joint communication and state estimation in [11], [2], [3], [4]; conditioned on the action sequence, we have such a problem. The role of the action sequence is to not only communicate the message, but to also determine a good communication channel for both the message as well as the state estimation.…”

“…The contributions of our work is as follows: we characterize the capacity distortion function for this problem via a two stage encoding scheme. In stage one, information is encoded in the action sequence; in stage two, conditioned on the action sequence, a block Markov strategy akin to that in [3] is shown to be capacity-distortion optimal. We show that strictly causal CSI improves the channel estimate, while the capacity is unchanged.…”

Coordination in Distributed Networks via Coded Actions With Application to Power Control

“…While [16] assumes that Agent 2 perfectly monitors the actions of Agent 1, we consider the case August 15, 2017 DRAFT of imperfect monitoring and analyze situations in which Agent 2 has a strictly causal knowledge (Theorem 4 and Corollary 12) or no knowledge (Theorem 5) of the state. • We clarify the connections between the game-theoretic formulation of [16] and information-theoretic considerations from the literature on state-dependent channels [28], [29], [30], [31], [32], separation theorems, and empirical coordination [5], [33]. We also formulate the determination of the long-run average payoff as an optimization problem, which we study in detail in Section IV and exploit for power control in Section V. • We establish a bridge between the coordination via actions and power control in wireless networks.…”