Joint communication and sensing over state dependent channels

The fundamental trade-off between communication rate and estimation error in sensing the channel state at the decoder is investigated for a discrete memoryless channel with discrete memoryless action dependent state when the state information is available either partially or fully at the encoder. We first investigate the capacity a relay channel with finite memory, where the action independent fixed channel state information is assumed to be known at both the encoder and decoder and then went on to investigate the problem of determining the trade-off between capacity and distortion for the channel with states known only at the encoder.;The relay channel with finite memory is modeled with channels with inter-symbol interference (ISI) and additive colored Gaussian noise. The channel state or channel impulse responses are assumed to be known at both the encoders and decoder. Prior results are used to show that the capacity of this channel can be computed by examining the circular degraded relay channel in the limit of infinite block length. The thesis provides single letter expressions for the achievable rates with decode-and-forward (DF) and compress-and-forward (CF) processing employed at the relay. Additionally, the cut-set bound for the relay channel is generalized for the ISI/colored Gaussian noise scenario. All results hinge on showing the optimality of the decomposition of the relay channel with ISI/colored Gaussian noise into an equivalent collection of coupled parallel, scalar, memoryless relay channels. The region of optimality of the DF and CF achievable rates is also discussed. The resulting rates are illustrated through the computation of numerical examples.;For non-causal channel state knowledge at the encoder, information-theoretic lower and upper bounds (based respectively on ideas from hybrid-coding and rate–distortion theory) are derived on the capacity–distortion function. Some examples are provided, for which the capacity–distortion functions are characterized by showing that the two bounds match. These coding theorems are then extended to the case of source coding with side information vending machine at the encoder (introduced in [5]) to provide an improved lower bound on the rate–distortion function. In some of the communication scenarios, however, the decoder is not interested in estimating the state directly, but it wants to reconstruct a function of the state with maximum fidelity. This problem of modified state estimation over a discrete memoryless implicit channels (DMIC) with discrete memoryless (DM) states is studied when the state information is available non-causally at the encoder. Lower and upper bounds on the optimal distortion in estimating the input of the implicit channel are derived. The methods developed for the DMIC with DM state model are then used to investigate the optimal distortion for the asymptotic version of the Witsenhausen counterexample, one of the fundamental problems in distributed control theory. The minimum distortion is characterized for the counterexample; furthermore it is shown that the combination of linear coding and dirty-paper coding (DPC) proposed in [42], in fact, achieves the minimum distortion for the Gaussian case when the proper amplification factor is determined.;The results obtained with discrete memoryless state dependent channels are then extended to channels with action-dependent states, as defined in [123]. While [123] investigated the scenario of message dependent nonadaptive action sequences, this work focuses on characterizing the benefits of allowing adaptive action sequences, where the action is not only a function of the message, but it also depends strictly causally on the past observed state sequences. To compare the two framework, the problem of joint communication and state estimation is considered over an action dependent channel. The capacity–distortion tradeoff of such a channel is characterized for the case when the state information is available strictly causally/causally at the channel encoder. It has been shown that although adaptive action is not useful in increasing the unconstrained capacity of the channel, but it helps in achieving a better capacity–distortion function by decreasing the state estimation error at the decoder. Since the capacity–distortion function is open with non-causal channel state information at the encoder, the capacity of such a channel is characterized and it is shown that the adaptive action is not useful in increasing the capacity. The result is illustrated with an example of action dependent additive Gaussian channel, whose capacity is 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 [130]. (Abstract shortened by UMI.).