Causal State Communication

Abstract

The problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available strictly causally at the encoder. It is shown that block Markov encoding, in which the encoder communicates a description of the state sequence in the previous block by incorporating side information about the state sequence at the decoder, yields the minimum state estimation error. When the same channel is 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 and the state estimation error is characterized via the capacitydistortion function. It is shown that any optimal tradeoff pair can be achieved via rate-splitting. These coding theorems are then extended optimally to the case of causal channel state information at the encoder using the Shannon strategy.

Joint State Estimation and Communication Over a State-Dependent Gaussian Multiple Access Channel

“…In [11], the problem of communicating a common source and two independent messages over a Gaussian broadcast channel (BC) without state was analyzed, and it was shown that a power splitting strategy to meet the two different goals is not optimal. The problem of communicating channel state information over a state dependent discrete memoryless channel with causal state information at the encoder was analyzed in [12]. More recently, it was shown in [13] that for simultaneous arXiv:1811.09973v1 [cs.IT] 25 Nov 2018 message and state communication over memoryless channels with memoryless states, feedback can improve the optimal trade-off region both for causal and strictly-causal encoder side information.…”

The Zero-Error Feedback Capacity of State-Dependent Channels

“…For the standard setting where the probability of a message error need not be zero but can be arbitrarily small, Kim, Sutivong, and Cover [13] introduced and solved a related problem with list decoding of state sequences. Choudhuri, Kim, and Mitra [14] studied the causal and strictly-causal settings subject to a constraint on the distortion between the state sequence and its receiver-side estimate. Analogous results in the presence of feedback were recently reported by Bross and Lapidoth [15].…”

On sparse sensing and sparse sampling of coded signals at sub‐Landau rates

“…The work most relevant to our problem is [13], which attempts to detect both c and b, the later known to the transmitter and derives the capacity region of the rates R c and R b using technique similar to Gel'fand-Pinsker [20]. The case with the side information known only casually is analysed also in [21]. The result of Kim et al [13] relevant to this work is mainly the capacity region [13, Theorem 1] defined in our notation by Equation (5) and by an additional constraint on R c identical to the Gel'fand-Pinsker capacity expressed in our notation by…”