Simultaneous transmission of data and state with common knowledge

Abstract

This work studies the problem of simultaneous transmission of independent data and state via a state controlled channel, under the requirement that the encoder can produce locally an exact copy of the state estimation constructed by the decoder. The common formulation of problems of lossy source coding and source-channel coding, does not require that the sender be acquainted with the reconstructed source at the decoder. Some applications, like the transmission of medical images, may require that both sides - the sender and the receiver - will share a common version of the distorted data, for the purpose of future discussions or consultation. This requirement, termed here as the common knowledge (CK) constraint, is satisfied automatically in rate-distortion theory for single sources. However, in problems involving joint source-channel coding, the receiver can exploit the signals it receives in a manner that cannot be exactly reproduced at the sender site. In this work a single letter characterization of the achievable rate and distortion pairs is developed, for the problem of simultaneous transmission of data and state under the CK constraint. In particular, it is shown that even under the CK constraint separation strategy is not optimal in general, and joint state-channel coding is necessary to achieve optimal rate-distortion pairs.