Source coding and transmission under common knowledge constraints

This work studies problems of source coding under the requirement that the encoder can produce an exact copy of the compressed source constructed by the decoder. This requirement, termed here as a common knowledge constraint, is satisfied automatically in rate-distortion theory for single sources. However, in the common formulation of problems of lossy source coding with side information at the decoder (the Wyner-Ziv problem), distributed source coding, and joint source-channel coding for networks, the destination can exploit the information it receives in a manner that cannot be exactly reproduced at the sender side. Some applications, like the transmission of sensitive medical information, may require that both sides - the sender and the receiver - will share a common version of the compressed data, for the purpose of future discussions or consulting. The purpose of this work is to study the implications of common knowledge constraints on the achievable rates in scenarios of lossy source coding. A single letter characterization of the rate distortion function is developed, for the problem of source coding with side information at the decoder, under a common knowledge constraint. Implications of this constraint on problems of joint source channel coding for the degraded broadcast channel are studied. Specifically, it is shown that in this setup, a scheme based on separation achieves optimal distortions.