Distortion Bounds for Source Broadcast Problem

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the achievable distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for degraded broadcast channel case. When specialized to Gaussian source broadcast or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also are used to generate some new results. Besides, we also extend the inner bound and outer bounds to Wyner-Ziv source broadcast problem, i.e., source broadcast with side information available at decoders. Some new bounds are obtained when specialized to Wyner-Ziv Gaussian case and Wyner-Ziv binary case. In addition, when specialized to lossless transmission of a source with independent components, the bounds for source broadcast problem (without side information) are also used to achieve an inner bound and an outer bound on capacity region of general broadcast channel with common messages, which respectively generalize Marton’s inner bound and Nair-El Gamal outer bound to K-user broadcast channel case.