Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, and also confined to, several existing interpretations in various source coding problems. This paper attempts to expand its practical significance by providing a new operational interpretation. In the context of the Gray-Wyner network, it is established that Wyner's common information has a new lossy source coding interpretation. Specifically, it is established that, under suitable conditions, Wyner's common information equals to the smallest common message rate when the total rate is arbitrarily close to the rate distortion function with joint decoding for the Gray-Wyner network. A surprising observation is that such equality holds independent of the values of distortion constraints as long as the distortions are within some distortion region. The new lossy source coding interpretation provides the first meaningful justification for defining Wyner's common information for continuous random variables and the result can also be extended to that of multiple variables. Examples are given for characterizing the rate distortion region for the Gray-Wyner lossy source coding problem and for identifying conditions under which Wyner's common information equals that of the smallest common rate. As a by-product, the explicit expression for the common information between a pair of Gaussian random variables is obtained.

Communicating arbitrarily correlated sources over interference channels is considered in this paper. A sufficient condition is found for lossless transmission of a pair of correlated sources over a discrete memoryless interference channel. With independent sources, the sufficient condition reduces to the Han-Kobayashi achievable rate region for interference channels. For sources with a special correlation structure, the proposed region reduces to the known achievable region for interference channels with common information. Moreover, the proposed coding scheme is optimal for transmitting such set of correlated sources over a class of deterministic interference channels as defined in El Gamal and Costa, 1982.

In this paper, we consider lossy transmission of two correlated sources over a two-user discrete memoryless interference channel (DMIC). An achievable distortion region is obtained and it is shown that it includes Salehi and Kurtas's result on lossless transmission of correlated sources over a DMIC as a special case. Sending correlated Gaussian sources over a Gaussian interference channel is also studied, and several achievable schemes as well as lower bounds are proposed.

In this paper, we consider transmission of two correlated Gaussian sources to two receivers through a two-user Gaussian Z interference channel (Z IC). To facilitate our study, we first investigate Gaussian multiple access channels with correlated Gaussian sources and a single distortion constraint at the receiver. Lower bounds on the distortion as well as several achievable schemes are proposed. In particular, a hybrid digital analog transmission scheme is proposed whose achievable region is resolved through coupling it with the quadratic Gaussian CEO problem. These lower bounds and achievable schemes are then applied to the source channel communication over a two-user Gaussian Z IC to derive inner and outer bounds for the distortion region. We conclude this paper by giving a sufficient condition for sending a correlated source over a general Z interference channel.