On functional duality in multiuser source and channel coding problems with one-sided collaboration

In this paper, we address duality in a variety of multiuser source and channel coding problems under different scenarios of "one-sided" inter-terminal collaboration at either the transmitter or at the receiver. First we consider duality between broadcast channel coding and distributed source coding problems. We also consider a new source coding problem in this paper, which we refer to as distributed reconstruction source coding. This problem is closely related to the multiple description source coding problem. We then consider duality between this problem and the multiple access channel coding problem. Our notion of duality in this paper is in a functional sense, where the optimal encoder mapping for a multiuser source coding problem becomes identical to the optimal decoder mapping for the dual multiuser channel coding problem, and vice versa. For ease of illustration we give the formulation only for systems which involve either two encoders or two decoders. Our formulation can be easily extended to the multiuser (more than two noncollaborating terminals) case. We present the precise mathematical conditions under which these encoder-decoder mappings are swappable in the two dual multiuser communication problems, identifying the key roles played by the source distortion and channel cost measures respectively in the multiuser source and channel coding problems in capturing this duality.