On functional duality in MIMO source and channel coding problems having one-sided collaboration

We address duality in a variety of multiple-input-multiple-output (MIMO) source and channel coding problems of interest under different scenarios of "one-sided" inter-terminal collaboration at either the transmitter or at the receiver, including certain cases of. duality between (i) broadcast channel coding and distributed source coding, and (ii) multi-access channel coding and multiple-descriptions source coding. Our notion of duality in this paper is in a functional sense, where the optimal encoder mapping for a MIMO source coding problem becomes identical to the optimal decoder mapping for the dual MIMO channel coding problem, and vice versa. For ease of illustration we give the formulation only for two-input-two-output systems, which can be easily extended to the MIMO case. We present the precise mathematical conditions under which these encoder-decoder mappings are swappable in the two dual MIMO problems, identifying the key roles played by the source distortion and channel cost measures respectively in the MIMO source and channel coding problems in capturing this duality.