Coding With Action-Dependent Side Information and Additional Reconstruction Requirements

Two classes of source/channel coding problems, namely, coding with action-dependent side information and coding with additional signal reconstruction are considered in a unified fashion. In the source coding setting, a decoder wishes to reconstruct the source subject to a distortion constraint, while an encoder is required to estimate the decoder's reconstruction reliably. Side information is action-dependent in the sense that its quality and/or availability at the encoder or decoder can be influenced by a cost-constrained action sequence. In the channel coding dual, the decoder wishes to decode both the message and the channel input sequence reliably, and the channel state information available at the encoder or decoder is assumed to depend on the action sequence. We consider discrete memoryless systems and characterize single letter expressions for the rate-distortion-cost function and channel capacity for the respective source and channel coding problems.

I. Introduction

Problems involving source and channel coding with side/state information were recently generalized to capture a new interaction between nodes in the form of side/state information acquisition. Instead of assuming that side information/channel state are given by nature, Weissman [1] and Permuter and Weissman [2] introduced coding with action-dependent side/state information in which the availability and/or quality of side/state information can be influenced by other nodes in the system via a cost-constrained action sequence. This novel action-dependent coding framework introduces new interesting features to the general system model involving cost-constrained communication. The action sequence has dual roles, namely, communicating the message/source description, and controlling the channel state/side information. It is therefore highly relevant to many applications including sensor networking and control, and multistage coding for memories [1], [2].