Source coding with a side information 'vending machine' at the decoder

Tsachy Weissman, Haim H. Permuter

Abstract: We have formalized and characterized the fundamental limits for the problem of source coding with decoder side information, where the decoder is allowed to choose actions that affect the nature and quality of the side information. In the context of the problem studied, and its motivation, it is natural to also look at the case where actions are taken at the encoder: Based on its observation of the source sequence X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , the encoder chooses a sequence of actions A <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . Nature then generates the side information sequence Y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> as the output of the memoryless channel P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y|X,A</sub> whose input is the pair (X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , A <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ). The encoder now chooses the index to be given to the decoder on the basis of both the source and the side information sequence. The reconstruction sequence X¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> is then based on the index and on the side information sequence. A challenging aspect of this scenario is that the actions chosen by the encoder not only affect the quality of the side information, but can also be used to directly convey information about the source sequence. This scenario is depicted in Figure 6. In , we characterize the achievable tradeoff between rate, distortion, and cost for this problem setting as well.