Fixed Binning Schemes for Channel and Source Coding Problems: An Operational Duality

We explore the connection between channel and source coding problems. Our study centers on the class of binning schemes that characterize the largest known achievable rates for channel and source coding problems with partial side information and multiterminal scenarios. The binning scheme can be viewed as a set of bins with each bin forming a channel code (with error probability 22) and set of all the codewords in the bins forms an overall channel code (with error probability 21). Our main result is a characterization of the performance of deterministic binning schemes for the channel and source coding problems solely as a function of the error probabilities 21, 22. This characterization shows the role of the two error probabilities to be reversed for the channel and source coding problems and suggests an operational duality between the two problems with respect to binning schemes. The algorithmic implications on constructing binning schemes are also discussed.