No Advantage of Non-Local Cooperation in Distributed Compression of Classical Sources

In this paper, we show that there is no advantage of using non-local cooperation between source encoders in improving the optimal compression rate (or rate region) for some canonical distributed compression tasks. The tasks are the lossless distributed compression, the lossless compression with a helper, and some special cases of the lossy distributed compression for 2-component discrete memoryless sources. These negative results for distributed source coding contrast with those for multi-user channel coding: quantum or general no-signaling cooperation between channel encoders improves the capacity region for some multiple access and interference channels.