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Hybrid Codes Needed for Coordination over the Point-to-Point Channel

We consider a new fundamental question regarding the point-to-point memoryless channel. The source-channel separation theorem indicates that random codebook construction for lossy source compression and channel coding can be independently constructed and paired to achieve optimal performance for coordinating a source sequence with a reconstruction sequence. But what if we want the channel input to also be coordinated with the source and reconstruction? Such situations arise in network communication problems, where the correlation inherent in the information sources can be used to correlate channel inputs. Hybrid codes have been shown to be useful in a number of network communication problems. In this work we highlight their advantages over purely digital codebook construction by applying them to the point-to-point setting, coordinating both the channel input and the reconstruction with the source.