Semantic Coding: Partial Transmission

Shannon wrote in 1948: rdquoThe semantic aspects of communication are irrelevant to the engineering problemrdquo. He demonstrated indeed that the information generated by a source depends only on its statistics and not on the meaning of the source output. The authors derived the fundamental limits for semantic compaction, transmission and compression systems recently. These systems have the property that the codewords are semantic however, i.e. close to the source sequences. In the present article we determine the minimum distortion for semantic partial transmission systems. In these systems only a quantized version of each source source symbol is transmitted to the receiver. It should be noted that our achievability proof is based on weak instead of strong typicality. This is unusual for Gelfand-Pinsker [1980] related setups as e.g. semantic coding and embedding.