Semantic compaction, transmission, and compression codes

In Bell Syst. Tech. J., 1948, Shannon wrote: "The semantic aspects of communication are irrelevant to the engineering problem." Indeed Shannon demonstrated that the information that is generated by a source depends only on the statistics of the source, and not on the meaning of the source output. By contrast with this we investigate here whether in a compaction system the codewords can be meaningful just like the source output sequences. We require the codeword to be close to the source sequence for some given distortion measure. For so-called semantic compaction systems we determine the fundamental limits for the i.i.d. case. Moreover we consider semantic transmission systems. These systems have the property that the codewords, i.e. the channel input sequences, are close to the source sequence. Finally we investigate semantic compression. A semantic compression system is actually a vector quantizer for which the codeword, i.e. the index to the reproduction vector, resembles the source sequence. Also for semantic transmission and semantic compression we determine the fundamental limits for the i.i.d. case