Semantic communication is a promising direction for the future of communication systems. Synonyms act as crucial bridges between semantics and syntax. Inspired by this, this paper introduces a semantic Markov chain model based on state synonymous mapping. This paper demonstrates that the syntactic Markov chain can be transformed into a semantic Markov chain through synonymous mapping. The stationary distribution of the semantic Markov chain can be obtained by partly summing the stationary distribution of the syntactic Markov chain. Similarly, the transition probability of the semantic Markov chain can be obtained by performing a weighted summation of the transition probabilities of the syntactic Markov chain. Additionally, we theoretically proves that the sequence entropy and the entropy rate of the semantic Markov source are no more than those of the syntactic Markov source.

With the deployment and commercial application of 5G, researchers start to think of 6G, which could meet more diversified and deeper intelligent communication requirements. In this paper, a four physical elements, i.e., man, machine, object, and genie, featured 6G concept is introduced. Genie is explained as a new element toward 6G. This paper focuses on the genie realization as an intelligent wireless transmission toward 6G, including sematic information theory, end-to-end artificial intelligence (AI) joint transceiver design, intelligent wireless transmission block design, and user-centric intelligent access. A comprehensive state-of-the-art of each key technology is presented and main questions as well as some novel suggestions are given. Genie will work comprehensively in 6G wireless communication and other major industrial vertical, while its realization is concrete and step by step. It is realized that genie-based wireless communication link works with high intelligence and performs better than that controlled manually.