On optimal stopping and free boundary problems

available up to now to prove the direct half of the coding theorem for a multiway channel is based on Shannon's random coding argument. So far no other type of proof has been given. Also, for multi-way channels there is a theory of coding for average errors and a theory of coding for maximal errors. Up to now a weak converse of the coding theorem for average errors has been proved for multi-way channels, but not yet a strong converse. This indicates that there are many unsolved problems in coding theory of multi-way channels, some of which we have stressed in our paper. Our survey is based on the following references: Ahlswede [1] and [2], Bergmans [3], Cover [4], Shannon [6], and van der Meulen [7] and [8].