verdu3 -- December94

I see trends in three different general directions. First, the trend towards results in information theory that apply to more sophisticated models of both sources and channels so that they are more relevant to real-world problems. In that respect I would emphasize universal coding problems and in particular, universal lossy source coding. For example, image processing with statistics that are not necessarily easy to model. That has been recognized for some time as a very important research direction. Wireless communication, as I mentioned, will continue to provide impetus to research in multiuser information theory, in particular in dealing with more relistic models. As technology progesses, it will become increasingly important to squeeze the last drop out of channels with limited bandwidth. We can predict that infor- mation theorists will play a major role if the development of fast phone-line modems is to serve as an indication.

Second, efforts will continue on some of the classical open problems in the field. For example, the capacity of the interference channel, the simplex conjecture, the capacity of the broadcast channel, etc. Despite intense efforts dur- ing the last forty years, the reliability function is still an open problem for even the binary symmetric channel. The problem of zero-error capacity is another longstanding problem which may or may not ever yield to solution.

And third, I foresee a lot of work on "postmodern" (postmo- dem?) information theory: Using the language of the classical theory to deal with problems outside the realm of conventional communication models. One example is information theory in the stock market, championed by Tom Cover. Will Wall Street embrace it now that they are getting serious about math? But, mainly, I expect a lot of action in the interface between in- formation theory and theoretical computer science. This includes problems on the complexity of interactive communication, the complexity of random process simulation, and various tradeoffs of randomness and complex- ity that we see in an increasing number of papers in theoretical computer science conferences such as STOC and FOCS.

Finally, I will conclude by saying that more than by its mathematical tools or its applications, Information Theory can be characterized by a way of thinking that combines in- tellec- tual rigor and engineering insights. That has been the tradi- tion in our field and it is our duty to ensure that that tradi- tion continues.