Information Theory modern topics

Question

I am an electrical engineer that just graduated, and I would like to know more about what's being done nowadays in the Information Theory area, as I am interested a lot in it and maybe I will start a PhD.

As far as I know, Information Theory has been used until now for data compression and communications, and multiple results have been obtained for both of them as Shannon's capacity theorem or capacity calculations for some specific channels as the AWGN channels and more.

However, I am not sure which path has this beautiful science taken, and I would like to know which areas of nowadays are making an extent use it, or need it. Apart from it, I would also like to know some problems in the theory that remain unsolved (as the deletion channels, see: https://en.wikipedia.org/wiki/Deletion_channel).

Seems that Quantum Information theory is being widely studied nowadays, so it is also interesting for me to know which is the trend there nowadays, and if a deep understanding of QM would be necessary to study that field.

I have also been reading that the concepts of the classical information theory change in the quantum approach (example, Von Neumann entropy: https://en.wikipedia.org/wiki/Von_Neumann_entropy). References or information to tohose will also be helpful.

I will receive happy any Information about those topics so as can be references, books or just a mention about what's being done. Thanks in advance.

Answer 1

The Shannon capacity of graphs beyond the pentagon is unknown. The pentagon capacity was found by Lovasz many decades ago.

The capacity of the general broadcast channel, as well as that of lots of multi terminal networks are unknown.

Quantum information theory is very active.

Answer 2

A good way to assess what topics are 'hot' right now is to look at past programs of International Symposium on Information Theory (ISIT).

Here is the link to ISIT in Barcelona http://www.isit2016.org/.

You can also look at the Information Theory News Letter available at the societies webpage http://www.itsoc.org/

You can also see recent research papers at arxiv at https://arxiv.org/list/cs.IT/recent

There are even some information theory blogs https://blogs.princeton.edu/blogit/

Information Theory and Applications (ITA) conference used to (maybe it still does) video tape student poster presentation. This should be a good way to see what students are working on. See https://www.youtube.com/user/Calit2ube

Answer 3

The "Future Directions" committee of the IEEE Information Theory Society has put together a list of interesting possible, well, future directions. The article is available on arXiv, and has also been published in the IEEE IT Society Newsletter.