verdu2 -- December94

I agree with Imre that communication should not be the only driving force behind information theory. In a sense I view in- formation theory as physics not only because we always carry units around (our logarithms) but because information theory is driven by the real world. Let it be communication, statistics, genetics or the stock market. I like to work on models that are practically relevant, but yet simple enough to admit solutions from which useful lessons can be learned. Others like to work on problems for their own sake--whether they have any relevance to practice or not, and that is a respectable approach.

I sense a "rennaisance of noise" in our field. Some time ago, some of our best minds moved away from physical-channel research, which at some point may have been viewed by some as old- fashioned. I think the pendulum is swinging back under the influence of, above all, wireless communications.

Wireless has brought multiuser information theory to the forefront once again. Lately, we have heard very heated arguments as to whether CDMA has higher capacity than TDMA and so on. Those arguments typically involve a dose of information theory mixed with some quasi-religious fervor. (Most of us in multiuser information theory are partial to CDMA, and not just be- cause it keeps us busier than TDMA or FDMA.) But we should not blame the practitioners for the lack of sophistication of some of their arguments. By and large, the development of mul- tiuser information theory did not capture until recently some of the essential issues that must be faced in real CDMA channels. The Cover-Wyner region was really all that was known for Gaussian multiple access chan- nels and that simple model did not come close to modeling CDMA. A widely-held misconception about the capacity region of more general multiaccess channels existed until Gallager came up with the right answer in 1988. Since then, the capacity of various CDMA and cellular channels has been found.

Networks is, I think, another case where the expectations have not materialized. In the late Seventies- early Eighties, there was a lot of hope for "network information theory". Today there are results that apply to some of the building blocks in wireless networks but there really is no such thing as network information theory. Perhaps there will never be.

I sense a decreasing reliance on combinatorics in information theory. We often admire (or become thoroughly frustrated with) the virtuoso combinatorial proofs for some very deep results within very specific classes of discrete memoryless channels. But, I would go as far as saying that none of the flagship results in information theory are real- ly combinatorial in nature. Perhaps, nowadays, the proba- bilistic school that does not rely on combinatorics is gain- ing ground. And that is salutary: sometimes in order to get to the heart of a result it is better to actually put it in a general framework of general channels (no just discrete memoryless channels) and sometimes that even leads to simpler proofs because you have fewer tools.