“...what the paper tries to do is quantify some fundamental limitations on how much information can be transported over wireless networks, regardless of how they are operated.”

An information theory for networks has been a long-sought holy grail. Information theory can potentially inform us about absolute limits to what is achievable, much like the laws of thermodynamics. Knowing such fundamental limits helps to calibrate our efforts by answering questions such as: "Is our design already pretty close to optimal?" or "Are some goals that we are aiming for unattainable?" Another reason is that an information theory for networks can potentially also shed light on what could be a good architecture for wireless networking. For example, information theory for a single source and destination not only tells us how many bits can be reliably pumped over a link, but it also provides us with an architecture for doing so: a separation of source coding from channel coding, and the use of long blocks. It has long been hoped that, just as has been done for single link communication, an information theory for networks could provide valuable insight and strategic guidance into what wireless networks are truly capable of, and how they might be operated. For example, can one get dramatic benefits from using multi-user receivers? Is amplify-and-forward better than decode-and-forward? Should packets be sent in one hop, or is it better to use multiple hops? Is higher path loss better than lower path loss when it comes to wireless networking? These are all fundamental questions that a good theory should answer in some way. However, progress on network information theory has fallen short of providing such guidance. The result is that there has been a gap between information theory and the world of networking. Perhaps one reason this paper has attracted attention is that it attempts to answer such questions in some way.

The paper studies the maximum amount of information that can be transported over wireless networks. It shows that when the attenuation suffered by radio signals as a function of distance is large enough, then the so-called transport capacity measuring the number of bit-meters/second that a network in its aggregate can pump—analogous to the man-miles per year metric used by airlines—can only grow linearly as the number of nodes, mutually separated by a minimum distance in the network, increase. This is something that can be supported by the multi-hop architecture of decode-and-forward based relaying, with interference simply treated as noise, at which much IETF (Internet Engineering Task Force) activity is aimed. Thus it provides a strategic result that current efforts are order-optimal. The paper also examines some intriguing possibilities for wireless networking when the path loss is low, which may be useful some time in the future. From a theoretical point of view, the paper brings the notion of "distance" more explicitly into information theory than has usually been the case. Distance between nodes is taken into account, attenuation as a function of distance is modeled, and distance also enters into the performance metric of bit-meters/second. Also the paper tries to make progress by asking for less. It studies the scaling law for the transport capacity, and bounds the pre-constants, which could be a useful way to make progress on otherwise intractable problems.

In layman's terms, what the paper tries to do is quantify some fundamental limitations on how much information can be transported over wireless networks, regardless of how they are operated. It has also given some insight into how wireless networks should be architected. This calibrates current IETF efforts as being order-optimal under some radio attenuation regimes. In another sense, the models advocated in the paper and the method of study may be of further interest to researchers in information theory.

In the late 1990s I decided to take a look at wireless networks. What fascinated me then was that this appeared to be an exciting arena for research in terms of the possibility of fashioning networks that are ubiquitous and can adapt themselves in terms of power, routes, etc., to whichever environment in which they are deployed. My ex-Ph.D. student Piyush Gupta and I studied the scaling laws for networks under some models of operation. I also got interested in protocol design, another fascinating area. A nagging question remaining from the earlier work was whether the limits obtained there were fundamental, or whether they only applied to the multi-hop interference limited model. To address this properly, the perfect tool was information theory; and network information theory—being well known as a graveyard of failed efforts—only made it even more attractive and challenging to work in! Then along came Liang-Liang Xie, my co-author on this paper, to work as my post-doctoral visitor. He had been previously engaged in the areas of control and identification, but not at all on any communication-related problems. Little did he realize what he would be doing when he came here! All in all, it’s been fun research!