Towards a New Era in Network Information Theory: A New Approach to Converse

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Network information theory provides the fundamental guidance to the optimal design of all kinds of multiuser information systems, including wireless networks. As a theory, it has made many very successful progresses, and has dramatically transformed our view of how to develop communication systems when multiple users are present. Technologies originated from these theoretical studies include the famous code-division multiple-access (CDMA), which has become the standard for all advanced cellular networks. However, this useful theory has met with many difficult problems in its own development, some of which have been long standing for many years. Although we can already learn a lot of interesting results from this theory, many of which are to provide significant improvement for practice, the theory itself has not completely solved its own basic problems. In fact, many of the best results we know so far are still those obtained in 1970s. This is really a frustrating situation for people working in this field. For one thing, it is without doubt that this field of research is of pivotal importance in this information age, when information is such an indispensable part of our daily life, and networking among multi-users becomes such an essential character of modern societies. This pure reason has attracted many talented and hard-working people into the field. However, after decades of effort without real breakthroughs, any determined mind will doubt the worth of it. In fact, it has become no secret in the field that more and more people are turning away from the fundamental problems, to more hopeful new application topics. However, for the theory itself, when it cannot solve its own basic problems, it may not be far from dying. Is it already hopeless? In retrospect, efforts in network information theory have been mostly concentrated on achievability results. Here, I will focus more on the converse. Instead of the classical approach of using Fano’s inequality, I will develop a new approach to the converse. Actually, if one really thinks about it, one may find it a real surprise that Shannon’s single user capacity result can be proved by a perfect match between two completely different approaches from both sides: typical sequences for achievability from the lower side and Fano’s inequality for converse from the upper side. Is it a general rule or more like a coincidence? If this perfect match has not happened in general except in a very small number of isolated cases, one has to question the generality of this approach. The idea I have for the new approach to converse can be briefly put as follows: Develop a way of proving the converse also based on typical sequences. Once this can be done, it will no longer be a surprise that the two sides can easily match, because they are based on the same approach. The way of proving one will always hint on the other. This will provide a general solution to many basic problems in network information theory.