Information theory has been
instrumental to many technological advances, particularly in the field
of communications. However, in what is referred to as an unconsummated
union, information theory has yet to make a comparable mark in the
field of communication networks. One of the fundamental problems
related to both fields, and which has yet to be solved, concerns the
maximal data rates which can be reliably sustained in multi-hop
wireless networks. Over the last decade there has been a significant
ongoing research effort to understand network capacity under some
simplifications of the problem, i.e., by dispensing with multi-user
coding schemes or by making certain ideal assumptions on
power-control, routing and scheduling. This line of research, which
partly departs from the traditional information theory approach, has
yielded the notorious result of Θ(1/√(n log n))
capacity scaling law.
Our own research is concerned with extending such asymptotic capacity results, whose practicality is highly questionable, to non-asymptotic regimes and also for networks with general topologies and broad arrival classes. The principal merit of non-asymptotic results is that they allow the understanding of the capacity, and even delay, for any time scale and network size, and can be thus immediately applied in practical protocol design. Our analysis relies on the theory of the stochastic network calculus, which can elegantly and rigorously deal with the fundamental problem of spatial-time correlations in wireless networks. On the long term, we believe that this line of research has the potential of paving the way towards the elusive goal of a network information theory.