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# Capacity Analysis

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.

## Selected Publications

Citation key | C-OSNACMANBT-11 |
---|---|

Author | Ciucu, Florin |

Title of Book | Proceedings of International Symposium on Information Theory (ISIT '11) |

Pages | 2547–2551 |

Year | 2011 |

ISBN | 978-1-4577-0596-0 |

Online ISBN | 978-1-4577-0594-6 |

ISSN | 2157-8095 |

DOI | http://dx.doi.org/10.1109/ISIT.2011.6034027 |

Location | Saint Petersburg, Russia |

Address | New York, NY, USA |

Month | July/August |

Publisher | IEEE |

Abstract | The practicality of available (throughput) capacity results in multi-access networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these limitations by providing capacity results in non-asymptotic regimes, i.e., holding at all time scales and network sizes, for the very broad class of exponentially bounded burstiness (EBB) traffic sources. Both upper and lower bounds on capacity are derived in terms of probability distributions, which immediately yield all the moments. The explicit and closed-form nature of the results enable the investigation of the impact of burstiness on non-asymptotic network capacity. In particular, the results show that for the EBB class the non-asymptotic end-to-end capacity rate decays linearly in the number of hops. |