Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

Fundamental rate-loss tradeoff for optical quantum key distribution

Since 1984, various optical quantum key distribution (QKD) protocols have been proposed and examined. In all of them, the rate of secret key generation decays exponentially with distance. A natural and fundamental question is then whether there are yet-to-be discovered optical QKD protocols (without quantum repeaters) that could circumvent this rate-distance tradeoff. This paper provides a major step towards answering this question. We show that the secret-key-agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use. Our result has major implications for understanding the secret-key-agreement capacity of optical channels---a long-standing open problem in optical quantum information theory---and strongly suggests a real need for quantum repeaters to perform QKD at high rates over long distances.Comment: 9+4 pages, 3 figures. arXiv admin note: text overlap with arXiv:1310.012