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/

On Cooperative Multiple Access Channels with Delayed CSI at Transmitters

We consider a cooperative two-user multiaccess channel in which the transmission is controlled by a random state. Both encoders transmit a common message and, one of the encoders also transmits an individual message. We study the capacity region of this communication model for different degrees of availability of the states at the encoders, causally or strictly causally. In the case in which the states are revealed causally to both encoders but not to the decoder we find an explicit characterization of the capacity region in the discrete memoryless case. In the case in which the states are revealed only strictly causally to both encoders, we establish inner and outer bounds on the capacity region. The outer bound is non-trivial, and has a relatively simple form. It has the advantage of incorporating only one auxiliary random variable. We then introduce a class of cooperative multiaccess channels with states known strictly causally at both encoders for which the inner and outer bounds agree; and so we characterize the capacity region for this class. In this class of channels, the state can be obtained as a deterministic function of the channel inputs and output. We also study the model in which the states are revealed, strictly causally, in an asymmetric manner, to only one encoder. Throughout the paper, we discuss a number of examples; and compute the capacity region of some of these examples. The results shed more light on the utility of delayed channel state information for increasing the capacity region of state-dependent cooperative multiaccess channels; and tie with recent progress in this framework.Comment: 54 pages. To appear in IEEE Transactions on Information Theory. arXiv admin note: substantial text overlap with arXiv:1201.327

Universal Quantization for Separate Encodings and Joint Decoding of Correlated Sources

We consider the multi-user lossy source-coding problem for continuous alphabet sources. In a previous work, Ziv proposed a single-user universal coding scheme which uses uniform quantization with dither, followed by a lossless source encoder (entropy coder). In this paper, we generalize Ziv's scheme to the multi-user setting. For this generalized universal scheme, upper bounds are derived on the redundancies, defined as the differences between the actual rates and the closest corresponding rates on the boundary of the rate region. It is shown that this scheme can achieve redundancies of no more than 0.754 bits per sample for each user. These bounds are obtained without knowledge of the multi-user rate region, which is an open problem in general. As a direct consequence of these results, inner and outer bounds on the rate-distortion achievable region are obtained.Comment: 24 pages, 1 figur

Asynchronous Joint Source-Channel Communication: An Information-Theoretic Perspective

Due to the increasing growth and demand for wireless communication services, new techniques and paradigms are required for the development of next generation systems and networks. As a first step to better differentiate between various options to develop future systems, one should consider fundamental theoretical problems and limitations in present systems and networks. Hence, some common ground between network information theory and mobile/wireless medium techniques should be explicitly addressed to better understand future generation trends. Among practical limitations, a major challenge, which is inherent and due to the physics of many mobile/wireless setups, is the problem of asynchronism between different nodes and/or clients in a wireless network. Although analytically convenient, the assumption of full synchronization between the end terminals in a network is usually difficult to justify. Thus, finding fundamental limits for communication systems under different types of asynchronism is essential to tackle real world problems. In this thesis, we study information theoretic limits that various multiuser wireless communication systems encounter under time or phase asynchronism between different nodes. In particular, we divide our research into two categories: phase asynchronous and time asynchronous systems. In the first part of this thesis, we consider several multiuser networks with phase fading communication links, i.e., all of the channels introduce phase shifts to the transmitted signals. We assume that the phase shifts are unknown to the transmitters as a practical assumption which results in a phase asynchronism between transmitter sides and receiver sides. We refer to these communication systems as phase incoherent (PI) communication systems and study the problem of communicating arbitrarily correlated sources over them. Specifically, we are interested in solving the general problem of joint source-channel coding over PI networks. To this end, we first present a lemma which is very useful in deriving necessary conditions for reliable communication of the sources over PI channels. Then, for each channel and under specific gain conditions, we derive sufficient conditions based on separate source and channel coding and show that the necessary and sufficient conditions match. Therefore, we are able to present and prove several separation theorems for channels under study under specific gain conditions. In the second part of this thesis, we consider time asynchronism in networks. In particular, we consider a multiple access channel with a relay as a general setup to model many wireless networks in which the transmitters are time asynchronous in the sense that they cannot operate at the same exact time. Based on the realistic assumption of a time offset between the transmitters, we again consider the problem of communicating arbitrarily correlated sources over such a time-asynchronous multiple access relay channel (TA-MARC). We first derive a general necessary condition for reliable communication. Then, by the use of separate source and channel coding and under specific gain conditions, we show that the derived sufficient conditions match with the general necessary condition for reliable communications. Consequently, we present a separation theorem for this class of networks under specific gain conditions. We then specialize our results to a two-user interference channel with time asynchronism between the encoders

Rate-Distortion-Based Physical Layer Secrecy with Applications to Multimode Fiber

Optical networks are vulnerable to physical layer attacks; wiretappers can improperly receive messages intended for legitimate recipients. Our work considers an aspect of this security problem within the domain of multimode fiber (MMF) transmission. MMF transmission can be modeled via a broadcast channel in which both the legitimate receiver's and wiretapper's channels are multiple-input-multiple-output complex Gaussian channels. Source-channel coding analyses based on the use of distortion as the metric for secrecy are developed. Alice has a source sequence to be encoded and transmitted over this broadcast channel so that the legitimate user Bob can reliably decode while forcing the distortion of wiretapper, or eavesdropper, Eve's estimate as high as possible. Tradeoffs between transmission rate and distortion under two extreme scenarios are examined: the best case where Eve has only her channel output and the worst case where she also knows the past realization of the source. It is shown that under the best case, an operationally separate source-channel coding scheme guarantees maximum distortion at the same rate as needed for reliable transmission. Theoretical bounds are given, and particularized for MMF. Numerical results showing the rate distortion tradeoff are presented and compared with corresponding results for the perfect secrecy case.Comment: 30 pages, 5 figures, accepted to IEEE Transactions on Communication