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/

Capacity of a Class of Deterministic Relay Channels

The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y_1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R_0, is shown to be C(R_0) = \max_{p(x)} \min \{I(X;Y)+R_0, I(X;Y, Y_1) \}. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, ``hash-and-forward'', is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usual ``compress-and-forward''. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and the output.Comment: 17 pages, submitted to IEEE Transactions on Information Theor

Joint source-channel coding with feedback

This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average distortion and guaranteed distortion ($d$-semifaithful codes). In contrast to the asymptotic fundamental limit, a general conclusion is that allowing variable-length codes and feedback leads to a sizable improvement in the fundamental delay-distortion tradeoff. In addition, we investigate the minimum energy required to reproduce $k$ source samples with a given fidelity after transmission over a memoryless Gaussian channel, and we show that the required minimum energy is reduced with feedback and an average (rather than maximal) power constraint.Comment: To appear in IEEE Transactions on Information Theor

Broadcast Channels with Cooperating Decoders

We consider the problem of communicating over the general discrete memoryless broadcast channel (BC) with partially cooperating receivers. In our setup, receivers are able to exchange messages over noiseless conference links of finite capacities, prior to decoding the messages sent from the transmitter. In this paper we formulate the general problem of broadcast with cooperation. We first find the capacity region for the case where the BC is physically degraded. Then, we give achievability results for the general broadcast channel, for both the two independent messages case and the single common message case.Comment: Final version, to appear in the IEEE Transactions on Information Theory -- contains (very) minor changes based on the last round of review