The Gaussian Multiple Access Wire-Tap Channel

We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define suitable security measures for this multi-access environment. Using codebooks generated randomly according to a Gaussian distribution, achievable secrecy rate regions are identified using superposition coding and TDMA coding schemes. An upper bound for the secrecy sum-rate is derived, and our coding schemes are shown to achieve the sum capacity. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints, quantifying the price paid for secrecy.Comment: Submitted to IEEE Transactions on Information Theor

Secure Communication over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established. This result is then specialized to give the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. Both the ergodic and outage performances are studied.Comment: Submitted to IEEE Transactions on Information Theory, Special Issue on Information Theoretic Security, November 200

Communication for Generating Correlation: A Unifying Survey

The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of communication, into perfectly shared uniform random variables. Such perfect shared randomness, in turn, enables the solutions of many tasks. Even the reverse conversion of perfectly shared uniform randomness into variables with a desired form of correlation turns out to be insightful and technically useful. In this survey article, we describe progress-to-date on such problems and lay out pertinent measures, achievability results, limits of performance, and point to new directions.Comment: A review article to appear in IEEE Transactions on Information Theor

The Common Randomness Capacity of a Network of Discrete Memoryless Channels

In this paper, we generalize our previous results on generating common randomness at two terminals to a situation where any finite number of agents, interconnected by an arbitrary network of independent, point-to-point, discrete memoryless channels, wish to generate common randomness by interactive communication over the network. Our main result is an exact characterization of the common randomness capacity of such a network, i.e., the maximum number of bits of randomness that all the agents can agree on per step of communication. As a by-product, we also obtain a purely combinatorial result, viz., a characterization of (the incidence vectors of) the spanning arborescences rooted at a specified vertex in a digraph, and having exactly one edge exiting the root, as precisely the extreme points of a certain unbounded convex polyhedron, described by a system of linear inequalities