Informational Divergence Approximations to Product Distributions

The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd\'{u} on resolvability. The result also extends to cases where the source distribution is unknown but the entropy is known

Coding Schemes for Achieving Strong Secrecy at Negligible Cost

We study the problem of achieving strong secrecy over wiretap channels at negligible cost, in the sense of maintaining the overall communication rate of the same channel without secrecy constraints. Specifically, we propose and analyze two source-channel coding architectures, in which secrecy is achieved by multiplexing public and confidential messages. In both cases, our main contribution is to show that secrecy can be achieved without compromising communication rate and by requiring only randomness of asymptotically vanishing rate. Our first source-channel coding architecture relies on a modified wiretap channel code, in which randomization is performed using the output of a source code. In contrast, our second architecture relies on a standard wiretap code combined with a modified source code termed uniform compression code, in which a small shared secret seed is used to enhance the uniformity of the source code output. We carry out a detailed analysis of uniform compression codes and characterize the optimal size of the shared seed.Comment: 15 pages, two-column, 5 figures, accepted to IEEE Transactions on Information Theor

Publicness, Privacy and Confidentiality in the Single-Serving Quantum Broadcast Channel

The 2-receiver broadcast channel is studied: a network with three parties where the transmitter and one of the receivers are the primarily involved parties and the other receiver considered as third party. The messages that are determined to be communicated are classified into public, private and confidential based on the information they convey. The public message contains information intended for both parties and is required to be decoded correctly by both of them, the private message is intended for the primary party only, however, there is no secrecy requirement imposed upon it meaning that it can possibly be exposed to the third party and finally the confidential message containing information intended exclusively for the primary party such that this information must be kept completely secret from the other receiver. A trade-off arises between the rates of the three messages, when one of the rates is high, the other rates may need to be reduced to guarantee the reliable transmission of all three messages. The encoder performs the necessary equivocation by virtue of dummy random numbers whose rate is assumed to be limited and should be considered in the trade-off as well. We study this trade-off in the one-shot regime of a quantum broadcast channel by providing achievability and (weak) converse regions. In the achievability, we prove and use a conditional version of the convex-split lemma as well as position-based decoding. By studying the asymptotic behaviour of our bounds, we will recover several well-known asymptotic results in the literature.Comment: 23 pages, 1 figure, journa

Distributed Channel Synthesis

Two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel, in which a stochastic channel output is generated based on a compressed description of the channel input. Wyner's common information is the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information. This work characterizes the optimal trade-off between the amount of common randomness used and the required rate of description. We also include a number of related derivations, including the effect of limited local randomness, rate requirements for secrecy, applications to game theory, and new insights into common information duality. Our proof makes use of a soft covering lemma, known in the literature for its role in quantifying the resolvability of a channel. The direct proof (achievability) constructs a feasible joint distribution over all parts of the system using a soft covering, from which the behavior of the encoder and decoder is inferred, with no explicit reference to joint typicality or binning. Of auxiliary interest, this work also generalizes and strengthens this soft covering tool.Comment: To appear in IEEE Trans. on Information Theory (submitted Aug., 2012, accepted July, 2013), 26 pages, using IEEEtran.cl