A Rate-Distortion Based Secrecy System with Side Information at the Decoders

A secrecy system with side information at the decoders is studied in the context of lossy source compression over a noiseless broadcast channel. The decoders have access to different side information sequences that are correlated with the source. The fidelity of the communication to the legitimate receiver is measured by a distortion metric, as is traditionally done in the Wyner-Ziv problem. The secrecy performance of the system is also evaluated under a distortion metric. An achievable rate-distortion region is derived for the general case of arbitrarily correlated side information. Exact bounds are obtained for several special cases in which the side information satisfies certain constraints. An example is considered in which the side information sequences come from a binary erasure channel and a binary symmetric channel.Comment: 8 pages. Allerton 201

Secure Lossy Source Coding with Side Information at the Decoders

This paper investigates the problem of secure lossy source coding in the presence of an eavesdropper with arbitrary correlated side informations at the legitimate decoder (referred to as Bob) and the eavesdropper (referred to as Eve). This scenario consists of an encoder that wishes to compress a source to satisfy the desired requirements on: (i) the distortion level at Bob and (ii) the equivocation rate at Eve. It is assumed that the decoders have access to correlated sources as side information. For instance, this problem can be seen as a generalization of the well-known Wyner-Ziv problem taking into account the security requirements. A complete characterization of the rate-distortion-equivocation region for the case of arbitrary correlated side informations at the decoders is derived. Several special cases of interest and an application example to secure lossy source coding of binary sources in the presence of binary and ternary side informations are also considered. It is shown that the statistical differences between the side information at the decoders and the presence of non-zero distortion at the legitimate decoder can be useful in terms of secrecy. Applications of these results arise in a variety of distributed sensor network scenarios.Comment: 7 pages, 5 figures, 1 table, to be presented at Allerton 201

Secure Multiterminal Source Coding with Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate --average uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bob --secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a non-zero distortion at Bob can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table

The Likelihood Encoder for Lossy Compression

A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma yields simple achievability proofs for classical source coding problems. The cases of the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic analysis is used for the point-to-point case to examine the upper bound on the excess distortion provided by this method. The likelihood encoder is also related to a recent alternative technique using properties of random binning

The Likelihood Encoder for Lossy Source Compression

In this work, a likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on a soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma gives alternative achievability proofs for classical source coding problems. The case of the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem) is carefully examined and an application of the likelihood encoder to the multi-terminal source coding inner bound (i.e. the Berger-Tung region) is outlined.Comment: 5 pages, 2 figures, ISIT 201

Optimal Equivocation in Secrecy Systems a Special Case of Distortion-based Characterization

Recent work characterizing the optimal performance of secrecy systems has made use of a distortion-like metric for partial secrecy as a replacement for the more traditional metric of equivocation. In this work we use the log-loss function to show that the optimal performance limits characterized by equivocation are, in fact, special cases of distortion-based counterparts. This observation illuminates why equivocation doesn't tell the whole story of secrecy. It also justifies the causal-disclosure framework for secrecy (past source symbols and actions revealed to the eavesdropper).Comment: Invited to ITA 2013, 3 pages, no figures, using IEEEtran.cl

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/

A Bit of Secrecy for Gaussian Source Compression

In this paper, the compression of an independent and identically distributed Gaussian source sequence is studied in an unsecure network. Within a game theoretic setting for a three-party noiseless communication network (sender Alice, legitimate receiver Bob, and eavesdropper Eve), the problem of how to efficiently compress a Gaussian source with limited secret key in order to guarantee that Bob can reconstruct with high fidelity while preventing Eve from estimating an accurate reconstruction is investigated. It is assumed that Alice and Bob share a secret key with limited rate. Three scenarios are studied, in which the eavesdropper ranges from weak to strong in terms of the causal side information she has. It is shown that one bit of secret key per source symbol is enough to achieve perfect secrecy performance in the Gaussian squared error setting, and the information theoretic region is not optimized by joint Gaussian random variables