Lossy Compression with Privacy Constraints: Optimality of Polar Codes

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources $X$ and $Y$ are compressed into a reconstruction $\hat{X}$ with some prescribed distortion $D$. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction $\hat{X}$ and $Y$. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information $Y$ must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.Comment: Submitted for publicatio

On the Construction of Polar Codes for Achieving the Capacity of Marginal Channels

Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect secrecy rates for binary-input degraded wiretap channels in symmetric settings, they are investigated extensively in the literature recently. In this paper, a polar coding scheme to achieve secrecy capacity in non-symmetric binary input channels is proposed. The proposed scheme satisfies security and reliability conditions. The wiretap channel is assumed to be stochastically degraded with respect to the legitimate channel and message distribution is uniform. The information set is sent over channels that are good for Bob and bad for Eve. Random bits are sent over channels that are good for both Bob and Eve. A frozen vector is chosen randomly and is sent over channels bad for both. We prove that there exists a frozen vector for which the coding scheme satisfies reliability and security conditions and approaches the secrecy capacity. We further empirically show that in the proposed scheme for non-symmetric binary-input discrete memoryless channels, the equivocation rate achieves its upper bound in the whole capacity-equivocation region

Secrecy Through Synchronization Errors

In this paper, we propose a transmission scheme that achieves information theoretic security, without making assumptions on the eavesdropper's channel. This is achieved by a transmitter that deliberately introduces synchronization errors (insertions and/or deletions) based on a shared source of randomness. The intended receiver, having access to the same shared source of randomness as the transmitter, can resynchronize the received sequence. On the other hand, the eavesdropper's channel remains a synchronization error channel. We prove a secrecy capacity theorem, provide a lower bound on the secrecy capacity, and propose numerical methods to evaluate it.Comment: 5 pages, 6 figures, submitted to ISIT 201

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