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

Strong Converse and Second-Order Asymptotics of Channel Resolvability

We study the problem of channel resolvability for fixed i.i.d. input distributions and discrete memoryless channels (DMCs), and derive the strong converse theorem for any DMCs that are not necessarily full rank. We also derive the optimal second-order rate under a condition. Furthermore, under the condition that a DMC has the unique capacity achieving input distribution, we derive the optimal second-order rate of channel resolvability for the worst input distribution.Comment: 7 pages, a shorter version will appear in ISIT 2014, this version includes the proofs of technical lemmas in appendice

A Stronger Soft-Covering Lemma and Applications

Wyner's soft-covering lemma is a valuable tool for achievability proofs of information theoretic security, resolvability, channel synthesis, and source coding. The result herein sharpens the claim of soft-covering by moving away from an expected value analysis. Instead, a random codebook is shown to achieve the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block-length, enabling more powerful applications through the union bound.Comment: IEEE CNS 2015, 2nd Workshop on Physical-layer Methods for Wireless Security, 4 page

MAC Resolvability: First And Second Order Results

Building upon previous work on the relation between secrecy and channel resolvability, we revisit a secrecy proof for the multiple-access channel from the perspective of resolvability. We then refine the approach in order to obtain some novel results on the second-order achievable rates.Comment: Slightly extended version of the paper accepted at the 4th Workshop on Physical-Layer Methods for Wireless Security during IEEE CNS 2017. v2: Fixed typos and extended literature section in accordance with reviewers' recommendation

Resolvability on Continuous Alphabets

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.Comment: v2: Corrected inaccuracies in proof of direct part. Statement of Theorem 3 slightly adapted; other results unchanged v3: Extended version of camera ready version submitted to ISIT 201

Strong Converse for a Degraded Wiretap Channel via Active Hypothesis Testing

We establish an upper bound on the rate of codes for a wiretap channel with public feedback for a fixed probability of error and secrecy parameter. As a corollary, we obtain a strong converse for the capacity of a degraded wiretap channel with public feedback. Our converse proof is based on a reduction of active hypothesis testing for discriminating between two channels to coding for wiretap channel with feedback.Comment: This paper was presented at Allerton 201

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

On Channel Resolvability in Presence of Feedback

We study the problem of generating an approximately i.i.d. string at the output of a discrete memoryless channel using a limited amount of randomness at its input in presence of causal noiseless feedback. Feedback does not decrease the channel resolution, the minimum entropy rate required to achieve an accurate approximation of an i.i.d. output string. However, we show that, at least over a binary symmetric channel, a significantly larger resolvability exponent (the exponential decay rate of the divergence between the output distribution and product measure), compared to the best known achievable resolvability exponent in a system without feedback, is possible. We show that by employing a variable-length resolvability scheme and using an average number of coin-flips per channel use, the average divergence between the distribution of the output sequence and product measure decays exponentially fast in the average length of output sequence with an exponent equal to $[R-I(U;V)]^+$ where $I(U;V)$ is the mutual information developed across the channel.Comment: 8 pages, 4 figures; to be presented at the 54th Annual Allerton Conference on Communication, Control, and Computin