Perfectly Secure Index Coding

In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set. We study the minimum key lengths for zero-error and perfectly secure index coding problem. On one hand, this problem is a generalization of the index coding problem (and thus a difficult one). On the other hand, it is a generalization of the Shannon's cipher system. We show that a generalization of Shannon's one-time pad strategy is optimal up to a multiplicative constant, meaning that it obtains the entire boundary of the cone formed by looking at the secure rate region from the origin. Finally, we consider relaxation of the perfect secrecy and zero-error constraints to weak secrecy and asymptotically vanishing probability of error, and provide a secure version of the result, obtained by Langberg and Effros, on the equivalence of zero-error and $\epsilon$-error regions in the conventional index coding problem.Comment: 25 pages, 5 figures, submitted to the IEEE Transactions on Information Theor

Simulation of a Channel with Another Channel

In this paper, we study the problem of simulating a DMC channel from another DMC channel under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a BSC channel can be simulated from a BEC channel when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of R\'enyi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.Comment: 31 pages, 10 figures, and some parts of this work were published at ITW 201

Adaptive Molecule Transmission Rate for Diffusion Based Molecular Communication

In this paper, a simple memory limited transmitter for molecular communication is proposed, in which information is encoded in the diffusion rate of the molecules. Taking advantage of memory, the proposed transmitter reduces the ISI problem by properly adjusting its diffusion rate. The error probability of the proposed scheme is derived and the result is compared with the lower bound on error probability of the optimum transmitter. It is shown that the performance of introduced transmitter is near optimal (under certain simplifications). Simplicity is the key feature of the presented communication system: the transmitter follows a simple rule, the receiver is a simple threshold decoder and only one type of molecule is used to convey the information

Wavefront-Guided Photorefractive Keratectomy for Correction of Residual Refractive Error after Intacs Implantation in Patients with Keratoconus

Purpose: To evaluate the efficacy of Wavefront-guided photorefractive keratectomy (PRK) for correction of residual refractiveerror after intrastromal corneal ring segments (ICRS) insertion for treatment of keratoconus.Patients and Methods: In this prospective case series five eyes of 5 keratoconus patients who had previous ICRS implantation (four Intacs TM and one Keraring), underwent Wavefront-guided PRK to correct residual refractive error.Results: Three months postoperatively, the mean spherical equivalent (SE) improved from 2.07 ± 1.38 Diopter to - 0.87 ± 0.54 Diopter. Four out of 5 eyes were within ± 1.00 D of Plano refraction. Three eyes had UCVA of 20/30 or better (all eyes; 20/40 or better). After 6 months, the mean SE was - 0.75 ± 0.50 Diopter and all eyes were within ± 1.00 D of Plano refraction. UCVA was 20/20 in 2 eyes, 20/30 or better in 2 eyes and 20/40 in one eye. One patient lost one line of BCVA.Conclusion: This case series showed that wavefront-guided PRK might be an effective procedure for correction of residual refractive error after ICRS insertion in keratoconus patients. Significant improvement in UCVA was seen in all cases after PRK without any complications and haze