On the Correlation Between Polarized BECs

We consider the $2^n$ channels synthesized by the $n$-fold application of Ar\i{}kan's polar transform to a binary erasure channel (BEC). The synthetic channels are BECs themselves, and we show that, asymptotically for almost all these channels, the pairwise correlations between their erasure events are extremely small: the correlation coefficients vanish faster than any exponential in $n$. Such a fast decay of correlations allows us to conclude that the union bound on the block error probability of polar codes is very tight.Comment: 9 pages, Extended version of a paper submitted to ISIT 201

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

Exact Random Coding Secrecy Exponents for the Wiretap Channel

We analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in Wyner's wiretap channel setting using wiretap channel codes constructed from both i.i.d. and constant-composition random codes. Our analysis for those sampled from i.i.d. random coding ensemble shows that the previously-known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble. Furthermore, our analysis on wiretap channel codes constructed from the ensemble of constant-composition random codes leads to an exponent which, in addition to being the exact exponent for an average code, is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble (which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i.i.d. random coding ensemble). We show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant-composition codes is larger than that of those constructed from i.i.d. random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i.i.d. random codes is larger than that of those constructed from constant-composition random codes. We, hence, conclude that, unlike the error correction problem, there is no general ordering between the two random coding ensembles in terms of their secrecy exponent.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information Theor

Spotlight the Negatives: A Generalized Discriminative Latent Model

Discriminative latent variable models (LVM) are frequently applied to various visual recognition tasks. In these systems the latent (hidden) variables provide a formalism for modeling structured variation of visual features. Conventionally, latent variables are de- fined on the variation of the foreground (positive) class. In this work we augment LVMs to include negative latent variables corresponding to the background class. We formalize the scoring function of such a generalized LVM (GLVM). Then we discuss a framework for learning a model based on the GLVM scoring function. We theoretically showcase how some of the current visual recognition methods can benefit from this generalization. Finally, we experiment on a generalized form of Deformable Part Models with negative latent variables and show significant improvements on two different detection tasks.Comment: Published in proceedings of BMVC 201

Self-reported health status after solid-organ transplantation:The development and application of an innovative assessment method

This PhD research is about assessment of health-related quality of life (HRQoL), which is a topic rapidly gaining ground in the medical field. HRQoL, which is also referred to as perceived health status, well-being, or simply quality of life, not only includes mental, and social domains, but also physical domains. Patient-reported outcome measures (PROMs) are among the best known tools used for measuring HRQoL. Generic PROMs, such as SF-36 and EQ-5D, were generally applied in previous studies to assess the effects of solid organ transplantation on HRQoL. These PROMs have proven to be beneficial in measuring patients’ health statuses and outcomes associated with various health-care interventions. However, because they are generic, these PROMs do not contain health items that are specifically relevant to solid organ transplant recipients. This doctoral research provides a description of the step-wise process that was developed to generate health items for a new transplant-specific patient-centered electronic PROM: TXP. A five-step, sequential, mixed-methods design was applied: a scoping literature review, expert meetings, focus group discussions with solid organ recipients, a special judgmental task administered through an online survey, and expert meetings were held to make the final selection of health items. Ultimately, nine health items were chosen for inclusion in the TXP: fatigue, skin, worry/anxiety, self-reliance, activities, weight, sexuality, stooling, and memory/concentration. These health items reflect the most prominent issues experienced by transplant recipients and were derived using a patient-centered approach. TXP generates a single numeric score, using only nine health items, for assessing the overall HRQoL of different solid organ recipients