Lossy Compression with Near-uniform Encoder Outputs

It is well known that lossless compression of a discrete memoryless source with near-uniform encoder output is possible at a rate above its entropy if and only if the encoder is randomized. This work focuses on deriving conditions for near-uniform encoder output(s) in the Wyner-Ziv and the distributed lossy compression problems. We show that in the Wyner-Ziv problem, near-uniform encoder output and operation close to the WZ-rate limit is simultaneously possible, whereas in the distributed lossy compression problem, jointly near-uniform outputs is achievable in the interior of the distributed lossy compression rate region if the sources share non-trivial G\'{a}cs-K\"{o}rner common information.Comment: Submitted to the 2016 IEEE International Symposium on Information Theory (11 Pages, 3 Figures

Strong Coordination over Multi-hop Line Networks

We analyze the problem of strong coordination over a multi-hop line network in which the node initiating the coordination is a terminal network node. We assume that each node has access to a certain amount of randomness that is local to the node, and that the nodes share some common randomness, which are used together with explicit hop-by-hop communication to achieve strong coordination. We derive the trade-offs among the required rates of communication on the network links, the rates of local randomness available to network nodes, and the rate of common randomness to realize strong coordination. We present an achievable coding scheme built using multiple layers of channel resolvability codes, and establish several settings in which this scheme is proven to offer the best possible trade-offs.Comment: 35 pages, 9 Figures, 4 Tables. A part of this work were published in the 2015 IEEE Information Theory Workshop, and a part was accepted for publication in the 50th Annual Conference on Information Sciences and System

Strong Coordination over Noisy Channels: Is Separation Sufficient?

We study the problem of strong coordination of actions of two agents $X$ and $Y$ that communicate over a noisy communication channel such that the actions follow a given joint probability distribution. We propose two novel schemes for this noisy strong coordination problem, and derive inner bounds for the underlying strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the communication channel to reduce the local randomness required in generating the action sequence at agent $Y$. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. Finally, we present an example in which the joint scheme is able to outperform the separate scheme in terms of coordination rate.Comment: 9 pages, 4 figures. An extended version of a paper accepted for the IEEE International Symposium on Information Theory (ISIT), 201

Strong Coordination over Noisy Channels: Is Separation Sufficient?

We study the problem of strong coordination of actions of two agents $X$ and $Y$ that communicate over a noisy communication channel such that the actions follow a given joint probability distribution. We propose two novel schemes for this noisy strong coordination problem, and derive inner bounds for the underlying strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the communication channel to reduce the local randomness required in generating the action sequence at agent $Y$. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. Finally, we present an example in which the joint scheme is able to outperform the separate scheme in terms of coordination rate.Comment: 9 pages, 4 figures. An extended version of a paper accepted for the IEEE International Symposium on Information Theory (ISIT), 201

Identification of gene-gene interactions for Alzheimer's disease using co-operative game theory

Thesis (Ph.D.)--Boston UniversityThe multifactorial nature of Alzheimer's Disease suggests that complex gene-gene interactions are present in AD pathways. Contemporary approaches to detect such interactions in genome-wide data are mathematically and computationally challenging. We investigated gene-gene interactions for AD using a novel algorithm based on cooperative game theory in 15 genome-wide association study (GWAS) datasets comprising of a total of 11,840 AD cases and 10,931 cognitively normal elderly controls from the Alzheimer Disease Genetics Consortium (ADGC). We adapted this approach, which was developed originally for solving multi-dimensional problems in economics and social sciences, to compute a Shapely value statistic to identify genetic markers that contribute most to coalitions of SNPs in predicting AD risk. Treating each GWAS dataset as independent discovery, markers were ranked according to their contribution to coalitions formed with other markers. Using a backward elimination strategy, markers with low Shapley values were eliminated and the statistic was recalculated iteratively. We tested all two-way interactions between top Shapley markers in regression models which included the two SNPs (main effects) and a term for their interaction. Models yielding a p-value<0.05 for the interaction term were evaluated in each of the other datasets and the results from all datasets were combined by meta-analysis. Statistically significant interactions were observed with multiple marker combinations in the APOE regions. My analyses also revealed statistically strong interactions between markers in 6 regions; CTNNA3-ATP11A (p=4.1E-07), CSMD1-PRKCQ (p=3.5E-08), DCC-UNC5CL (p=5.9e-8), CNTNAP2-RFC3 (p=1.16e-07), AACS-TSHZ3 (p=2.64e-07) and CAMK4-MMD (p=3.3e-07). The Shapley value algorithm outperformed Chi-Square and ReliefF in detecting known interactions between APOE and GAB2 in a previously published GWAS dataset. It was also more accurate than competing filtering methods in identifying simulated epistastic SNPs that are additive in nature, but its accuracy was low in identifying non-linear interactions. The game theory algorithm revealed strong interactions between markers in novel genes with weak main effects, which would have been overlooked if only markers with strong marginal association with AD were tested. This method will be a valuable tool for identifying gene-gene interactions for complex diseases and other traits

An Equivalence Between Secure Network and Index Coding

We extend the equivalence between network coding and index coding by Effros, El Rouayheb, and Langberg to the secure communication setting in the presence of an eavesdropper. Specifically, we show that the most general versions of secure network-coding setup by Chan and Grant and the secure index-coding setup by Dau, Skachek, and Chee, which also include the randomised encoding setting, are equivalent

On the Capacity Region for Secure Index Coding

We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region