8 research outputs found
Gaussian Secure Source Coding and Wyner's Common Information
We study secure source-coding with causal disclosure, under the Gaussian
distribution. The optimality of Gaussian auxiliary random variables is shown in
various scenarios. We explicitly characterize the tradeoff between the rates of
communication and secret key. This tradeoff is the result of a mutual
information optimization under Markov constraints. As a corollary, we deduce a
general formula for Wyner's Common Information in the Gaussian setting.Comment: ISIT 2015, 5 pages, uses IEEEtran.cl
Computing the Rate-Distortion Function of Gray-Wyner System
In this paper, the rate-distortion theory of Gray-Wyner lossy source coding
system is investigated. An iterative algorithm is proposed to compute
rate-distortion function for general successive source. For the case of jointly
Gaussian distributed sources, the Lagrangian analysis of scalable source coding
in [1] is generalized to the Gray-Wyner instance. Upon the existing
single-letter characterization of the rate-distortion region, we compute and
determine an analytical expression of the rate-distortion function under
quadratic distortion constraints. According to the rate-distortion function,
another approach, different from Viswanatha et al. used, is provided to compute
Wyner's Common Information. The convergence of proposed iterative algorithm, RD
function with different parameters and the projection plane of RD region are
also shown via numerical simulations at last.Comment: This work has been submitted to the IEEE for possible publication.
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A Gaussian Source Coding Perspective on Caching and Total Correlation
Communication technology has advanced up to a point where children are getting unfamiliar with themost iconic symbol in IT: the loading icon. We no longer wait for something to come on TV, nor for a download to complete. All the content we desire is available in instantaneous and personalized streams. Whereas users benefit tremendously from the increased freedom, the network suffers. Not only do personalized data streams increase the load overall, the instantaneous aspect concentrates traffic around peak hours. The heaviest (mostly video) applications are used predominantly during the evening hours. Caching is a tool to balance traffic without compromising the ‘on-demand’ aspect of content delivery; by sending data in advance a server can avoid peak traffic. The challenge is, of course, that in advance the server has no clue what data the user might be interested in. We study this problem in a lossy source coding setting with Gaussian sources specifically, using amodel based on the Gray–Wyner network. Ultimately caching is a trade-off between anticipating the precise demand through user habits versus ‘more bang for buck’ by exploiting correlation among the files in the database. For two Gaussian sources and using Gaussian codebooks we derive this trade-off completely. Particularly interesting is the case when the user has no preference for some content a-priori, caching then becomes an application of the concepts ofWyner’s common information and Watanabe’s total correlation. We study these concepts in databases of more than two sources where we derive that caching all of the information shared by multiple Gaussians is easy, whereas caching some is hard. We characterize the former, provide an inner bound for the latter and conjecture for which class of Gaussians it is tight. Later we also study how to most efficiently capture the total correlation that exists between two sets of Gaussians. As a final chapter, we study the applicability of caching of discrete information sources by actually building such algorithms, using convolutional codes to ‘cache and compress’. We provide a proof of concept of the practicality for doubly symmetric and circularly symmetric binary sources. Lastly we provide a discussion on challenges to be overcome for generalizing such algorithms