1,721,036 research outputs found
Joint Universal Lossy Coding and Identification of I.I.D. Vector Sources
No full textAbstract — The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuousalphabet memoryless sources. We show that, for bounded distortion measures, any compactly parametrized family of i.i.d. real vector sources with absolutely continuous marginals (satisfying appropriate smoothness and Vapnik–Chervonenkis learnability conditions) admits a joint scheme for universal lossy block coding and parameter estimation, and give nonasymptotic estimates of convergence rates for distortion redundancies and variational distances between the active source and the estimated source. We also present explicit examples of parametric sources admittin
Logarithmic Sobolev inequalities and strong data processing theorems for discrete channels
No full textAlmost any quantum spin system with short-range interactions can support toric codes," Phys
No full textAbstract Inspired by Kitaev's argument that physical error correction is possible in a system of interacting anyons, we demonstrate that such "self-correction" is fairly common in spin systems with classical Hamiltonians that admit the Peierls argument and where errors are modelled by quantum perturbations
Empirical processes, typical sequences and coordinated actions in standard Borel spaces
No full textAbstract—This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of measurable “test functions. ” In the finite-alphabet case, we can take all uniformly bounded functions and recover the usual notion of strong typicality (or typicality under the total variation distance). For a general alphabet, however, this function class turns out to be too large, and must be restricted. With this in mind, we define typicality with respect to any Glivenko–Cantelli function class (i.e., a function class that admits a Uniform Law of Large Numbers) and demonstrate its power by giving simple derivations of the fundamental limits on the achievable rates in several source coding scenarios, in which the relevant operational criteria pertain to reproducing empirical averages of a general-alphabet stationary memoryless source with respect to a suitable function class. Index Terms—Coordination via communication, empirical processes, Glivenko–Cantelli classes, rate distortion, source coding, standard Borel spaces, typical sequences, uniform laws of large numbers. I
Divergence-based characterization of fundamental limitations of adaptive dynamical systems
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