Browsing by Subject "Source coding"

Now showing 1 - 3 of 3

Open Access
Guessing subject to distortion
(Institute of Electrical and Electronics Engineers, 1998-05) Arikan, E.; Merhav, N.
We investigate the problem of guessing a random vector X within distortion level D. Our aim is to characterize the best attainable performance in the sense of minimizing, in some probabilistic sense, the number of required guesses G(X) until the error falls below D. The underlying motivation is that G(X) is the number of candidate codewords to be examined by a rate-distortion block encoder until a satisfactory codeword is found. In particular, for memoryless sources, we provide a single-letter characterization of the least achievable exponential growth rate of the ρth moment of G(X) as the dimension of the random vector X grows without bound. In this context, we propose an asymptotically optimal guessing scheme that is universal both with respect to the information source and the value of ρ. We then study some properties of the exponent function E(D, ρ) along with its relation to the source-coding exponents. Finally, we provide extensions of our main results to the Gaussian case, guessing with side information, and sources with memory.
Open Access
Large deviations of probability rank
(IEEE, 2000) Arıkan, Erdal
Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.
Open Access
Source polarization
(IEEE, 2010) Arıkan, Erdal
The notion of source polarization is introduced and investigated. This complements the earlier work on channel polarization. An application to Slepian-Wolf coding is also considered. The paper is restricted to the case of binary alphabets. Extension of results to non-binary alphabets is discussed briefly.