Guessing subject to distortion
IEEE Trans on Information Theory
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Arikan, E., & Merhav, N. (1998). Guessing subject to distortion. Information Theory, IEEE Transactions on, 44(3), 1041-1056.
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/11047
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 pth 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 rho. We then study some properties of the exponent function E(D,rho) 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.