Hierarchical guessing with a fidelity criterion
In an earlier paper, we studied the problem of guessing a random vector X within distortion D, and characterized the best attainable exponent E(D, rho) of the rho th moment of the number of required guesses G(X) until the guessing error falls below D. In this correspondence, we extend these results to a multistage, hierarchical guessing model, which allows for a faster search for a codeword vector at the encoder of a rate-distortion codebook. In the two-stage case of this model, if the target distortion level is D-2, the guesser first makes guesses with respect to (a higher) distortion level D-1, and then, upon his/her first success, directs the subsequent guesses to distortion D-2. As in the above-mentioned earlier paper, we provide a single-letter characterization of the best attainable guessing exponent, which relies heavily on well-known results on the successive refinement problem. We also relate this guessing exponent function to the source-coding error exponent function of the two-step coding process.
guessing successive refinement source-coding error exponent rate-distortion theory