Cost of Guessing: Applications to Distributed Data Storage and Repair
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In this paper, we introduce the notion of the cost of guessing and provide an optimal strategy for guessing a random variable taking values on a finite set whereby each choice may be associated with a positive finite cost value. Moreover, we drive asymptotically tight upper and lower bounds on the moments of cost of guessing problem. Similar to previous studies on the standard guesswork, established bounds on the moments quantify the accumulated cost of guesses required for correctly identifying the unknown choice and are expressed in terms of the Rényi's entropy. A new random variable is introduced to bridge between the cost of guessing and the standard guesswork. Finally, we establish the guessing cost exponent on the moments of the optimal guessing by considering a sequence of random variables. Furthermore, these bounds are shown to serve quite useful for bounding the overall repair latency cost (data repair complexity) for distributed data storage systems in which sparse graph codes may be utilized.
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