Guessing Cost: Applications to Distributed DataStorage and Repair in Cellular Networks
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The notion of guessing cost (also referred to as the cost of guessing) is introduced and an optimal strategy for the ρ-th moment of guessing cost is provided for a random variable taking values on a finite set whereby each choice is 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 of guessing cost quantify the accumulated cost of guesses required for correctly identifying the unknown choice and are expressed in terms of the Renyi's entropy. Moreover, anew random variable is introduced to establish connections between the guessing cost and the standard guesswork. Based on this observation, further improved bounds are conjectured in the non-asymptotic region by borrowing ideas from recent works given for the standard guesswork. Finally, we establish the guessing cost exponent in terms of the Renyi's entropy rate on the moments of the optimal guessing cost by considering a sequence of independent random variables. Finally, these bounds are shown to be very useful for bounding the overall repair bandwidth for distributed data storage systems. Our particular application utilizes a sparse graph code (low-density parity-check codes) in conjunction with a back-up master which is pretty common in cellular networks.
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