Estimation of Bit and Frame Error Rates of Finite-Length Low-Density Parity-Check Codes on Binary Symmetric Channels
Auctions have been proposed as a way to provide economic incentives for primary users to dynamically allocate unused spectrum to other users in need of it. Previously proposed schemes do not take into account the fact that the power constraints of users might prevent them from transmitting their bid prices to the auctioneer with high precision and that transmitted bid prices must travel through a noisy channel. These schemes also have very high overheads which cannot be accommodated in wireless standards. We propose auction schemes where a central clearing authority auctions spectrum to users who bid for it, while taking into account quantization of prices, overheads in bid revelation, and noise in the channel explicitly. Our schemes are closely related to channel output feedback problems and, specifically, to the technique of posterior matching. We consider several scenarios where the objective of the clearing authority is to award spectrum to the bidders who value spectrum the most. We prove theoretically that this objective is asymptotically attained by our scheme when the bidders are nonstrategic with constant bids. We propose separate schemes to make strategic users reveal their private values truthfully, to auction multiple sub-channels among strategic users, and to track slowly timevarying bid prices. Our simulations illustrate the optimality of our schemes for constant bid prices, and also demonstrate the effectiveness of our tracking algorithm for slowly time-varying bids.