Abstract
This paper designs non-adaptive querying policies (NQPs) for the noisy 20 questions game based on error-correction codes. The querying accuracy of a specific NQP is upper bounded by a function of the minimum distance among its codewords. As a result, the row-column constraint is put on codewords of NQPs for scenarios with limited detection to enlarge their minimum distance for improving the querying accuracy, where the limited detection means that only a small number of intervals can be detected at each querying round. Then, it is used to protect the least significant bits in unequal error protection NQPs with linear codes for unlimited detection scenarios. In particular, these structures allow us to deterministically optimize parameters for better querying accuracy. Simulation results show that our methods achieve quantized mean squared error up to several magnitudes compared with the NQPs based on random block coding.
Highlights
In the noisy 20 questions game [1], the player repeatedly asks queries to the oracle who knows the answer, and receives noisy responses from the oracle
An upper bound on the quantized mean squared error (QMSE) of unequal error protection (UEP)-non-adaptive querying policies (NQPs) is derived from minimum distances related to most significant bits (MSBs) and least significant bits (LSBs)
The RC constraint and linearity allow us to show the accuracy trade-offs between the designs for MSBs and LSBs with the help of Gilbert bound [8] and our upper bound on the QMSE of UEP-NQPs
Summary
In the noisy 20 questions game [1], the player repeatedly asks queries to the oracle who knows the answer, and receives noisy responses from the oracle. When estimating the value of a target variable is the purpose of the player, the core problem here is to design the optimal query sequence for a minimum estimation error given a fixed number of queries [2] This game and its querying policies are important for target localization in various areas including computer vision and molecular biology, such as character localization [1], chemometric toxin-detection [3] and mitochondria localization [4]. An upper bound on the QMSE of UEP-NQPs is derived from minimum distances related to MSBs and LSBs. Following the above bounds, we design NQPs for target localization problem for various scenarios. The RC constraint and linearity allow us to show the accuracy trade-offs between the designs for MSBs and LSBs with the help of Gilbert bound [8] and our upper bound on the QMSE of UEP-NQPs. As a result, our proposed UEP-NQP can be deterministically optimized to obtain better querying accuracy.
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