Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem

TL;DR

This paper introduces a non-adaptive, superposition coding-based querying policy for the noisy 20 questions problem, achieving exponential error decay rates comparable to adaptive schemes and outperforming previous equal error protection methods.

Contribution

It proposes a novel open-loop UEP querying strategy using superposition coding, improving error decay rates in the noisy 20 questions problem without feedback.

Findings

Error probability decreases exponentially with the number of queries.

The proposed method matches the performance of adaptive schemes.

It outperforms previous UEP repetition coding in error exponent.

Abstract

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection.