  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.
