  Digital crowdsourcing (CS) is a modern approach to perform certain large
projects using small contributions of a large crowd. In CS, a taskmaster
typically breaks down the project into small batches of tasks and assigns them
to so-called workers with imperfect skill levels. The crowdsourcer then
collects and analyzes the results for inference and serving the purpose of the
project. In this work, the CS problem, as a human-in-the-loop computation
problem, is modeled and analyzed in an information theoretic rate-distortion
framework. The purpose is to identify the ultimate fidelity that one can
achieve by any form of query from the crowd and any decoding (inference)
algorithm with a given budget. The results are established by a joint source
channel (de)coding scheme, which represent the query scheme and inference, over
parallel noisy channels, which model workers with imperfect skill levels. We
also present and analyze a query scheme dubbed $k$-ary incidence coding and
study optimized query pricing in this setting.
