  This paper models the crowdsourced labeling/classification problem as a
sparsely encoded source coding problem, where each query answer, regarded as a
code bit, is the XOR of a small number of labels, as source information bits.
In this paper we leverage the connections between this problem and well-studied
codes with sparse representations for the channel coding problem to provide
querying schemes with almost optimal number of queries, each of which involving
only a constant number of labels. We also extend this scenario to the case
where some workers can be unresponsive. For this case, we propose querying
schemes where each query involves only log n items, where n is the total number
of items to be labeled. Furthermore, we consider classification of two
correlated labeling systems and provide two-stage querying schemes with almost
optimal number of queries each involving a constant number of labels.
