This correspondence considers the use of punctured quasi-arithmetic (QA) codes for the Slepian-Wolf problem. These entropy codes are defined by finite state machines for memoryless and first-order memory sources. Puncturing an entropy coded bit-stream leads to an ambiguity at the decoder side. The decoder makes use of a correlated version of the original message in order to remove this ambiguity. A complete distributed source coding (DSC) scheme based on QA encoding with side information at the decoder is presented, together with iterative structures based on QA codes. The proposed schemes are adapted to memoryless and first-order memory sources. Simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well-known DSC solutions using channel codes.