This paper addresses the issue of robust and joint source-channel decoding of quasi-arithmetic codes. Quasi-arithmetic coding is a reduced precision and complexity implementation of arithmetic coding. This paper provides first a state model of a quasi-arithmetic decoder for binary and M-ary sources. The design of an error-resilient soft decoding algorithm follows quite naturally. The compression efficiency of quasi-arithmetic codes allows to add extra redundancy in the form of markers designed specifically to prevent de-synchronization. The algorithm is directly amenable for iterative source-channel decoding in the spirit of serial turbo codes. The coding and decoding algorithms have been tested for a wide range of channel signal-to-noise ratios. Experimental results reveal improved SER and SNR performances against Huffman and optimal arithmetic codes.