Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.