It was demonstrated in recent contributions that Joint Source/Channel (JSC) decoding could be a good issue to make error correction in the case of transmission of entropy-encoded data. This paper addresses a new scheme for JSC decoding of Variable-Length Codes (VLC) and Arithmetic Codes (AC) based on Maximum a posteriori (MAP) sequence estimation. Previous contributions used a trellis description of the entropy encoding machine to perform soft input decoding. Referred to hard input classical decoding, significant improvements are achieved. Nevertheless, for realistic contexts, the complexity of the trellis-based technique becomes intractable. The decoding algorithm we propose performs Chase-like decoding using a priori knowledge of the source symbol sequence and the compressed bit-stream lengths. Performance in the case of transmission on an Additive White Gaussian Noise (AWGN) channel is evaluated in terms of Packet Error Rate (PER). Simulation results show that the proposed decoding algorithm leads to significant performance gain in comparison to classical VLC and AC decoding while exhibiting very low complexity. The practical relevance of the proposed technique is validated in the case of image transmission across the AWGN channel. Lossless and lossy image compression schemes are considered, and the Chase-like entropy decoder shows excellent results in terms of PER and reconstructed image quality.