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Most source coding standards (voice, audio, image and video) use Variable-Length Codes (VLCs) for compression. However, the VLC decoder is very sensitive to transmission errors in the compressed bit-stream. Previous contributions, using a trellis description of the VLC codewords to perform soft decoding, have been proposed. Significant improvements are achieved by this approach when compared with prefix decoding. Nevertheless, for realistic VLCs, the complexity of the trellis technique becomes intractable. In this paper, we propose a soft-input VLC decoding method using an a priori knowledge of the lengths of the source-symbol sequence and the compressed bit-stream with Maximum A Posteriori (MAP) sequence estimation. Performance in the case of transmission over an Additive White Gaussian Noise (AWGN) channel is evaluated. Simulation results show that the proposed decoding algorithm leads to significant performance gain in comparison with the prefix VLC decoding besides exhibiting very low complexity. A new VLC decoding method generating additional information regarding the reliability of the bits of the compressed bit-stream is also proposed. We consider the serial concatenation of a VLC with two types of channel code and perform iterative decoding. Results show that, when concatenated with a recursive systematic convolutional code (RSCC), iterative decoding provides remarkable error correction performance. In fact, a gain of about 2.3 dB is achieved, in the case of transmission over an AWGN channel, with respect to tandem decoding. Second, we consider a concatenation with a low-density parity-check (LDPC) code and it is shown that iterative joint source/channel decoding outperforms tandem decoding and an additional coding gain of 0.25 dB is achieved.