Joint source-channel coding with variable length codes

We consider an information transmission scheme where a stream of messages is encoded using a variable length code, and the code sequence, obtained as a concatenation of codewords, is transmitted over a noisy discrete memoryless channel. The decoder constructs a stream of estimates of the messages. Note that the problems that concern the use of variable length codes for transmission over noisy channels also appear if the code is used only for source encoding since any channel coding scheme cannot reduce the level of noise up to zero. We propose a convolutional-type decoding algorithm assuming that: (1) the total length of the transmitted code sequence is known to the decoder and (2) decoding delay is allowed and the decoder constructs a maximum likelihood estimate of the whole stream of messages.