Joint Source-Channel Coding Using Variable-Length Codes

We address the problem of joint source-channel coding when variable-length codes are used for information transmission over a discrete memoryless channel. Data transmitted over the channel are interpreted as pairs $(m_k,t_k)$, where $m_k$ is a message generated by the source and $t_k$ is a time instant when the transmission of the kth codeword begins. The decoder constructs an estimate of the transmitted sequence of pairs, and the kth decoding error is introduced as the event that the pair $(m_k,t_k)$ does not belong to this sequence. We describe the maximum likelihood decoding algorithm and prove a lower bound on the exponent of the decoding error probability. For a subclass of discrete memoryless sources and discrete memoryless channels, this bound is asymptotically tight.