Bounds on the rates of joint source-channel codes for general sources and channels

In this paper, upper bounds on the rates of joint source-channel codes are derived for any finite blocklength and any positive error probability. For a discrete memoryless source and a general, possibly non-discrete channel, an upper bound on the rate of a joint source-channel code with average symbol error probability constraint is shown. For any general discrete source and general channel, a lower bound on the block error probability of a joint source-channel code is shown. These bounds can easily be simplified to handle discrete stationary memoryless source and discrete memoryless channel.