Error Exponents for Joint Source-Channel Coding with Delay-Constraints

Traditionally, joint source-channel coding is viewed in the block coding context — all the source symbols are known in advance by the encoder. Here, we consider source symbols to be revealed to the encoder in real time and require that they be reconstructed at the decoder within a certain fixed end-to-end delay. We derive upper and lower bounds on the reliability function with delay for cases with and without channel feedback. For erasure channels with feedback, the upper-bound is shown to be achievable and the resulting scheme shows that from a delay perspective, nearly separate source and channel coding is optimal.