Reliability function for streaming over a DMC with feedback

Conventionally, posterior matching is investigated in channel coding and block encoding contexts – the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols progressively arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback under regularity conditions. We propose a novel instantaneous encoding phase that operates during the symbol arriving period and that achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. The instantaneous encoding phase partitions the evolving message alphabet into groups whose priors are close to the capacity-achieving distribution, and randomizes the group indices to ensure that the transmitted group index has the capacity-achieving distribution. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage in terms of the reliability function.