Exact Moderate Deviation Asymptotics in Streaming Data Transmission

TL;DR

This paper analyzes the fundamental limits of streaming data transmission in the moderate deviations regime, showing that the error exponent improves proportionally with the delay T for output symmetric channels.

Contribution

It establishes the exact moderate deviations constant for streaming transmission, demonstrating a T-fold improvement over non-streaming setups, and introduces a new change-of-measure lemma for the converse proof.

Findings

Moderate deviations constant is T times larger for streaming over non-streaming.

Error probability bounds are derived using a new change-of-measure lemma.

Achievability is shown with joint encoding and decoding of current and past messages.

Abstract

In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of $T$ for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.