Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

TL;DR

This paper investigates streaming data transmission over discrete memoryless channels, demonstrating how the rate-error tradeoff improves in the moderate deviations and central limit regimes through novel coding techniques and analyzing various setup variants.

Contribution

It introduces new coding strategies for streaming over DMCs that enhance error exponents and second-order rates in key regimes, including variants with erasure options and variable message rates.

Findings

Moderate deviations constant improves by factor T.

Second-order coding rate improves by approximately √T.

Enhanced error exponents with erasure options.

Abstract

We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of $T$ blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show that i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of $T$ and ii) in the central limit regime, the second-order coding rate improves by a factor of approximately $\sqrt{T}$ for a wide range of channel parameters. For both regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis. Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder and show that both the exponents of the total error and the undetected error probabilities improve by factors of $T$. Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay. Finally, we also extend our results to the case where the message rate is not fixed but alternates between two values.