# Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios

## TL;DR

This paper develops a unified analysis of lossless source coding in various scenarios, providing third-order performance characterizations and introducing a novel random access coding scheme with rateless coding and feedback.

## Contribution

It introduces a third-order analysis for multiple scenarios and proposes a new random access source coding method with provable optimality.

## Key findings

- Third-order characterization of Slepian-Wolf rate region.
- Independent encoders can match joint encoder performance.
- A rateless coding scheme with feedback achieves optimal performance.

## Abstract

This work studies point-to-point, multiple access, and random access lossless source coding in the finite-blocklength regime. In each scenario, a random coding technique is developed and used to analyze third-order coding performance. Asymptotic results include a third-order characterization of the Slepian-Wolf rate region with an improved converse that relies on a connection to composite hypothesis testing. For dependent sources, the result implies that the independent encoders used by Slepian-Wolf codes can achieve the same third-order-optimal performance as a single joint encoder. The concept of random access source coding is introduced to generalize multiple access (Slepian-Wolf) source coding to the case where encoders decide independently whether or not to participate and the set of participating encoders is unknown {\em a priori} to both the encoders and the decoder. The proposed random access source coding strategy employs rateless coding with scheduled feedback. A random coding argument proves the existence of a single deterministic code of this structure that simultaneously achieves the third-order-optimal Slepian-Wolf performance for each possible active encoder set.