# On the Capacity of the Slotted Strongly Asynchronous Channel with a Bursty User

## TL;DR

This paper analyzes the fundamental limits of asynchronous communication in slotted channels with bursty users, deriving bounds on the trade-offs between transmission rate, asynchronism, and burstiness in the asymptotic regime.

## Contribution

It provides the first comprehensive bounds on the capacity of strongly asynchronous channels with bursty users, including models with random access and matching bounds in special cases.

## Key findings

- Achievability and converse bounds on the $(R,
u, ext{or } eta)$ trade-offs.
- Bounds coincide for $
u=0$ and $R=0$, and for $eta= ext{or }
u$ and $R=0$.
- Characterization of the capacity region in asymptotic regimes.

## Abstract

In this paper, the trade-off between the number of transmissions (or burstiness) $K_n=e^{n\nu}$ of a user, the asynchronism level $A_n=e^{n\alpha}$ in a slotted strongly asynchronous channel, and the ability to distinguish $M_n=e^{nR}$ messages per transmission with vanishingly error probability is investigated in the asymptotic regime as blocklength $n$ goes to infinity. The receiver must locate and decode, with vanishing error probability in $n$, all of the transmitted messages. Achievability and converse bounds on the trade-off among $(R,\alpha,\nu)$ is derived. For cases where $\nu=0$ and $ R=0$, achievability and converse bounds coincide. A second model for a bursty user with random access in which the user may access and transmit a message in each block with probability $e^{-n\beta}$ in then considered. Achievability and converse bounds on the trade-off between $(R, \alpha, \beta)$ is also characterized. For cases where $\beta =\alpha$ and $R=0$, the achievability and converse bounds match.