# Coding theory for noiseless channels realized by anonymous oblivious mobile robots

## TL;DR

This paper introduces a coding scheme for noiseless communication using anonymous, oblivious mobile robots on graphs, analyzing its efficiency and providing algorithms for optimal code size and transmission delay.

## Contribution

It presents novel coding algorithms for robot swarms that optimize either code size or transmission delay, with bounds and performance analysis.

## Key findings

- Lower bound of delay depends on swarm size
- Code size is exponentially bounded by swarm size
- Two algorithms achieve near-optimal and optimal trade-offs

## Abstract

We propose an information transmission scheme by a swarm of anonymous oblivious mobile robots on a graph. The swarm of robots travel from a sender vertex to a receiver vertex to transmit a symbol generated at the sender. The codeword for a symbol is a pair of an initial configuration at the sender and a set of terminal configurations at the receiver. The set of such codewords forms a code. We analyze the performance of the proposed scheme in terms of its code size and transmission delay. We first demonstrate that a lower bound of the transmission delay depends on the size of the swarm, and the code size is upper bounded by an exponent of the size of the swarm. We then give two algorithms for a swarm of a fixed size. The first algorithm realizes a near optimal code size with a large transmission delay. The second algorithm realizes an optimal transmission delay with a smaller code size. We then consider information transmission by swarms of different sizes and present upper bounds of the expected swarm size by the two algorithms. We also present lower bounds by Shannon's lemma and noiseless coding theorem.