1 research outputs found
Coding theory for noiseless channels realized by anonymous oblivious mobile robots
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