The Binary-Symmetric Parallel-Relay Network

TL;DR

This paper analyzes the capacity of the binary-symmetric parallel-relay network, demonstrating how different relay strategies achieve capacity depending on the number of relays and transmission methods.

Contribution

It provides capacity results for the network and characterizes when forwarding or decoding relays are optimal for achieving capacity.

Findings

Forwarding relays achieve capacity with coded transmission and few relays.

Uncoded transmission with many relays also achieves capacity.

Decoding relays are optimal when the number of relays is small.

Abstract

We present capacity results of the binary-symmetric parallel-relay network, where there is one source, one destination, and K relays in parallel. We show that forwarding relays, where the relays merely transmit their received signals, achieve the capacity in two ways: with coded transmission at the source and a finite number of relays, or uncoded transmission at the source and a sufficiently large number of relays. On the other hand, decoding relays, where the relays decode the source message, re-encode, and forward it to the destination, achieve the capacity when the number of relays is small.