On the Capacity of the Binary-Symmetric Parallel-Relay Network

TL;DR

This paper analyzes the capacity of binary-symmetric parallel-relay networks, showing that forwarding relays can achieve capacity with either coded or uncoded transmission depending on the number of relays, while decoding relays are optimal only when few.

Contribution

It characterizes the capacity-achieving strategies for different relay configurations and demonstrates the suboptimality of decoding relays in large networks.

Findings

Forwarding relays achieve capacity with coded transmission and finite relays.

Uncoded transmission with many relays also achieves capacity.

Decoding relays are optimal only in small networks.

Abstract

We investigate the binary-symmetric parallel-relay network where there is one source, one destination, and multiple 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. In addition, we show that any coding scheme that requires decoding at any relay is suboptimal in large parallel-relay networks, where forwarding relays achieve strictly higher rates.