A Partial Decode-Forward Scheme For A Network with N relays

TL;DR

This paper introduces a partial decode-forward relaying scheme for N-relay networks, achieving a new lower bound on capacity that generalizes existing bounds and applies to various network topologies.

Contribution

It proposes a novel partial decode-forward scheme with Nth-order block Markov coding and sliding window decoding, extending relay network capacity bounds.

Findings

Achieves a compact expression for the scheme's achievable rate.

Reduces to known decode-forward bounds for special cases.

Provides a capacity lower bound for Gaussian two-level relay networks.

Abstract

We study a discrete-memoryless relay network consisting of one source, one destination and N relays, and design a scheme based on partial decode-forward relaying. The source splits its message into one common and N+1 private parts, one intended for each relay. It encodes these message parts using Nth-order block Markov coding, in which each private message part is independently superimposed on the common parts of the current and N previous blocks. Using simultaneous sliding window decoding, each relay fully recovers the common message and its intended private message with the same block index, then forwards them to the following nodes in the next block. This scheme can be applied to any network topology. We derive its achievable rate in a compact form. The result reduces to a known decode-forward lower bound for an N-relay network and partial decode-forward lower bound for a two-level relay network. We then apply the scheme to a Gaussian two-level relay network and obtain its capacity lower bound considering power constraints at the transmitting nodes.