# Optimal Routing for Decode-and-Forward based Cooperation in Wireless Networks

## TL;DR

This paper explores optimal routing strategies in cooperative wireless relay networks using decode-and-forward coding, proposing algorithms to maximize data rates and demonstrating practical performance with LDPC codes.

## Contribution

It introduces an optimal routing algorithm for decode-and-forward strategies and a polynomial heuristic, enhancing cooperative network data transmission.

## Key findings

- Decode-and-forward achieves higher rates than multi-hop coding.
- The heuristic algorithm finds optimal routes for independent codewords.
- Practical LDPC codes validate the theoretical strategies.

## Abstract

We investigate cooperative wireless relay networks in which the nodes can help each other in data transmission. We study different coding strategies in the single-source single-destination network with many relay nodes. Given the myriad of ways in which nodes can cooperate, there is a natural routing problem, i.e., determining an ordered set of nodes to relay the data from the source to the destination. We find that for a given route, the decode-and-forward strategy, which is an information theoretic cooperative coding strategy, achieves rates significantly higher than that achievable by the usual multi-hop coding strategy, which is a point-to-point non-cooperative coding strategy. We construct an algorithm to find an optimal route (in terms of rate maximizing) for the decode-and-forward strategy. Since the algorithm runs in factorial time in the worst case, we propose a heuristic algorithm that runs in polynomial time. The heuristic algorithm outputs an optimal route when the nodes transmit independent codewords. We implement these coding strategies using practical low density parity check codes to compare the performance of the strategies on different routes.