1. ACHIEVEMENT DESCRIPTION
Scheduling for Network Coded Multicast Medard, Traskov, Heindlmaier, Koetter
IMPACT
NEXT-PHASE GOALS
ACHIEVEMENT DESCRIPTION
STATUS QUO
NEW INSIGHTS
No systematic approach to multi-access for network coding.
Shows that the performance of well-known scheduling techniques is very poor.
Suggests a largely improved bandwidth efficiency.
New notion of scheduling conflicts, when network coding is used.
MAIN ACHIEVEMENT:
Hyperarc scheduling outperforms well-known scheduling techniques.
HOW IT WORKS:
Valid network configurations can be identified as stable sets in the conflict graph.
Jointly solve subgraph selection and scheduling problem.
Distributed algorithm.
ASSUMPTIONS AND LIMITATIONS:
Convergence speed of algorithm.
Scaling with the size of the network.
Current scheduling techniques use the bandwidth very inefficiently.
Include notes that would be helpful to the reader or someone (other than yourself) who needs to understand the details. Ideally the chart will be useful even without the author to explain the details. Also include references to published papers plus URLs to online versions if available.
Keep in mind that somewhere or other in this chart, each of these questions should be answered:
What technical challenge is being undertaken on behalf of the project
In short, the challenge is to organize network coding (bandwidth-) efficiently in networks with limited resources. More precisely, ee suggest a framework, where network coding subgraph optimization and channel access are treated jointly. We construct a hypergraph that takes into account possible transmissions to every subset of neighbors of a node. Each such subset is represented by a hyperarc. The essential novelty of our approach is that we consider subsets of hyperarcs that can be activated simultaneously without interfering. These scheduling constraints are transformed into a conflict graph representation, that is new in the context of intra-session coded multicast.
2. Why is it hard and what are the open problems
The overall problem is hard, because at its core we have to solve a difficult problem from combinatorial optimization - the maximum weighted stable set problem. In general, even the question whether a point belongs to the stable set polytope cannot be answered in polynomial time, except for certain special classes of graphs. Open problems are furthermore to distribute this computation within the network and to find ways to speed up the algorithm, without much performance loss.
3. How has this problem been addressed in the past
The prevalent approach to this problem has been to construct an interference-free transmission schedule by means of some heuristic and then to compute an optimal subgraph over this, now essentially orthogonal, network. This is not only theoretically suboptimal, but also has been shown to lead to a very poor bandwidth efficiency.
4. What new intellectual tools are being brought to bear on the problem
The main new tool is an appropriately defined conflict graph that takes into account broadcasting and the nature of network-coded information flow. We use results from graph theory and combinatorial optimization.
5. What is the main intermediate achievement
We formulate the joint medium access and subgraph optimization problem by means of a graphical conflict model. The nature of network coded flows is not captured by classical link-based scheduling and therefore requires a novel approach based on conflicting hyperarcs. By means of simulations, we evaluate the performance of our algorithm and conclude that it significantly outperforms existing scheduling techniques.
6. How and when does this achievement align with the project roadmap (end-of-phase or end-of-project goal)
The intermediate results are milestones within the project roadmap and based on these we are on track with the end-of-project goals.
7. What are the even long-term objectives and consequences?
In the long term, we are interested in extending the work to a) include also INTER-session network coding, and b) to further explore the achievable trade-offs between performance (e.g. throughput) and computational complexity. This includes also more efficient distributed implementations.
8. Which thrusts and SOW tasks does this contribution fit under and why?
This overlaps thrust 1 (where the conflict graph originated) with thrust 3 (optimization) but also thrust 2 through the MAC-layer.
Graphical model for conflicts between hyperarcs.
Do not try to minimize the number of collisions per se.
• Extension to INTER-session network coding.
• Investigations on performance/complexity trade-offs.
Scheduling matched to the network coding subgraph largely improves performance.

2. Scheduling for Network Coded Multicast
Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project
Thrust 3
Scheduling for Network Coded Multicast
M. Medard, D. Traskov, M. Heindlmaier, R. Koetter

3. Challenges in Mobile Ad-hoc Networks
How to deal with packet losses and network volatility?
Solution: Random linear network coding (RLNC) acts as a rateless code and can capitalize on overhearing of packets (wireless broadcast advantage)
Challenge 2:
How to support multicast efficiently?
Solution: Again, RLNC: It is capacity achieving and network flow is much easier to compute than Steiner trees.
Challenge 3:
If we use RLNC, how should the MAC-layer be designed in order to support network coding?
Our contribution.

4. Our Approach
Design of a MAC-mechanism that supports random linear network coding.
Basic Idea: activate hyperarcs instead of links and find conflict-free hyperarc configurations.
Valid network configurations are represented by stable sets in a properly defined conflict graph.
Jointly (and globally) optimize the MAC-layer and the network coding subgraph.
Simulations show dramatic improvement in bandwidth efficiency compared to common scheduling heuristics.

5. Hypergraph Model
An example of a hyperarc:

6. From the Hypergraph to the Conflict Graph Model
Half-duplex and secondary interference constraints
Hard interference constraints (e.g. protocol model [GuptaKumar99])
Conflict graph construction: Conflicting hyperarcs are adjacent.

7. Putting the Pieces Together
Joint optimization of subgraph and schedule

8. Simulation Setup
Simulations on random networks with the following properties:
Nodes scattered in a square area with unit density.
Two nodes are in radio range if their distance is below a certain threshold.
Packet erasure probability from i to j proportional to dist(i , j)−2.
One source to two receivers multicast; we are interested in the
maximum achievable rate.
We compare our scheduling techniques with two commonly used approaches: full channelization and two-hop constraint.
NUM/AM measures performance in terms of application metrics, instead of spectral efficiency (average transmission rate over a fixed bandwidth), which has gained considerable research interest and commercial activity recently.

9. Simulation Results
Baseline: Full orthogonalization and 2-hop constraint model.
Our approach: Optimal technique (up to 14 nodes) and heuristics based on it.

10. Conclusion Scheduling performance: In summary, we presented:
For networks of moderate size the 2-hop constraint is a marginal improvement over full channelization.
Our scheduling technique increases the rate up to 90%
In summary, we presented:
A systematic scheduling framework for network coded traffic.
New Idea 1: Activation of hyperarcs instead of edges.
New Idea 2: Don’t try to minimize the number of collisions per se.
Surprising result: 2-hop constraint not better than full channelization.
Not so surprisingly: Significant scheduling gains.