1. ACHIEVEMENT DESCRIPTION
On the stability region of networks with instantaneous decoding Traskov, Medard, Sadeghi, Koetter
IMPACT
NEXT-PHASE GOALS
ACHIEVEMENT DESCRIPTION
STATUS QUO
NEW INSIGHTS
Network coding (red) increases the stability region over routing (blue) and leads, on average, to smaller delays.
MAIN ACHIEVEMENT:
Derive stability region under instantaneous decoding and provide online scheduling and network coding algorithm.
HOW IT WORKS:
ASSUMPTIONS AND LIMITATIONS:
Need ACKs or NACKs
Network coding limited to relay
• Opportunistic XOR-coding shows significant gains.
• However, stability region of instantaneous decoding is not known.
• Can formulate decoding constraints in a graphical model
• Constrained queuing system
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1. What technical challenge is being undertaken on behalf of the project
We study the stability region of networks under instantaneous decoding. This is a special form if INTER-session network coding which is tractable in practice as opposed to the general network coding problem. Furthermore, we provide a joint scheduling and network coding online algorithm that stabilizes every rate vector within the stability region, even without explicit knowledge of the latter.
2. Why is it hard and what are the open problems
As opposed to INTRA-session network coding (where random linear coding is capacity achieving) the general network coding problem is difficult. The challenge lies in restricting the set of coding possibilities to make the problem tractable, while still allowing enough coding to achieve throughput gains.
3. How has this problem been addressed in the past
In the past the opportunistic, local, XOR-coding scheme COPE has been proposed by Katti, Katabi et al. While it demonstrates significant gains, the stability region under instantaneous decoding was not known.
4. What new intellectual tools are being brought to bear on the problem
We have formulated the constraints on the code as well as on the schedule in a graphical model. While coding constraints have been addressed by Sundararajan et al. and scheduling constraints have been suggested by many previous works, this combination of coding and scheduling is new.
5. What is the main intermediate achievement
We have demonstrated that the online algorithm stabilizes every point within the rate region and leads to smaller delays. Furthermore, we have computed network coding gains by means of a volume ratio between appropriately defined polytopes.
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?
We want to include analog network coding (which is in the same trust) in our formulation and evaluate the performance gains as well as the implications on scheduling.
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.
PUBLICATION:
D. Traskov, M. Medard, P. Sadeghi, R. Koetter „Joint Scheduling and Instantaneously Decodable Network Coding,“ in proceedings of GLOBECOM 2009, Hawaii, USA, Dec
• Include analog network coding. Here, nodes a and b coordinate their transmission.
Instantaneous decoding increases the stability region and reduces delay.

2. Introduction Setup: Wireless network with INTER-session network coding
Each packet should be immediately useful ‘‘instantaneously decodable‘‘.
Motivated by COPE (Katti, Katabi, Medard et al.)
Set up a queuing model to optimize transmission scheduling and network coding.
Derive an optimal instantaneous decoding policy.
Compute stability region of the network.
Provide online algorithm to stabilize every point within this region.
Online algorithm needs no knowledge of the stability region.

3. Queuing Network Model
Transmission scheduling and network coding jointly, by means of the system of (virtual) queues.
Activation based on maximizing the differential backpressure.
Network coding by means of forming instantaneously decodable packets.

4. Network Coding
Constraints on the code are formulated on a conflict graph.
Two virtual queues that cannot be served together are connected.
Queues corresponding to instantaneously decodable packets form a stable set.
Given the queue occupancies as weights, the online algorithm computes the maximum weighted stable set.

5. Stability Region
For the simple network with four nodes, we fix a common rate for each pair of nodes.
Routing stabilizes all rates smaller than , while network coding pushes the stability region further to , or roughly 5% more.
For larger networks, larger gains.
In the next slide: Plot of the queuing dynamics for the critical points that are marked in the plot.

6. Queuing Dynamics
Total number of queued packets under the online algorithm
The 4 different rates reflect the breaking points of the stability regions.
Even if both routing and network coding are stable, network coding leads, on average, to smaller delays.
Different classes of users, with different preference between accuracy and reliability
Accuracy vs. reliability is essentially the tradeoff between image resolution vs. number of image re-loadings
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7. Implications and Further Work
Consequences:
We have derived the stability region under instantaneous decoding.
Combining (XORing) packets optimally leads to smaller backlogs than a heuristic search.
Conflict graph model allows wide flexibility in implementing suboptimal, but computationally light-weight network coding techniques.
Further work:
Extend results to more general multi-hop schemes.
Include analog network coding.
Exploit the performance of network coding heuristics within this framework.