Network Coding and Wireless Physical-layer ... - Jacobs University

114 Chapter 8: Summary, Conclusion, and Future Works
and Bob can then derive the overall channel gain h ar h rb from the signal they receive in
the first and the third time slots. Since the channel information sent out by the relay is
neither h ar nor h rb but a network-coded combination, which is h ar + h rb , the enemy will
find it more difficult to derive h ar h rb .
Investigation of Different Network Coding and Relaying Patterns
When Alice and Bob are within each other’s transmission range, the efficiency of key
generation can be enhanced as shown by our proposed scheme in Fig. 8.2(c). With an
extension by one time slot, Alice and Bob can now generate a secret key from two paths,
the direct one and the relayed one.
Apart from the triangular shape in Fig. 8.2(c), it is interesting to investigate the
graphs with other shapes, such as a quadrilateral or a polygon in general, and compare
the key generation efficiency. Also, one might design a scheme to generate secret keys not
only for Alice and Bob, but also for the relays. One may further ask such graph-theoretic
questions as how the convexity of the shape, or the completeness of the graph, affect key
generation. (A shape is convex if all the points along the straight line connecting any two
points within it lie inside. A graph is complete if every pair of nodes is connected by an
edge.)
Generalizing the MA-AF Scheme
When the distance between Alice and Bob is larger, we need more than one relay and
thus a generalized network coding scheme. The main question is whether a corresponding
scheme can be derived by using Shimizu’s procedure as a building block, and how.
Protocols for WPSG with Network Coding
If some local key is generated by the triangular geometry in Fig. 8.2(c), how can we make it
compatible with the key generation schemes using different geometry and network coding
patterns in other locations?