References & Further Reading

References

1. P. Gupta and P. R. Kumar, The Capacity of Wireless Networks, 2000

   The foundational paper on capacity scaling in wireless networks. Establishes the $\Theta(1/\sqrt{n\log n})$ per-node throughput limit for multi-hop routing.

2. A. Özgür, O. Lévêque, and D. N. C. Tse, Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks, 2007

   Shows that hierarchical MIMO cooperation achieves $\Theta(n)$ total throughput, dramatically beating multi-hop routing. Establishes the role of cooperation in scalable wireless networks.

3. S. H. Lim, Y.-H. Kim, A. El Gamal, and S.-Y. Chung, Noisy Network Coding, 2011

   Introduces the noisy network coding scheme: a universal relay strategy that achieves within a constant gap of the cut-set bound for any Gaussian network. The key insight is joint decoding of compression indices.

4. A. S. Avestimehr, S. N. Diggavi, and D. N. C. Tse, Wireless Network Information Flow: A Deterministic Approach, 2011

   Introduces the deterministic channel model as a tool for approximating Gaussian network capacity. The quantize-map-and-forward scheme achieves the constant-gap result via a different route than NNC.

5. A. El Gamal and Y.-H. Kim, Network Information Theory, Cambridge University Press, 2011

   Chapters 16-19 provide comprehensive treatment of relay channels, relay networks, and capacity scaling. Essential reference for all results in this chapter.

6. M. Franceschetti, O. Dousse, D. N. C. Tse, and P. Thiran, Closing the Gap in the Capacity of Wireless Networks via Percolation Theory, 2007

   Tightens the Gupta-Kumar result to $\Theta(1/\sqrt{n})$ (removing the $\log n$ factor) using percolation theory to establish connectivity.

7. L.-L. Xie and P. R. Kumar, A Network Information Theory for Wireless Communication: Scaling Laws and Optimal Operation, 2004

   Extends the scaling law analysis to networks with different traffic patterns and node capabilities. Bridges the gap between Gupta-Kumar and cooperative schemes.

8. T. M. Cover and A. A. El Gamal, Capacity Theorems for the Relay Channel, 1979

   The foundational paper on relay channel coding. All Gaussian relay channel results in this chapter trace back to the general formulas established here.

9. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 2nd ed., 2006

   Chapter 16 provides a concise introduction to relay channels; Chapter 15 covers Gaussian channels. The standard reference for the Gaussian capacity formula.

10. G. Kramer, M. Gastpar, and P. Gupta, Cooperative Strategies and Capacity Theorems for Relay Networks, 2005

    Extends relay results to multi-relay networks. Essential for the diamond network and noisy network coding discussion.

Further Reading

• Capacity scaling with cooperation

  A. Özgür, O. Lévêque, and D. N. C. Tse, "Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks," IEEE Trans. Inf. Theory, 2007. Also: A. Ozgur and O. Leveque, "Throughput-Delay Tradeoff for Hierarchical Cooperation in Ad Hoc Wireless Networks," IEEE Trans. Inf. Theory, 2010.

  The original papers on hierarchical cooperation. The 2010 follow-up adds the delay analysis, showing that the throughput gain comes at a cost of increased latency.

• Deterministic models for wireless networks

  A. S. Avestimehr, S. N. Diggavi, and D. N. C. Tse, "Wireless Network Information Flow," IEEE Trans. Inf. Theory, 2011.

  The deterministic approach provides a simpler path to capacity approximation results and gives clean structural insights into optimal network coding strategies.

• Practical relay protocols

  J. N. Laneman, D. N. C. Tse, and G. W. Wornell, "Cooperative Diversity in Wireless Networks," IEEE Trans. Inf. Theory, 2004.

  Bridges the gap between information-theoretic relay channel results and practical wireless protocol design. Essential reading for understanding how DF and CF map to actual system implementations.

• Noisy network coding extensions

  S. H. Lim, Y.-H. Kim, A. El Gamal, and S.-Y. Chung, "Layered Noisy Network Coding," in Proc. Allerton Conference, 2014.

  Extends NNC to handle layered coding structures, improving the gap for certain network topologies and connecting to practical layered communication architectures.