References & Further Reading

References

1. T. M. Cover, Broadcast Channels, 1972

   The foundational paper that introduced the broadcast channel and superposition coding. Cover proved the capacity region for degraded channels and posed the general BC problem.

2. P. P. Bergmans, Random Coding Theorem for Broadcast Channels with Degraded Components, 1973

   Proved the converse for the Gaussian degraded BC using the entropy power inequality.

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

   Chapter 15 covers broadcast channels comprehensively. Our treatment follows Cover and Thomas closely for the degraded case.

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

   Chapters 5-8 develop the broadcast channel theory in full generality. The definitive modern reference for multiuser information theory.

5. R. G. Gallager, Capacity and Coding for Degraded Broadcast Channels, 1974

   Independent derivation of the degraded BC capacity using a different proof technique than Bergmans.

6. H. Weingarten, Y. Steinberg, and S. Shamai (Shitz), The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel, 2006

   Established the capacity region of the MIMO BC via dirty paper coding. Uses the channel enhancement technique for the converse.

7. S. Vishwanath, N. Jindal, and A. Goldsmith, Duality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels, 2003

   Established the MAC-BC duality for Gaussian MIMO channels, providing the computational framework for BC capacity region optimization.

8. G. Caire and S. Shamai (Shitz), On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel, 2003

   Early work on the MIMO BC using zero-forcing beamforming with dirty paper coding. Showed that DPC with successive encoding achieves the MIMO BC capacity.

9. D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005

   Chapter 6 covers the broadcast channel from a wireless communications perspective, with emphasis on practical implications.

10. A. A. El Gamal and E. C. Van der Meulen, A Proof of Marton's Coding Theorem for the Discrete Memoryless Broadcast Channel, 1981

Further Reading

• The general (non-degraded) broadcast channel

  A. El Gamal and Y.-H. Kim, *Network Information Theory*, Cambridge University Press, 2011, Chapters 5-8

  The degraded BC is the starting point, but the general BC requires Marton coding. Chapter 16 of this book covers this, and El Gamal-Kim provides the full technical development.

• MIMO broadcast channel and dirty paper coding

  G. Caire and S. Shamai, "On the achievable throughput of a multiantenna Gaussian broadcast channel," IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 1691-1706, Jul. 2003

  Bridges the scalar BC theory of this chapter to the MIMO case. Essential reading before Chapter 16 and Book telecom, Chapter 17.

• NOMA for 5G: theory and practice

  Z. Ding, Y. Liu, J. Choi, Q. Sun, M. Elkashlan, C.-L. I, and H. V. Poor, "Application of non-orthogonal multiple access in LTE and 5G networks," IEEE Communications Magazine, vol. 55, no. 2, pp. 185-191, Feb. 2017

  The practical incarnation of superposition coding in cellular systems. Discusses user pairing, SIC design, and comparison with OFDMA.

• Entropy power inequality: proofs and extensions

  O. Rioul, "Information theoretic proofs of entropy power inequalities," IEEE Trans. Inf. Theory, vol. 57, no. 1, pp. 33-55, Jan. 2011

  A comprehensive treatment of the EPI and its many proofs. Clarifies the connection to Fisher information and the de Bruijn identity.

• MAC-BC duality and iterative water-filling

  W. Yu, "Sum-capacity computation for the Gaussian vector broadcast channel via dual decomposition," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 754-759, Feb. 2006

  The algorithmic companion to the duality theory. Shows how to compute the BC capacity region boundary via the dual MAC formulation and iterative optimization.

• Broadcast channels with common and private messages

  J. Körner and K. Marton, "General broadcast channels with degraded message sets," IEEE Trans. Inf. Theory, vol. 23, no. 1, pp. 60-64, Jan. 1977

  Extends the BC model to include a common message decoded by both receivers. The capacity region involves superposition coding with an additional common-message layer.