References & Further Reading
References
- K. Marton, A coding theorem for the discrete memoryless broadcast channel, 1979
The seminal inner bound for the general broadcast channel using binning. Still the best known achievable region after over 40 years.
- C. Nair and A. El Gamal, An outer bound to the capacity region of the broadcast channel, 2007
The tightest known outer bound for the general BC. Matches Marton's bound for degraded, deterministic, and binary-input BCs.
- H. Weingarten, Y. Steinberg, and S. Shamai (Shitz), The capacity region of the Gaussian multiple-input multiple-output broadcast channel, 2006
Proves DPC achieves the MIMO BC capacity region via the channel enhancement converse technique.
- G. Caire and S. Shamai (Shitz), On the achievable throughput of a multiantenna Gaussian broadcast channel, 2003
Establishes DPC sum-capacity optimality for the MISO BC. A key stepping stone to the full capacity result.
- S. Vishwanath, N. Jindal, and A. Goldsmith, Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels, 2003
Establishes the MAC-BC duality with sum power constraint and uses it for DPC sum-rate computation.
- P. Viswanath and D. N. C. Tse, Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality, 2003
Independent proof of MAC-BC duality and DPC sum-rate optimality via a minimax approach.
- M. H. M. Costa, Writing on dirty paper, 1983
The foundational result on pre-canceling known interference. The key building block for DPC in the MIMO BC.
- A. El Gamal and Y.-H. Kim, Network Information Theory, Cambridge University Press, 2011
Comprehensive treatment of broadcast channels (Ch. 5, 8). Contains rigorous proofs of Marton's bound, the UV outer bound, and Nair-El Gamal.
- T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 2nd ed., 2006
Chapter 15 covers the degraded BC. A good starting point before tackling the general case.
- S. S. Christensen, R. Agrawal, and J. Cioffi, Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design, 2008
The WMMSE algorithm for direct BC optimization. Widely used in practical system design.
- W. Yu and J. Cioffi, Sum capacity of Gaussian vector broadcast channels, 2004
Iterative water-filling algorithm for computing the dual MAC sum capacity.
- P. P. Bergmans, Random coding theorem for broadcast channels with degraded components, 1973
The original converse for the degraded BC using the entropy power inequality.
Further Reading
Resources for deeper exploration of broadcast channel theory and applications.
The general BC capacity problem
A. El Gamal and Y.-H. Kim, Network Information Theory, Chapter 8
Contains the most complete treatment of Marton's bound, the Nair-El Gamal outer bound, and open problems. Essential for anyone working on the BC capacity conjecture.
Practical MU-MIMO precoding
Book telecom, Chapter 17 (MU-MIMO Downlink)
Covers ZF, MMSE, and RZF precoding with implementation details. Bridges the gap between the DPC capacity theory here and what 5G NR actually uses.
MIMO BC with imperfect CSIT
N. Jindal, 'MIMO broadcast channels with finite-rate feedback,' IEEE Trans. IT, 2006
DPC requires perfect CSIT. This paper quantifies the rate loss with limited feedback — critical for understanding the theory-practice gap.
Massive MIMO and the BC
Book MIMO (Massive MIMO chapters)
When $n_t \to \infty$ with fixed $K$, the MIMO BC simplifies dramatically: channels become orthogonal, linear precoding is near-optimal, and the DPC theory becomes less relevant for system design.