References & Further Reading

References

1. M. Costa, Writing on Dirty Paper, 1983

   The seminal dirty paper coding paper. Shows that for the Gaussian channel with additive interference known at the encoder, the interference can be completely canceled at no cost. One of the most cited papers in information theory.

2. S. I. Gel'fand and M. S. Pinsker, Coding for Channel with Random Parameters, 1980

   The general coding theorem for channels with non-causal state information at the encoder. The capacity formula $\max[\ntn{mi}(U;Y) - \ntn{mi}(U;S)]$ introduced the binning technique that became central to multiuser information theory.

3. C. E. Shannon, Channels with Side Information at the Transmitter, 1958

   Shannon's analysis of channels with causal state information at the encoder, introducing the concept of Shannon strategies.

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

   The modern reference for multiuser information theory. Chapter 7 covers channels with state in full generality, including the Gel'fand-Pinsker theorem, Costa's theorem, and extensions.

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

   Proves that DPC achieves the capacity region of the Gaussian MIMO broadcast channel. The paper that connected Costa's theorem to practical multiuser MIMO systems.

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

   One of the first papers to connect DPC to the MIMO broadcast channel, showing that DPC achieves the sum-rate capacity of the degraded MIMO BC.

7. F. Liu and G. Caire, Capacity-Distortion Tradeoff for Integrated Sensing and Communications, 2023

   Establishes the fundamental capacity-distortion tradeoff for ISAC under the state-dependent channel framework, extending Costa's setting to dual-function radar-communications.

8. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2006

   Chapter 7 covers channels with state information. Essential reading for the general theory behind the Gel'fand-Pinsker theorem.

9. U. Erez, S. Shamai, and R. Zamir, Capacity and Lattice Strategies for Canceling Known Interference, 2005

   Shows that nested lattice codes can approach DPC capacity with structured codes, providing a constructive alternative to random binning.

10. C. Heegard and A. El Gamal, On the Capacity of Computer Memory with Defects, 1983

    Independently derives the Gel'fand-Pinsker result for the memory with defects model. Provides operational motivation for channels with non-causal state.

Further Reading

• A. El Gamal and Y.-H. Kim, 'Network Information Theory,' Ch. 7 and 9

  Provides the most complete and rigorous treatment of channels with state, including extensions to multiple access channels with state, the cognitive interference channel, and compound channels.

• S. Shamai (Shitz) and M. Merhav, 'Information Rates Subject to State Masking,' IEEE Trans. IT, 2007

  Explores the dual problem: when the encoder wants to simultaneously communicate and hide the state from the decoder. An interesting complement to DPC where the encoder codes around the state.

• U. Erez, S. Shamai, and R. Zamir, 'Capacity and Lattice Strategies for Canceling Known Interference,' IEEE Trans. IT, 2005

  Shows that lattice strategies (nested lattice codes) can approach the DPC capacity with structured codes, providing a constructive path toward practical DPC implementations.

• Y. Sun, P. Babu, and D. P. Palomar, 'Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning,' IEEE TSP, 2017

  Covers optimization algorithms relevant to practical precoding design for MIMO broadcast channels, where DPC serves as the capacity-achieving benchmark.