References & Further Reading

References

  1. C. E. Shannon, The Zero Error Capacity of a Noisy Channel, 1956

    Contains the proof that feedback does not increase the capacity of a point-to-point DMC. The result is also presented in Shannon's 1961 two-way channel paper.

  2. C. E. Shannon, Two-Way Communication Channels, 1961

    The foundational paper on two-way channels. Establishes the inner and outer bounds and initiates the study of interactive communication. The capacity remains open.

  3. T. M. Cover and C. S. K. Leung, An Achievable Rate Region for the Multiple-Access Channel with Feedback, 1981

    Introduces the Cover-Leung inner bound for the MAC with feedback, showing that feedback can enlarge the capacity region through input correlation via shared observations.

  4. L. H. Ozarow, The Capacity of the White Gaussian Multiple Access Channel with Feedback, 1984

    Determines the exact capacity region of the two-user Gaussian MAC with feedback. Shows that feedback-induced input correlation achieves the full beamforming gain.

  5. G. Kramer and M. Gastpar, Dependence Balance and the Gaussian Multiaccess Channel with Feedback, 2005

    Establishes the sum-rate capacity of the Gaussian MAC with feedback using the dependence balance approach. Shows the sum-rate equals the coherent combining capacity.

  6. G. Dueck, The Capacity Region of the Two-Way Channel Can Exceed the Inner Bound, 1981

    Constructs a counterexample showing that feedback can strictly enlarge the broadcast channel capacity region for non-degraded channels.

  7. O. Shayevitz and M. Wigger, On the Capacity of the Discrete Memoryless Broadcast Channel with Feedback, 2011

    Develops a feedback coding scheme for the BC using linear retransmissions and dirty-paper coding. Shows significant capacity gains for the Gaussian BC.

  8. J. P. M. Schalkwijk and T. Kailath, A Coding Scheme for Additive Noise Channels with Feedback, 1966

    The elegant feedback scheme achieving doubly exponential error decay for the Gaussian channel. The iterative refinement idea underlies many feedback coding schemes.

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

    Chapter 17 covers feedback in multiuser channels, including the MAC with feedback, the BC with feedback, and the two-way channel. Complete proofs and historical notes.

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

    Chapter 17 provides a concise treatment of feedback in channels, including the proof that feedback does not increase point-to-point DMC capacity.

Further Reading

For readers who want to explore feedback, interaction, and two-way communication in depth.

  • Feedback in the MAC: beyond the Cover-Leung bound

    G. Kramer, "Directed Information for Channels with Feedback," PhD Thesis, ETH Zurich, 1998. Also: J. Massey, "Causality, Feedback, and Directed Information," in Proc. ISITA, 1990.

    Directed information provides the natural information measure for channels with feedback. Kramer's thesis develops the theory systematically and applies it to multiuser channels.

  • Interactive communication and communication complexity

    L. J. Schulman, "Coding for Interactive Communication," IEEE Trans. Inf. Theory, 1996. Also: M. Braverman, "Interactive Information Complexity," STOC, 2012.

    Bridges information theory and computer science. Schulman shows how to protect interactive protocols against noise using tree codes. Braverman's information complexity provides tight bounds on communication requirements.

  • Limited feedback in wireless systems

    D. J. Love et al., "An Overview of Limited Feedback in Wireless Communication Systems," IEEE Journal on Selected Areas in Communications, 2008.

    Connects the information-theoretic feedback results to practical wireless systems. Covers quantized feedback, codebook-based feedback, and the rate-feedback tradeoff.

  • Two-way channels and physical-layer network coding

    S. Zhang, S. C. Liew, and P. P. Lam, "Hot Topic: Physical-Layer Network Coding," in Proc. ACM MobiCom, 2006.

    Physical-layer network coding for two-way relay channels uses the algebraic structure of wireless superposition to achieve rates predicted by two-way channel theory. Bridges theory and practice for bidirectional communication.

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