Prerequisites & Notation

Before You Begin

This chapter studies the role of feedback and interaction in multiuser channels. We assume familiarity with the point-to-point capacity theorem, the MAC and BC capacity results, and the Gaussian channel.

  • DMC capacity and the coding theorem (Chapter 9)(Review ch09)

    Self-check: Can you prove that feedback does not increase the capacity of a point-to-point DMC?

  • MAC capacity region (Chapter 14)(Review ch14)

    Self-check: Can you describe the pentagon capacity region and explain successive cancellation decoding?

  • Broadcast channel capacity (Chapter 15)(Review ch15)

    Self-check: Can you state the capacity region of the degraded BC and explain superposition coding?

  • Gaussian channel capacity and water-filling (Chapter 10)(Review ch10)

    Self-check: Can you compute the capacity of the AWGN channel and the Gaussian MAC?

  • The Schalkwijk-Kailath scheme (Chapter 9)(Review ch09)

    Self-check: Can you describe how feedback achieves doubly exponential error decay for the Gaussian channel?

Notation for This Chapter

Key symbols for feedback and interactive communication.

SymbolMeaningIntroduced
CfbC_{\text{fb}}Capacity with feedbacks01
CMAC\mathcal{C}_{\text{MAC}}MAC capacity region (without feedback)s01
CMAC-fb\mathcal{C}_{\text{MAC-fb}}MAC capacity region with feedbacks01
ρ\rhoNoise correlation coefficient (Gaussian MAC with feedback)s01
R1,R2R_{1}, R_{2}Rates of users 1 and 2s01
αi\alpha_iMMSE coefficient in Schalkwijk-Kailath-type schemes01
← Ch 23Feedback in the MAC