Prerequisites & Notation

Before You Begin

This chapter surveys the frontiers of information theory. It draws on concepts from across the book — entropy, channel coding, multi-user theory, relay channels, and network coding. The reader should have a working knowledge of the main achievability and converse techniques (random coding, typicality, Fano's inequality) and the capacity results for the DMC, Gaussian channel, MAC, and broadcast channel.

  • Channel capacity and the coding theorem(Review ita/ch09)

    Self-check: Can you state the achievability and converse proofs for the DMC?

  • Gaussian channel capacity(Review ita/ch10)

    Self-check: Can you derive the water-filling solution for parallel Gaussian channels?

  • Multiple access channel(Review ita/ch14)

    Self-check: Can you sketch the MAC capacity region?

  • Broadcast channel(Review ita/ch15)

    Self-check: Can you state the superposition coding achievable region for the degraded BC?

  • Interference channel basics(Review ita/ch17)

    Self-check: Can you state the Han-Kobayashi inner bound?

  • Relay channel(Review ita/ch22)

    Self-check: Can you describe decode-forward and compress-forward relaying?

Notation for This Chapter

This chapter uses notation from across the book. Key symbols are listed here for reference.

SymbolMeaningIntroduced
CCChannel capacitych09
IIMutual informationch01
HHShannon entropych01
SNR\text{SNR}Signal-to-noise ratioch10
DoF\text{DoF}Degrees of freedom (pre-log factor of capacity at high SNR)s01
C\mathcal{C}Capacity region (set of achievable rate tuples)ch14