Prerequisites & Notation

This chapter introduces information-theoretic secrecy, which requires a solid background in channel coding and multiuser information theory.

Channel capacity and the channel coding theorem(Review ch09)
Self-check: Can you state the channel coding theorem and sketch the random coding achievability proof?
The Gaussian channel and its capacity(Review ch10)
Self-check: Can you derive $C = \frac{1}{2}\log(1 + \text{SNR})$ and explain why Gaussian input is optimal?
Random binning and Slepian–Wolf coding(Review ch07)
Self-check: Can you explain how random binning assigns multiple source sequences to the same index?
The broadcast channel and superposition coding(Review ch15)
Self-check: Can you describe superposition coding for the degraded BC and state its capacity region?
Mutual information and the data processing inequality(Review ch01)
Self-check: Can you prove the data processing inequality from the chain rule of mutual information?
MIMO channel model and capacity
Self-check: Can you write the MIMO channel capacity formula $C = \log\det(\mathbf{I} + \text{SNR}\mathbf{H}\mathbf{H}^{H})$ ?

Symbols introduced or heavily used in this chapter.

Symbol	Meaning	Introduced
$C_s$	Secrecy capacity (bits per channel use)	s01
$Z$	Eavesdropper's observation (or eavesdropper's channel output)	s01
$Y$	Legitimate receiver's channel output	s01
$R_e$	Equivocation rate at the eavesdropper	s01
$I(X; Z)$	Information leakage to the eavesdropper	s01
$C_K$	Secret key capacity	s02
$\mathbf{H}_{E}$	Eavesdropper's channel matrix (MIMO wiretap)	s03
$\mathbf{Q}$	Input covariance matrix	s03
$\mathbf{v}_{\text{AN}}$	Artificial noise beamforming direction	s03