Prerequisites & Notation

Before You Begin

This chapter combines coded caching with multi-antenna broadcast. The reader should be comfortable with the MAN scheme and with basic MIMO-BC information theory. Prior exposure to zero-forcing beamforming and degrees-of-freedom analysis helps but is not strictly required.

The MAN scheme and the rate formula (Ch 2)(Review ch02)
Self-check: Can you state the delivery structure for integer $t$ and compute the rate for $K = 10$ , $t = 2$ ?
Index coding perspective on coded caching (Ch 4)(Review ch04)
Self-check: Can you explain why the MAN conflict graph admits a tight fractional-chromatic coloring?
MIMO broadcast channel capacity and DoF(Review ch15)
Self-check: Can you state the DoF of an $L$ -antenna Gaussian BC with $K$ single-antenna users (for $L \leq K$ )?
Zero-forcing and dirty paper coding(Review ch17)
Self-check: Can you sketch how ZF beamforming achieves $\min(L, K)$ DoF?
Complex Gaussian random variables and noise models
Self-check: Are you comfortable with $\mathbf{w} \sim \mathcal{CN}(\mathbf{0}, \sigma^2 \mathbf{I})$ ?
Interference alignment basics(Review ch26)
Self-check: Can you sketch the interference alignment idea for a 3-user interference channel?

Notation for This Chapter

New symbols for the multi-antenna setting. In this chapter $L$ denotes the number of transmit antennas (CC-specific convention); cross-book chapters may use $N_t$ instead.

Symbol	Meaning	Introduced
$L$	Number of transmit antennas (single transmitter)	s01
$K$	Number of single-antenna users	s01
$\mathbf{h}_k \in \mathbb{C}^L$	Channel vector from the $L$ -antenna transmitter to user $k$	s01
$\mathbf{x} \in \mathbb{C}^L$	Transmitted vector per channel use	s01
$y_k$	Received scalar at user $k$ : $y_k = \mathbf{h}_k^H \mathbf{x} + w_k$	s01
$\mathbf{w}_{k}, \mathcal{CN}(0, \sigma^2)$	Additive noise at user $k$ , complex Gaussian	s01
$\text{SNR}$	Signal-to-noise ratio (transmit SNR)	s01
$\mathrm{DoF}$	Degrees of Freedom: $\lim_{\text{SNR} \to \infty} R/\log_2 \text{SNR}$	s02
$t$	Coded caching gain $t = KM/N$	s02
$\mathcal{S}'$	$(t + L)$ -subset of $[K]$ : Lampiris-Caire delivery group	s03

← Ch 4 The Cache-Aided MIMO Broadcast Channel