Prerequisites & Notation

Before You Begin

This chapter refines Chapter 5's MIMO BC model to incorporate heterogeneous channel qualities (the degraded BC) and mixed traffic types (cacheable + uncacheable). The reader needs familiarity with broadcast channel capacity, superposition coding, and the GDoF (generalized degrees of freedom) framework.

Cache-aided MIMO BC and DoF = $t+L$ (Ch 5)(Review ch05)
Self-check: Can you state the Lampiris-Caire scheme and its DoF bound?
Degraded Gaussian broadcast channel capacity(Review ch15)
Self-check: Can you derive the capacity region via superposition coding with rate-split $(\alpha, 1-\alpha)$ ?
GDoF: generalized degrees of freedom(Review ch17)
Self-check: Can you state the GDoF of a 2-user interference channel with SNR exponents $(\alpha_1, \alpha_2)$ ?
Superposition coding and successive decoding(Review ch17)
Self-check: Can you sketch how the stronger user decodes both layers in a 2-user superposition scheme?
Coded-caching gain parameter $t = K M/N$ (Review ch02)
Self-check: Can you state the MAN rate for integer $t$ ?

Notation for This Chapter

Symbols for the degraded BC with heterogeneous users and mixed traffic types.

Symbol	Meaning	Introduced
$\rho_k$	Per-user channel SNR at user $k$ (ordered $\rho_1 \geq \ldots \geq \rho_K$ )	s01
$C_k = \log_2(1 + \rho_k)$	Per-user point-to-point capacity at user $k$	s01
$C_{\min} = \log_2(1 + \rho_K)$	Worst-user capacity — the multicast bottleneck	s02
$R_c$	Cacheable-content rate per user	s03
$R_u$	Uncacheable-content rate per user	s03
$\alpha_k$	SNR exponent of user $k$ : $\rho_k = \rho^{\alpha_k}$	s04
$\text{GDoF}$	Generalized degrees of freedom: scale-invariant rate metric	s04
$t$	Caching gain $t = K M/N$	s01
$L$	Transmit antennas (per base station)	s01

← Ch 5 The Degraded Broadcast Channel with Caches