Prerequisites & Notation

Before You Begin

This chapter introduces device-to-device (D2D) caching networks. Prerequisites: the MAN scheme, basic Gupta-Kumar wireless scaling theory, and familiarity with random geometric graph models.

The MAN scheme and caching gain (Ch 2)(Review ch02)
Self-check: Can you state $t = KM/N$ and the MAN rate formula?
Multi-antenna coded caching DoF (Ch 5)(Review ch05)
Self-check: Can you contrast a single-server $L$ -antenna setup with a distributed D2D network?
Gupta-Kumar capacity scaling for ad-hoc networks(Review ch22)
Self-check: Can you state the $\Theta(1/\sqrt{n\log n})$ per-user throughput result for ad-hoc?
Random geometric graphs and wireless network models
Self-check: What does 'interference radius' $r(n)$ mean in a protocol model?
Asymptotic analysis / big-Theta notation
Self-check: What is the difference between $\Theta(f)$ and $O(f)$ ?
Zipf-distributed demands for popular content(Review ch01)
Self-check: Can you state the hit ratio for a Zipf-α distribution with cache size $M$ ?

Notation for This Chapter

Symbols for D2D network analysis.

Symbol	Meaning	Introduced
$n$	Number of users (network size), also playing the role of $K$ in D2D	s01
$M$	Per-user cache size in file units	s01
$N$	Library size	s01
$\mu$	Memory ratio $M/N$	s01
$T_n(M)$	Per-user aggregate throughput in a network of $n$ users	s02
$r(n)$	Interference radius: minimum distance between simultaneous transmitters	s01
$\Theta(\cdot), O(\cdot), \Omega(\cdot)$	Asymptotic growth notation	s02

← Ch 9 The D2D Caching Network Model