Prerequisites & Notation

Before You Begin

This chapter generalizes MAN from single-access (one cache per user) to multi-access (each user accesses a subset of caches). Prerequisites: MAN basics and combinatorial placement.

MAN coded caching (Ch 2)(Review ch02)
Self-check: Can you state MAN placement and delivery for $K$ users, $N$ files, memory $M$ ?
D2D coded caching (Ch 11)(Review ch11)
Self-check: What is the coded D2D gain structure?
Combinatorial designs (block designs, BIBD)
Self-check: What is a resolvable design?
Cyclic groups / $\mathbb{Z}_n$ arithmetic
Self-check: What does 'cyclic wrap-around' mean in a group of $n$ elements?
Decentralized caching (Ch 13)(Review ch13)
Self-check: How does random placement compare to combinatorial placement?

Notation for This Chapter

Symbols for multi-access coded caching.

Symbol	Meaning	Introduced
$K$	Number of users	s01
$\Lambda$	Number of caches (can differ from $K$ )	s01
$L$	Number of caches each user accesses	s01
$\mathcal{A}_k$	Set of caches accessed by user $k$ ; $\|\mathcal{A}_k\| = L$	s01
$R_\text{MA}(L)$	Multi-access delivery rate as function of $L$	s02
$\mu = M/N$	Per-cache memory ratio	s01
$L\mu$	Effective per-user memory ratio (if caches disjoint)	s02

← Ch 17 The Multi-Access Model