Notation Preferences — Coded Caching and Content Delivery

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Key	Meaning	Default
gauss	Real Gaussian distribution	$\mathcal{N}$
cgauss	Circularly symmetric complex Gaussian	$\mathcal{CN}$
covmat	Covariance matrix	$\boldsymbol{\Sigma}$
rate	Code rate (bits/symbol or bits/channel use)	$R$
snr	Signal-to-noise ratio	$\text{SNR}$
n0	One-sided noise power spectral density	$N_0$
bw	Signal bandwidth (Hz)	$W$
noisevar	Noise variance / noise power	$\sigma^2$
cc_users	Number of users in the shared-link caching network	$K$
cc_files	Number of files in the library	$N$
cc_memory	Per-user cache size in file units	$M$
cc_rate	Delivery rate (file units per channel use of the shared link)	$R$
cc_t	Coded caching gain parameter $t = KM/N$ (each XOR message serves $t+1$ users)	$t$
cc_ratio	Memory ratio $M/N$ (fraction of the library each user caches)	$\mu$
cc_antennas	Number of transmit antennas (MIMO coded caching)	$L$
cc_fronthaul	Fronthaul capacity (cloud-RAN edge caching)	$C_F$
cc_ndt	Normalized delivery time (cloud-RAN edge caching)	$\Delta$
cc_subfile	MAN subfile $W_{n,\mathcal{S}}$ of file $n$ cached by users in subset $\mathcal{S}$	$W$
cc_cache	Cache content of user $k$ : $\mathcal{Z}_k$	$\mathcal{Z}$
cc_demand	Demand vector $\mathbf{d} = (d_1, \ldots, d_K)$	$\mathbf{d}$

Universal Conventions

Fixed conventions used throughout this book. Coded caching introduces a compact combinatorial vocabulary on top of the standard information-theoretic notation; this page collects both.

General Mathematics

Symbol	Meaning
$\mathbb{R}, \mathbb{C}$	Real and complex number fields
$\mathbb{F}_2$	Binary field (bitwise XOR additions in delivery messages)
$[K] = \{1, \ldots, K\}$	Shorthand for the first $K$ positive integers
$\binom{K}{t}$	Binomial coefficient (number of $t$ -subsets of $[K]$ )
$\oplus$	Bitwise XOR / addition in $\mathbb{F}_2$
$\triangleq$	Defined as
$\|\mathcal{S}\|$	Cardinality of the set $\mathcal{S}$

Coded Caching Model

Symbol	Meaning
$K$	Number of users
$N$	Number of files in the library $W_1, \ldots, W_N$
$M$	Per-user cache size in file units ( $0 \leq M \leq N$ )
$M/N$	Memory ratio (fractional cache size); x-axis of the tradeoff curve
$t = KM/N$	Coded caching parameter; each coded message serves $t+1$ users
$R$	Delivery rate (file units per channel use of the shared link)
$R^*(M)$	Optimal delivery rate as a function of cache size
$\mathcal{Z}_k$	Cache content of user $k$ (random variable of size $M$ files)
$\mathbf{d} = (d_1, \ldots, d_K)$	Demand vector; $d_k \in [N]$ is user $k$ 's requested file
$W_n$	File $n$ in the library; typically of size $F$ bits
$W_{n,\mathcal{S}}$	MAN subfile of $W_n$ cached by exactly the users in $\mathcal{S} \subseteq [K]$

Operational Quantities

Symbol	Meaning
$F$	Subpacketization (number of subfiles per file)
$L$	Number of transmit antennas (multi-antenna coded caching)
$C_F$	Fronthaul capacity (cloud-RAN edge caching)
$\Delta$	Normalized delivery time (NDT)
$\mathrm{DoF}$	Degrees of freedom

Information-Theoretic Symbols Used

Symbol	Meaning
$\mathrm{H}(X)$	Shannon entropy
$\mathrm{I}(X;Y)$	Mutual information
$\mathcal{CN}(0, \sigma^2)$	Circularly symmetric complex Gaussian (noise model)
$\text{SNR}$	Signal-to-noise ratio