Notation Preferences — Coded Modulation and Space-Time Coding

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Key	Meaning	Default
gauss	Real Gaussian distribution	$\mathcal{N}$
cgauss	Circularly symmetric complex Gaussian	$\mathcal{CN}$
qfn	Gaussian tail probability: $Q(x) = 1 - \Phi(x) = \frac{1}{\sqrt{2\pi}}\int_x^{\infty} e^{-t^2/2}\,dt$	$Q$
covmat	Covariance matrix	$\boldsymbol{\Sigma}$
mi	Mutual information	$I$
cap	Channel capacity	$C$
rate	Code rate (bits/symbol or bits/channel use)	$R$
ch	Channel matrix (MIMO, OFDM, general)	$\mathbf{H}$
snr	Signal-to-noise ratio	$\text{SNR}$
es	Energy per transmitted symbol	$E_s$
n0	One-sided noise power spectral density	$N_0$
bw	Signal bandwidth (Hz)	$W$
noise	AWGN noise vector (system model)	$\mathbf{w}$
sym_period	Symbol period / duration	$T_s$
noisevar	Noise variance / noise power	$\sigma^2$
pe	Symbol/bit error probability	$P_e$
dmin	Minimum Euclidean distance of constellation	$d_{\min}$

Global Notation — Coded Modulation and Space-Time Coding

Notation registry for the Coded Modulation book. Standard symbols for channel capacity, code rates, constellation parameters, channel matrices, and space-time codeword matrices are defined globally. Chapter-specific notation tables extend this registry where needed.

Information-theoretic quantities

Symbol	Meaning
$C$	Channel capacity (bits per channel use)
$R$	Code rate (bits per channel use or bits per symbol)
$\eta$	Spectral efficiency (bits/s/Hz)
$I(X;Y)$	Mutual information between $X$ and $Y$

Signal-space and constellation parameters

Symbol	Meaning
$\mathcal{X}$	Signal constellation (set of points in $\mathbb{C}$ or $\mathbb{C}^n$ )
$\|\mathcal{X}\| = M$	Constellation size (number of points)
$E_s$	Average energy per transmitted symbol
$N_0$	One-sided noise power spectral density
$d_{\min}$	Minimum Euclidean distance of constellation
$d_H$	Minimum Hamming distance of a binary code

Channel and system model

Symbol	Meaning
$\mathbf{H}$	MIMO channel matrix, size $n_r \times n_t$
$\mathbf{w}$	Additive white Gaussian noise vector
$\mathbf{x}$	Transmitted signal vector
$\mathbf{y}$	Received signal vector
$\text{SNR}$	Signal-to-noise ratio $E_s / N_0$ or $P/\sigma^2$

Space-time coding

Symbol	Meaning
$\mathbf{X}$	Space-time codeword matrix, size $n_t \times T$
$\Delta = \mathbf{X} - \hat{\mathbf{X}}$	Codeword difference (error) matrix
$n_t, n_r$	Number of transmit and receive antennas
$d^*(r)$	Diversity-multiplexing tradeoff (DMT) curve

Code-design parameters

Symbol	Meaning
$d$	Diversity order (integer)
$\gamma_c$	Coding gain
$\Lambda$	Lattice in $\mathbb{R}^n$
$V(\Lambda)$	Volume of the fundamental region of $\Lambda$