Appendix A — Notation

This table is the canonical notation register for the book. New symbols should be added here before they are used in chapters.

Symbol	Meaning
x	Activation vector
w	Floating-point weight vector
\hat{w}	Quantized weight vector
v	Generic vector being quantized (a weight block or a residual)
u	Coordinate-wise rounded integer vector
C	Finite codebook (classical vector quantization)
c_b	Codeword with index b in a finite codebook
g_i	Basis vector used as a generator matrix column
z	Integer coefficient vector used to generate a lattice point
G	Generator matrix
L	Lattice
V	Voronoi cell of L around the origin
Q_L(v)	Nearest lattice point in L to v
\beta	Scaling factor applied before quantization
A_q	Finite Hierarchical Nested Lattice Quantization (HNLQ) codebook, A_q = L \cap qV
b	Codebook index
b_m	Digit index at hierarchy level m (a coset index)
z_m	Coefficient quotient at hierarchy level m during digit extraction
\tilde{c}_b	Digit representative G \cdot bits(b), linear in the index bits
M	Hierarchy depth
q	Hierarchy radix
d	Vector dimension
K	Number of codewords in a classical codebook
T_x(b)	One-sided lookup-table entry for activation block x and codebook index b

Conventions:

• Q_L(\cdot) accepts any vector; in this book it is applied to weight blocks and residuals, never to activations, which remain in floating point.
• L is reserved for the lattice; the one-sided lookup table is written T_x(b) to avoid overloading L.
• n appears only as the dimension subscript of the lattice family Dn and in the complexity of its decoder; everywhere else the vector dimension is d.
• HNLQ expands to Hierarchical Nested Lattice Quantization.

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