point in each copy.Fig.5.11 shows that around each lattice point is a region known as the undamental parallelotope(用阴影表示) Fig.5.11 The fundamental parallelotopes around the lattice points. The key geometrical parameters of a lattice A are (a)the minimum squared Euclidean distance d2(A)between lattice points; (b)the kissing number K(A),which is the number of nearest neighbors to any lattice point. (c)the fundamental volume V(A),which is the volume of the n-space corresponding to each lattice point.As indicated in Fig.5.11,this volume is the volume of the fundamental region.Let A=GG".It can be shown that V(A)det()2=det(G)for any generator matrix GofA These parameters will directly affect the performance of a lattice constellation(lattice code) A normalized density parameter d(A) will be identified as the nomial coding gain Definition 2:A lattice constellation C(A,R)=(A+t)oR is the finite set of points in a lattice translate A+t that lie within a compact bounding regionR of n-space. (Note:A lattice is constrained to have a point at zero.The translate vector t make the resulting constellation has no point at zero.The intersection of A with the regionR results in a finite 5-125-12 point in each copy. Fig. 5.11 shows that around each lattice point is a region known as the fundamental parallelotope (用阴影表示). Fig. 5.11 The fundamental parallelotopes around the lattice points. The key geometrical parameters of a lattice Λ are: (a) the minimum squared Euclidean distance 2 min d ( ) Λ between lattice points; (b) the kissing number min K ( ) Λ , which is the number of nearest neighbors to any lattice point; (c) the fundamental volume V(Λ), which is the volume of the n-space corresponding to each lattice point. As indicated in Fig. 5.11, this volume is the volume of the fundamental region. Let T A GG = . It can be shown that 1/2 V AG ( ) det( ) det( ) Λ≡ = for any generator matrix G of Λ. These parameters will directly affect the performance of a lattice constellation (lattice code). A normalized density parameter 2 min 2 / ( ) ( ) ( ) c n d V γ Λ Λ = Λ will be identified as the nomial coding gain. Definition 2: A lattice constellation C(, ) ( ) Λ R R = Λ+ ∩t is the finite set of points in a lattice translate Λ+t that lie within a compact bounding region R of n-space. (Note: A lattice is constrained to have a point at zero. The translate vector t make the resulting constellation has no point at zero. The intersection of Λ with the region R results in a finite