
i
i
i
i
i
i
i
i
356 16 DCast: Distributed Video Multicast
the same channel (if assuming that S −X is available to the encoder) [417]. Actu-
ally, according to the theorem by Kochman and Zamir [417] (the existence of good
lattice), the coset value C of each subband has the same variance with the prediction
residue S −X of each subband, that is,
σ
2
C
i
= E{C
2
i
} = E{(S
i
−X
i
)
2
}. (16.43)
Thus, the coset value and the prediction residue have the same variance in frame
level, that is,
σ
2
C
= E{(S −X)
2
} = σ
2
S−X
. (16.44)
Therefore, Eq. (16.41), Eq. (16.42), and Eq. (16.44) implies
D = σ
2
ˆ
C−C
≈ α
coset
σ
2
S−X
P
coset
n
coset
N
0
−1
. (16.45)
This means D is proportional to the prediction ...