第1题
有一信源输出X∈{0,1,2},其概率为p0=1/4,p1=1/4,p2=1/2。设计两个独立实验去观察它,其结果分别为Y1∈{0,1}和Y2∈{0,1}。已知条件概率为:
求:(1)I(X;Y1)和I(X;Y2),并判断哪个实验好些。 (2)I(X;Y1Y2),并计算做Y1和Y2两个实验比做Y1或Y2中的一个实验各可多得多少关于X的信息。 (3)I(X;Y1|Y2)和I(X;Y2|Y1),并解释它们的含义。
第2题
dent. let ρ=1 - H(X1|X2)/H(X1) (1)Show ρ=I(X1;X2)/H(X1) (2)Show 0≤ρ≤1 (3)When is ρ=0? (4)When is ρ=1?
第3题
(XY) - I(X;Y) =2H(XY) - H(X) - H(Y)
第4题
t ρ(X,Y) is the number of bits needed for X and to communicate their values to each other.
第5题
e variance of I(x;y)=0.Prove that the input assignment achieves channel capacity.
第6题
;0 and VAR[I(x;y)]=0.Calculate I(X;Y).
第8题
(xy)=αP(x)P(y)
第9题
acity?
第10题
With 0,1,as both input and output,the transition probabilites for 0 to 0 and 1 are 1-ε and ε respectively while those for 1 to 1 and 0 are 1-δ and δ respectively.Assuming that 0<ε<1 and 0<δ<1,find the capacity of the channel.
Suppose that the output of the first channel is connected directly to the input of the second with no processing between: What is the capacity of the composite channel?
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