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?
第2题
Consider the following channel(is shown in Fig.3.26) is (1/2,0,1/2) an input distribution that achieves capacity?
Show that I(X;Y)=H(Y) - H(Z).
第4题
2,而其他概率值不变。试证明由此所得新的概率空间的熵是增加的,并用熵的物理意义加以解释。
第7题
同时扔一对均匀的骰子,当得知“两骰子面朝上点数之和为2”或“面朝上点数之和为8”或“骰子面朝上点数是3和4”时,试问这三种情况分别获得多少信息量?
若仅有质点A,求A落入任一个格的平均自信息量是多少?
第9题
- α)log(1/(1 - α))+(1 - α)H(Y) where Y is an ensemble of M-1 points a1,…,aM-1 with probabilities PY(aj)=PX(aj)/(1 - α);1≤j≤M - 1.Show that H(X)≤αlog(1/α)+(1 - α)log(1/(1 - α))+(1 - α)log(M - 1) and determine the condition for equality.
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